:: Automatization of {T}ernary {B}oolean {A}lgebras
:: by Wojciech Ku\'smierowski and Adam Grabowski
::
:: Received September 30, 2021
:: Copyright (c) 2021-2026 Association of Mizar Users
:: (Stowarzyszenie Uzytkownikow Mizara, Bialystok, Poland).
:: This code can be distributed under the GNU General Public Licence
:: version 3.0 or later, or the Creative Commons Attribution-ShareAlike
:: License version 3.0 or later, subject to the binding interpretation
:: detailed in file COPYING.interpretation.
:: See COPYING.GPL and COPYING.CC-BY-SA for the full text of these
:: licenses, or see http://www.gnu.org/licenses/gpl.html and
:: http://creativecommons.org/licenses/by-sa/3.0/.
environ
vocabularies LATTBA_1, VECTSP_1, LATTICE2, XBOOLE_0, LATTICES, SUBSET_1,
EQREL_1, ROBBINS1, FUNCT_1, STRUCT_0, BINOP_1, FUNCT_5, ZFMISC_1, CARD_1,
ALGSTR_3, MULTOP_1, FUNCT_7, XXREAL_2;
notations TARSKI, ZFMISC_1, BINOP_1, SUBSET_1, FUNCT_2, FUNCT_5, ORDINAL1,
MULTOP_1, STRUCT_0, LATTICES, LATTICE2, ROBBINS1, LATTICE4;
constructors BINOP_1, LATTICE2, OPOSET_1, FUNCT_5, RELSET_1, MULTOP_1,
LATTICE4;
registrations RELAT_1, STRUCT_0, LATTICES, CARD_1, LATTICE2;
requirements SUBSET, BOOLE;
equalities LATTICES;
theorems BINOP_1, FUNCT_2, TARSKI, MULTOP_1, STRUCT_0, LATTICES, LATTICE2,
ROBBINS1, LATTICE4;
schemes BINOP_1, MULTOP_1;
begin
definition
struct (ComplStr) TBAStruct (#carrier -> set,
Compl -> (UnOp of the carrier),
TernOp -> TriOp of the carrier #);
end;
definition
struct (TBAStruct, LattStr) TBALattStr (#carrier -> set,
L_join, L_meet -> (BinOp of the carrier),
Compl -> (UnOp of the carrier),
TernOp -> TriOp of the carrier #);
end;
definition
func op3 -> TriOp of {0} means
it.(0,0,0) = 0;
existence
proof
set X = {0};
deffunc F(Element of X, Element of X, Element of X) = In (0,X);
consider ff being Function of [:X,X,X:],X such that
A1: for x,y,z being Element of X holds
ff.(x,y,z) = F(x,y,z) from MULTOP_1:sch 4;
reconsider ff as TriOp of {0};
take ff;
0 in X by TARSKI:def 1; then
ff.(0,0,0) = In(0,{0}) by A1
.= 0 by TARSKI:def 1;
hence thesis;
end;
uniqueness by FUNCT_2:51;
end;
registration
cluster trivial non empty for TBAStruct;
existence
proof
take T = TBAStruct (# {0}, op1, op3 #);
thus thesis;
end;
end;
definition let T be non empty TBAStruct;
let a,b,c be Element of T;
func Tern(a,b,c) -> Element of T equals
(the TernOp of T).(a,b,c);
coherence;
end;
definition let T be non empty TBAStruct; :: split into 5 attributes
attr T is ternary-distributive means :TDis: :: (2.1)
for a,b,c,d,e being Element of T holds
Tern(Tern(a,b,c),d,Tern(a,b,e)) = Tern(a,b,Tern(c,d,e));
attr T is ternary-left-idempotent means :TLIDef: :: (2.2)
for a,b being Element of T holds Tern(b,b,a) = b;
attr T is ternary-right-idempotent means :TRIDef: :: (2.2)
for a,b being Element of T holds Tern(a,b,b) = b;
attr T is ternary-left-absorbing means :TLADef: :: (2.3)
for a,b being Element of T holds Tern(b`,b,a) = a;
attr T is ternary-right-absorbing means :TRADef: :: (2.3)
for a,b being Element of T holds Tern(a,b,b`) = a;
end;
:: It seems that only three are enough
registration
cluster trivial -> ternary-distributive ternary-left-idempotent
ternary-right-idempotent ternary-left-absorbing
ternary-right-absorbing for non empty TBAStruct;
coherence by STRUCT_0:def 10;
end;
definition
mode Ternary_Boolean_Algebra is
ternary-distributive ternary-left-idempotent
ternary-right-idempotent ternary-left-absorbing
ternary-right-absorbing non empty TBAStruct;
end;
begin :: Converting TBAs into ordinary binary Boolean algebras
:: Section 4 of Grau: Associated Boolean Algebra
definition let T be Ternary_Boolean_Algebra;
let x be Element of T;
func JoinTBA (T,x) -> BinOp of the carrier of T means :JoinDef:
for a,b being Element of T holds
it.(a,b) = Tern (a,x,b);
existence
proof
deffunc F(Element of T,Element of T) = Tern ($1,x,$2);
consider ff being BinOp of T such that
A1: for a,b being Element of T holds
ff.(a,b) = F(a,b) from BINOP_1:sch 4;
take ff;
thus thesis by A1;
end;
uniqueness
proof
let f1,f2 being BinOp of T such that
A1: for a,b being Element of T holds f1.(a,b) = Tern (a,x,b) and
A2: for a,b being Element of T holds f2.(a,b) = Tern (a,x,b);
for a,b being Element of T holds f1.(a,b) = f2.(a,b)
proof
let a,b be Element of T;
f1.(a,b) = Tern (a,x,b) by A1
.= f2.(a,b) by A2;
hence thesis;
end;
hence thesis by BINOP_1:2;
end;
func MeetTBA (T,x) -> BinOp of the carrier of T means :MeetDef:
for a,b being Element of T holds
it.(a,b) = Tern (a,x`,b);
existence
proof
deffunc F(Element of T,Element of T) = Tern ($1,x`,$2);
consider ff being BinOp of T such that
A1: for a,b being Element of T holds
ff.(a,b) = F(a,b) from BINOP_1:sch 4;
take ff;
thus thesis by A1;
end;
uniqueness
proof
let f1,f2 being BinOp of T such that
A1: for a,b being Element of T holds f1.(a,b) = Tern (a,x`,b) and
A2: for a,b being Element of T holds f2.(a,b) = Tern (a,x`,b);
for a,b being Element of T holds f1.(a,b) = f2.(a,b)
proof
let a,b be Element of T;
f1.(a,b) = Tern (a,x`,b) by A1
.= f2.(a,b) by A2;
hence thesis;
end;
hence thesis by BINOP_1:2;
end;
end;
definition let T be Ternary_Boolean_Algebra;
let x be Element of T;
func TBA2BA (T,x) -> non empty LattStr equals
LattStr (# the carrier of T,
JoinTBA (T,x),
MeetTBA (T,x)
::: the Compl of T
#);
correctness;
end;
:: Then we should prove theorems that, starting with arbitrary
:: TBA, we end up with a Boolean algebra.
begin :: Basic Properties of Ternary Operation
reserve T for Ternary_Boolean_Algebra;
reserve a,b,c,d,e for Element of T;
reserve x,y,z for Element of T;
theorem Th32: :: Theorem 3.2
Tern (a,b,a) = a
proof
Tern (a,b,a) = Tern (Tern (a,b,b`),b,a) by TRADef
.= Tern (Tern (a,b,b`),b,Tern (a,b,b`)) by TRADef
.= Tern (a,b,Tern(b`,b,b`)) by TDis
.= Tern (a,b,b`) by TLADef
.= a by TRADef;
hence thesis;
end;
theorem Lemma33: :: Lemma to Theorem 3.3 :: formula 3.31
Tern (Tern (a,b,c), b, a) = Tern (a,b,c)
proof
Tern (Tern (a,b,c), b, a) = Tern (Tern(a,b,c),b,Tern(a,b,b`)) by TRADef
.= Tern (a,b,Tern(c,b,b`)) by TDis
.= Tern (a,b,c) by TRADef;
hence thesis;
end;
theorem Th33: :: Theorem 3.3
Tern (a,b,Tern (c,b,d)) = Tern(Tern(a,b,c),b,d)
proof
set b1 = Tern (a,b,c);
set b2 = Tern (a,b,d);
Tern (a,b,Tern (c,b,d)) = Tern (b1,b,b2) by TDis
.= Tern(Tern(b1,b,a),b, Tern(b1,b,d)) by TDis
.= Tern(b1,b, Tern(b1,b,d)) by Lemma33
.= Tern(Tern(b1,b,b`),b,Tern(b1,b,d)) by TRADef
.= Tern(b1,b,Tern(b`,b,d)) by TDis
.= Tern(b1,b,d) by TLADef;
hence thesis;
end;
theorem
Tern (b`,b,a) = Tern (a,b,b`)
proof
Tern (b`,b,a) = a by TLADef;
hence thesis by TRADef;
end;
theorem Lemma34: :: Lemma to Theorem 3.4
Tern (a,b`,b) = a
proof
Tern (a,b`,b) = Tern (Tern (a,b,b`), b`, b) by TRADef
.= Tern (Tern (a,b,b`), b`, Tern (a,b,b)) by TRIDef
.= Tern (a,b,Tern (b`,b`,b)) by TDis
.= Tern (a,b,b`) by TLIDef
.= a by TRADef;
hence thesis;
end;
theorem Lemma0: :: Theorem 3.4
a`` = a
proof
a = Tern(a``, a`, a) by TLADef
.= a`` by Lemma34;
hence thesis;
end;
theorem Th35: :: Theorem 3.5
Tern (a,b,a`) = b
proof
Tern (a,b,a`) = Tern (a,b,Tern (b,a`,a`)) by TRIDef
.= Tern (Tern(a,b,b), a`, Tern (a,b,a`)) by TDis
.= Tern (b, a`, Tern (a,b,a`)) by TRIDef
.= Tern (Tern(b,a`,a),b, Tern (b,a`,a`)) by TDis
.= Tern (Tern(b,a`,a``),b, Tern (b,a`,a`)) by Lemma0
.= Tern (b, b, Tern (b,a`,a`)) by TRADef
.= b by TLIDef;
hence thesis;
end;
theorem Th36a: :: Theorem 3.6 a)
Tern (a,b,c) = Tern (a,c,b)
proof
Tern (a,b,c) = Tern (a,b,Tern(a,c,a`)) by Th35
.= Tern (Tern(a,b,a),c,Tern(a,b,a`)) by TDis
.= Tern (a,c,Tern(a,b,a`)) by Th32
.= Tern (a,c,b) by Th35;
hence thesis;
end;
theorem Th36b: :: Theorem 3.6 b)
Tern (a,b,c) = Tern (b,c,a)
proof
Tern (a,b,c) = Tern (a,b,Tern(b,c,b`)) by Th35
.= Tern (Tern(a,b,b),c,Tern(a,b,b`)) by TDis
.= Tern (b,c,Tern(a,b,b`)) by TRIDef
.= Tern (b,c,a) by TRADef;
hence thesis;
end;
theorem Th36c: :: Theorem 3.6 c)
Tern (a,b,c) = Tern (c,b,a)
proof
Tern (a,b,c) = Tern (a,c,b) by Th36a
.= Tern (c,b,a) by Th36b;
hence thesis;
end;
theorem :: Theorem 3.7
for x being Element of T holds
Tern (a,b,c) =
Tern (Tern (Tern (a,x,b), x`, Tern (b,x,c)), x`, Tern (c,x,a))
proof
let x be Element of T;
W1: Tern(a,x,x`) = a by TRADef;
W2: Tern (x`,x,b) = b by TLADef;
K1: Tern(a,b,x) = Tern(a,x,b) by Th36a;
K2: Tern(a,b,x`) = Tern (a,x`,b) by Th36a;
POM1: Tern(a,x,b) = Tern(b,x,a) by Th36c;
POM2: Tern(x`,x,b) = Tern(b,x,x`) by Th36c;
POM3: Tern(Tern(b,x,a),c,Tern(b,x,x`)) = Tern(b,x,Tern(a,c,x`)) by TDis;
POM4: Tern(b,x,Tern(a,c,x`)) = Tern(Tern(a,c,x`), x,b) by Th36c;
POM5: Tern(b,c,x`) = Tern (b,x`,c) by Th36a;
Tern(a,b,c) = Tern (a,b, Tern(x,c,x`)) by Th35
.= Tern(Tern(a,b,x),c, Tern(a,b,x`)) by TDis
.= Tern(Tern(Tern(a,x,b),c,Tern(a,x,x`)),x`,Tern(Tern(a,x,b),c,Tern(x`,x,b)))
by TDis,W1,W2,K1,K2
.= Tern(Tern(a,x,Tern(b,c,x`)),x`,Tern(Tern(a,c,x`),x,b))
by POM1, POM2,POM3, POM4, TDis
.= Tern (Tern (Tern(a,x,b),x`, Tern(a,x,c)),x`, Tern(Tern(a,c,x`),x,b))
by POM5,TDis
.= Tern (Tern (Tern(a,x,b),x`, Tern(a,x,c)),x`,Tern(x,b,Tern(a,c,x`)))
by Th36b
.= Tern (Tern (Tern(a,x,b),x`, Tern(a,x,c)),x`,Tern(x,b,Tern(a,x`,c)))
by Th36a
.= Tern (Tern (Tern(a,x,b),x`, Tern(a,x,c)),x`,
Tern(Tern(x,b,a), x`, Tern(x,b,c))) by TDis
.= Tern (Tern(Tern(a,x,b),x`, Tern(a,x,c)),x`,
Tern(Tern(a,b,x),x`,Tern(x,b,c))) by Th36c
.= Tern (Tern(Tern(a,x,b),x`, Tern(a,x,c)),x`,
Tern(Tern(a,b,x),x`,Tern(c,b,x))) by Th36c
.= Tern (Tern(Tern(a,x,b),x`, Tern(a,x,c)),x`,
Tern(Tern(a,x,b),x`,Tern(c,b,x))) by Th36a
.= Tern (Tern(Tern(a,x,b),x`, Tern(a,x,c)),x`,
Tern(Tern(a,x,b),x`,Tern(c,x,b))) by Th36a
.= Tern (Tern(Tern(a,x,b),x`, Tern(c,x,a)),x`,
Tern(Tern(a,x,b),x`,Tern(c,x,b))) by Th36c
.= Tern (Tern(Tern(a,x,b),x`, Tern(c,x,a)),x`,
Tern(Tern(a,x,b),x`,Tern(b,x,c))) by Th36c
.= Tern (Tern(Tern(a,x,b),x`,Tern(b,x,c)),x`,
Tern(Tern(a,x,b),x`,Tern(c,x,a))) by Th36c
.= Tern (Tern (a,x,b), x`,
Tern (Tern (b,x,c), x`, Tern (c,x,a))) by TDis
.= Tern (Tern (Tern (a,x,b), x`,
Tern (b,x,c)), x`, Tern (c,x,a)) by Th33;
hence thesis;
end;
begin :: The Rosetta Operation
definition let L be B_Lattice;
let a,b,c be Element of L;
func Ros (a,b,c) -> Element of L equals
(a "/\" b) "\/" (b "/\" c) "\/" (c "/\" a);
coherence;
end;
definition let B be B_Lattice;
func RosTrn B -> TriOp of the carrier of B means :RosTrnDef:
for a,b,c being Element of B holds
it.(a,b,c) = Ros (a,b,c);
existence
proof
set X = the carrier of B;
deffunc F(Element of B, Element of B, Element of B) = Ros($1,$2,$3);
consider ff being Function of [:X,X,X:],X such that
A1: for x,y,z being Element of X holds
ff.(x,y,z) = F(x,y,z) from MULTOP_1:sch 4;
reconsider ff as TriOp of the carrier of B;
take ff;
thus thesis by A1;
end;
uniqueness
proof
let f1,f2 being TriOp of the carrier of B such that
A1: for a,b,c being Element of B holds f1.(a,b,c) = Ros (a,b,c) and
A2: for a,b,c being Element of B holds f2.(a,b,c) = Ros (a,b,c);
for a,b,c being Element of B holds f1.(a,b,c) = f2.(a,b,c)
proof
let a,b,c be Element of B;
f1.(a,b,c) = Ros (a,b,c) by A1
.= f2.(a,b,c) by A2;
hence thesis;
end;
hence thesis by MULTOP_1:3;
end;
end;
definition let B be Boolean Lattice;
func BA2TBA B -> TBAStruct equals
TBAStruct (# the carrier of B, comp B, RosTrn B #);
coherence;
end;
definition let B be Boolean Lattice;
func BA2TBAA B -> TBALattStr equals
TBALattStr (# the carrier of B, the L_join of B,
the L_meet of B, comp B, RosTrn B #);
coherence;
end;
registration
let B be Boolean Lattice;
cluster BA2TBA B -> non empty;
coherence;
end;
registration
let B be Boolean Lattice;
cluster BA2TBAA B -> non empty;
coherence;
end;
begin :: Proof that TBA2BAA T is Boolean, similarly as Sect. 4 of Gray
reserve T for Ternary_Boolean_Algebra;
ThCom:
for x,a,b being Element of T holds
JoinTBA (T,x).(a,b) = JoinTBA (T,x).(b,a)
proof
let x,a,b be Element of T;
JoinTBA (T,x).(a,b) = Tern (a,x,b) by JoinDef
.= Tern (b,x,a) by Th36c
.= JoinTBA (T,x).(b,a) by JoinDef;
hence thesis;
end;
registration let T;
let x be Element of T;
cluster JoinTBA (T,x) -> commutative;
coherence
proof
set ff = JoinTBA (T,x);
for a,b being Element of T holds ff.(a,b) = ff.(b,a) by ThCom;
hence thesis by BINOP_1:def 2;
end;
end;
ThAssoc:
for x,a,b,c being Element of T holds
JoinTBA(T,x).(JoinTBA (T,x).(a,b),c) =
JoinTBA (T,x).(a,JoinTBA (T,x).(b,c))
proof
let x,a,b,c be Element of T;
set ff = JoinTBA (T,x);
ff.(ff.(a,b),c) = ff.(Tern (a,x,b),c) by JoinDef
.= Tern(Tern (a,x,b),x,c) by JoinDef
.= Tern(a,x,Tern (b,x,c)) by Th33
.= Tern(a,x,ff.(b,c)) by JoinDef
.= ff.(a,ff.(b,c)) by JoinDef;
hence thesis;
end;
registration let T;
let x be Element of T;
cluster JoinTBA (T,x) -> associative;
coherence
proof
set ff = JoinTBA (T,x);
for a,b,c being Element of T holds
ff.(ff.(a,b),c) = ff.(a,ff.(b,c)) by ThAssoc;
hence thesis by BINOP_1:def 3;
end;
end;
ThCom1:
for x,a,b being Element of T holds
MeetTBA (T,x).(a,b) = MeetTBA (T,x).(b,a)
proof
let x,a,b be Element of T;
MeetTBA (T,x).(a,b) = Tern (a,x`,b) by MeetDef
.= Tern (b,x`,a) by Th36c
.= MeetTBA (T,x).(b,a) by MeetDef;
hence thesis;
end;
registration let T;
let x be Element of T;
cluster MeetTBA (T,x) -> commutative;
coherence
proof
set ff = MeetTBA (T,x);
for a,b being Element of T holds ff.(a,b) = ff.(b,a) by ThCom1;
hence thesis by BINOP_1:def 2;
end;
end;
reserve x for Element of T;
ThV2:
for x,a,b,c being Element of T holds
MeetTBA(T,x).(MeetTBA (T,x).(a,b),c) =
MeetTBA (T,x).(a,MeetTBA (T,x).(b,c))
proof
let x,a,b,c be Element of T;
set ff = MeetTBA (T,x);
ff.(ff.(a,b),c) = ff.(Tern (a,x`,b),c) by MeetDef
.= Tern(Tern (a,x`,b),x`,c) by MeetDef
.= Tern(a,x`,Tern (b,x`,c)) by Th33
.= Tern(a,x`,ff.(b,c)) by MeetDef
.= ff.(a,ff.(b,c)) by MeetDef;
hence thesis;
end;
registration let T;
let x be Element of T;
cluster MeetTBA (T,x) -> associative;
coherence
proof
set ff = MeetTBA (T,x);
for a,b,c being Element of T holds
ff.(ff.(a,b),c) = ff.(a,ff.(b,c)) by ThV2;
hence thesis by BINOP_1:def 3;
end;
end;
V4: MeetTBA (T,x) absorbs JoinTBA (T,x)
proof
set ff = MeetTBA (T,x);
set gg = JoinTBA (T,x);
for a,b being Element of the carrier of T holds
ff.(a,gg.(a,b)) = a
proof
let a,b be Element of the carrier of T;
ff.(a,gg.(a,b)) = ff.(a,Tern(a,x,b)) by JoinDef
.= Tern(a,x`,Tern(a,x,b)) by MeetDef
.= Tern(Tern(a,x,x`),x`,Tern(a,x,b)) by TRADef
.= Tern(a,x,Tern(x`,x`,b)) by TDis
.= Tern(a,x,x`) by TLIDef
.= a by TRADef;
hence thesis;
end;
hence thesis by LATTICE2:def 1;
end;
V3: JoinTBA (T,x) absorbs MeetTBA (T,x)
proof
set ff = JoinTBA (T,x);
set gg = MeetTBA (T,x);
for a,b being Element of the carrier of T holds
ff.(a,gg.(a,b)) = a
proof
let a,b be Element of the carrier of T;
ff.(a,gg.(a,b)) = ff.(a,Tern(a,x`,b)) by MeetDef
.= Tern(a,x,Tern(a,x`,b)) by JoinDef
.= Tern(Tern(a,x,x`),x,Tern(a,x`,b)) by TRADef
.= Tern(Tern(a,x`,x),x,Tern(a,x`,b)) by Th36a
.= Tern(a,x`,Tern(x,x,b)) by TDis
.= Tern(a,x`,Tern(x,b,x)) by Th36a
.= Tern(a,x`,x) by Th32
.= Tern(a,x,x`) by Th36a
.= a by TRADef;
hence thesis;
end;
hence thesis by LATTICE2:def 1;
end;
registration let T be Ternary_Boolean_Algebra;
let p be Element of T;
cluster the LattStr of TBA2BA (T,p) -> Lattice-like;
coherence
proof
set L = the LattStr of TBA2BA (T,p);
the L_join of L is commutative associative &
the L_meet of L is commutative associative &
the L_join of L absorbs the L_meet of L &
the L_meet of L absorbs the L_join of L implies L is Lattice-like
by LATTICE2:11;
hence thesis by V3,V4;
end;
end;
begin :: Proof that BA2BAA B returns standard example of Ternary Boolean Algebra
registration
let B be Boolean Lattice;
cluster BA2TBAA B -> Lattice-like;
coherence
proof
set L = BA2TBAA B;
the L_join of B absorbs the L_meet of B by LATTICE2:26;
hence thesis by LATTICE2:11,27;
end;
end;
theorem TBACompl:
for B being Boolean Lattice,
x being Element of B,
xx being Element of BA2TBA B st xx = x holds
x` = xx`
proof
let B be Boolean Lattice,
x be Element of B,
xx be Element of BA2TBA B;
assume
A1: xx = x;
xx` = (the Compl of BA2TBA B).xx by ROBBINS1:def 3
.= x` by A1,LATTICE4:def 13;
hence thesis;
end;
theorem TBAComplA:
for B being Boolean Lattice,
x being Element of B,
xx being Element of BA2TBAA B st xx = x holds
x` = xx`
proof
let B be Boolean Lattice,
x be Element of B,
xx be Element of BA2TBAA B;
assume
A1: xx = x;
xx` = (the Compl of BA2TBAA B).xx by ROBBINS1:def 3
.= x` by A1,LATTICE4:def 13;
hence thesis;
end;
registration
let B be Boolean Lattice;
cluster BA2TBA B -> ternary-left-idempotent
ternary-right-idempotent ternary-left-absorbing
ternary-right-absorbing;
coherence
proof
set T = BA2TBA B;
set ff = RosTrn B;
t1: for a,b being Element of T holds Tern(b,b,a) = b
proof
let a,b be Element of T;
reconsider aa = a, bb = b as Element of B;
Tern(b,b,a) = Ros (bb,bb,aa) by RosTrnDef
.= bb "\/" ((aa "/\" bb) "\/" (aa "/\" bb)) by LATTICES:def 5
.= b by LATTICES:def 8;
hence thesis;
end;
T4: for a,b being Element of T holds Tern(a,b,b) = b
proof
let a,b be Element of T;
reconsider aa = a, bb = b as Element of B;
Tern(a,b,b) = Ros (aa,bb,bb) by RosTrnDef
.= bb "\/" (bb "/\" aa) by LATTICES:def 8
.= bb by LATTICES:def 8;
hence thesis;
end;
T5: for a,b being Element of T holds Tern(b`,b,a) = a
proof
let a,b be Element of T;
reconsider aa = a, bb = b as Element of B;
b` = bb` by TBACompl; then
Tern(b`,b,a) = Ros (bb`,bb,aa) by RosTrnDef
.= ((Bottom B) "\/" (bb "/\" aa)) "\/" (aa "/\" bb`)
by LATTICES:20
.= ((bb "/\" aa) "\/" aa) "/\" ((bb "/\" aa) "\/" bb`)
by LATTICES: 11
.= aa "/\" ((bb "/\" aa) "\/" bb`) by LATTICES:def 8
.= aa "/\" ((bb` "\/" bb) "/\" (bb` "\/" aa)) by LATTICES:11
.= aa "/\" ((Top B) "/\" (bb` "\/" aa)) by LATTICES:21
.= a by LATTICES:def 9;
hence thesis;
end;
for a,b being Element of T holds Tern(a,b,b`) = a
proof
let a,b be Element of T;
reconsider aa = a, bb = b as Element of B;
b` = bb` by TBACompl; then
Tern(a,b,b`) = Ros (aa,bb,bb`) by RosTrnDef
.= ((Bottom B) "\/" (bb "/\" aa)) "\/" (aa "/\" bb`)
by LATTICES:20
.= ((bb "/\" aa) "\/" aa) "/\" ((bb "/\" aa) "\/" bb`)
by LATTICES:11
.= aa "/\" ((bb "/\" aa) "\/" bb`) by LATTICES:def 8
.= aa "/\" ((bb` "\/" bb) "/\" (bb` "\/" aa)) by LATTICES:11
.= aa "/\" ((Top B) "/\" (bb` "\/" aa)) by LATTICES:21
.= a by LATTICES:def 9;
hence thesis;
end;
hence thesis by t1,T4,T5;
end;
end;
registration
let B be Boolean Lattice;
cluster BA2TBAA B -> ternary-left-idempotent
ternary-right-idempotent ternary-left-absorbing ternary-right-absorbing;
coherence
proof
set T = BA2TBAA B;
set ff = RosTrn B;
T1: for a,b being Element of T holds Tern(b,b,a) = b
proof
let a,b be Element of T;
reconsider aa = a, bb = b as Element of B;
Tern(b,b,a) = Ros (bb,bb,aa) by RosTrnDef
.= bb "\/" ((aa "/\" bb) "\/" (aa "/\" bb)) by LATTICES:def 5
.= b by LATTICES:def 8;
hence thesis;
end;
T4: for a,b being Element of T holds Tern(a,b,b) = b
proof
let a,b be Element of T;
reconsider aa = a, bb = b as Element of B;
Tern(a,b,b) = Ros (aa,bb,bb) by RosTrnDef
.= bb "\/" (bb "/\" aa) by LATTICES:def 8
.= bb by LATTICES:def 8;
hence thesis;
end;
T5: for a,b being Element of T holds Tern(b`,b,a) = a
proof
let a,b be Element of T;
reconsider aa = a, bb = b as Element of B;
b` = bb` by TBAComplA; then
Tern(b`,b,a) = Ros (bb`,bb,aa) by RosTrnDef
.= ((Bottom B) "\/" (bb "/\" aa)) "\/" (aa "/\" bb`)
by LATTICES:20
.= ((bb "/\" aa) "\/" aa) "/\" ((bb "/\" aa) "\/" bb`)
by LATTICES:11
.= aa "/\" ((bb "/\" aa) "\/" bb`) by LATTICES:def 8
.= aa "/\" ((bb` "\/" bb) "/\" (bb` "\/" aa)) by LATTICES:11
.= aa "/\" ((Top B) "/\" (bb` "\/" aa)) by LATTICES:21
.= a by LATTICES:def 9;
hence thesis;
end;
for a,b being Element of T holds Tern(a,b,b`) = a
proof
let a,b be Element of T;
reconsider aa = a, bb = b as Element of B;
b` = bb` by TBAComplA; then
Tern(a,b,b`) = Ros (aa,bb,bb`) by RosTrnDef
.= ((Bottom B) "\/" (bb "/\" aa)) "\/" (aa "/\" bb`)
by LATTICES:20
.= ((bb "/\" aa) "\/" aa) "/\" ((bb "/\" aa) "\/" bb`)
by LATTICES:11
.= aa "/\" ((bb "/\" aa) "\/" bb`) by LATTICES:def 8
.= aa "/\" ((bb` "\/" bb) "/\" (bb` "\/" aa)) by LATTICES:11
.= aa "/\" ((Top B) "/\" (bb` "\/" aa)) by LATTICES:21
.= a by LATTICES:def 9;
hence thesis;
end;
hence thesis by T1,T4,T5;
end;
end;
reserve B for Boolean Lattice;
reserve v0,v1,v2,v3,v4,v5,v6,v103,v100,v102,v104,v105,v101 for
Element of BA2TBAA B;
theorem TBA1:
(for v1,v0 holds Tern(v0,v0,v1) = v0) &
(for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v2,v0,v1)) &
(for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v0,v2,v1)) &
(for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v1,v3) = Tern(v0,v1,Tern(v2,v1,v3))) implies
for v1,v2,v3,v4,v5 holds
Tern(Tern(v1,v2,v3),v4,Tern(v1,v2,v5)) = Tern(v1,v2,Tern(v3,v4,v5))
proof
assume A2: for v1,v0 holds Tern(v0,v0,v1) = v0;
assume A3: for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v2,v0,v1);
assume A4: for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v0,v2,v1);
assume A5: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v1,v3) = Tern(v0,v1,Tern(v2,v1,v3));
A7: for v3,v2,v1,v0 holds Tern(v3,Tern(v0,v1,v2),v1)=Tern(v0,v1,Tern(v2,v1,v3))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),v1,v3)=Tern(v3,Tern(v0,v1,v2),v1) by A3;
hence thesis by A5;
end;
A10: for v0,v3,v2,v1 holds
Tern(v2,v0,Tern(v1,v2,v3))=Tern(v1,v2,Tern(v3,v2,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v2)=Tern(v2,v0,Tern(v1,v2,v3)) by A3;
hence thesis by A7;
end;
A13: for v1,v3,v0,v2 holds
Tern(v0,v1,Tern(v2,v0,v3)) = Tern(v2,v0,Tern(v0,v1,v3))
proof let v1,v3,v0,v2;
Tern(v0,v1,v3) = Tern(v3,v0,v1) by A3;
hence thesis by A10;
end;
A15: for v1,v3,v0,v2 holds
Tern(v0,v1,Tern(v2,v0,v3)) = Tern(v2,v0,Tern(v0,v3,v1))
proof let v1,v3,v0,v2;
Tern(v0,v1,v3) = Tern(v0,v3,v1) by A4;
hence thesis by A13;
end;
A17: for v1,v2,v3,v0 holds
Tern(v0,v1,Tern(v0,v3,v2)) = Tern(v2,v0,Tern(v0,v3,v1))
proof let v1,v2,v3,v0;
Tern(v0,v3,v2) = Tern(v2,v0,v3) by A3;
hence thesis by A15;
end;
A20: for v1,v2,v3,v0 holds
Tern(v0,v1,Tern(v0,v3,v2)) = Tern(v3,v0,Tern(v0,v2,v1))
proof let v1,v2,v3,v0;
Tern(v0,v2,v3) = Tern(v0,v3,v2) by A4;
hence thesis by A17;
end;
A23: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,v3)) = Tern(v2,v0,Tern(v0,v1,v3))
proof let v1,v3,v2,v0;
Tern(v0,v3,v1) = Tern(v0,v1,v3) by A4;
hence thesis by A20;
end;
A25: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,v3)) = Tern(v0,Tern(v0,v1,v3),v2)
proof let v1,v3,v2,v0;
Tern(v0,Tern(v0,v1,v3),v2) = Tern(v2,v0,Tern(v0,v1,v3)) by A3;
hence thesis by A23;
end;
A27: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,v3)) = Tern(v0,v2,Tern(v0,v1,v3))
proof let v1,v3,v2,v0;
Tern(v0,Tern(v0,v1,v3),v2) = Tern(v0,v2,Tern(v0,v1,v3)) by A4;
hence thesis by A25;
end;
assume not thesis; then
consider c1,c2,c3,c4,c5 being Element of BA2TBAA B such that
A28: not Tern(Tern(c1,c2,c3),c4,Tern(c1,c2,c5)) =
Tern(c1,c2,Tern(c3,c4,c5));
A30: not Tern(c4,Tern(c1,c2,c5),Tern(c1,c2,c3)) =
Tern(c1,c2,Tern(c3,c4,c5)) by A3,A28;
A32: not Tern(c4,Tern(c1,c2,c3),Tern(c1,c2,c5)) =
Tern(c1,c2,Tern(c3,c4,c5)) by A4,A30;
A34: for v0,v1 holds Tern(v1,v0,v0) = v0
proof let v0,v1;
Tern(v0,v0,v1) = Tern(v1,v0,v0) by A3;
hence thesis by A2;
end;
A38: for v100,v3,v2,v102 holds
Tern(v100,Tern(v102,v2,v3),v102) = Tern(v102,v2,Tern(v102,v100,v3))
proof let v100,v3,v2,v102;
Tern(v102,v100,Tern(v102,v2,v3)) = Tern(v102,v2,Tern(v102,v100,v3)) by A27;
hence thesis by A3;
end;
A41: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3))=Tern(v1,v2,Tern(v1,v0,v3))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v1) = Tern(v0,v1,Tern(v1,v2,v3)) by A4;
hence thesis by A38;
end;
A43: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3)) = Tern(v1,v2,Tern(v0,v3,v1))
proof let v0,v3,v2,v1;
Tern(v0,v3,v1) = Tern(v1,v0,v3) by A3;
hence thesis by A41;
end;
A45: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3)) = Tern(v1,v2,Tern(v0,v1,v3))
proof let v0,v3,v2,v1;
Tern(v0,v3,v1) = Tern(v0,v1,v3) by A4;
hence thesis by A43;
end;
A49: for v1,v2,v0,v3 holds
Tern(v0,v1,Tern(v3,v0,v2)) = Tern(v0,v2,Tern(v0,v1,v3))
proof let v1,v2,v0,v3;
Tern(v0,v2,v3) = Tern(v3,v0,v2) by A3;
hence thesis by A27;
end;
A52: for v1,v2,v3,v0 holds
Tern(v0,v1,Tern(v0,v3,v2)) = Tern(v0,v3,Tern(v0,v1,v2))
proof let v1,v2,v3,v0;
Tern(v0,v3,v2) = Tern(v2,v0,v3) by A3;
hence thesis by A49;
end;
A55: for v1,v2,v3,v0 holds
Tern(v0,v1,Tern(v0,v3,v2)) = Tern(v0,v2,Tern(v0,v1,v3))
proof let v1,v2,v3,v0;
Tern(v0,v2,v3) = Tern(v0,v3,v2) by A4;
hence thesis by A52;
end;
A59: for v101,v2,v3,v102,v100 holds
Tern(v100,v101,Tern(v100,v2,Tern(v100,v102,v3))) =
Tern(v100,v102,Tern(v100,v101,Tern(v100,v2,v3)))
proof let v101,v2,v3,v102,v100;
Tern(v100,v102,Tern(v100,v2,v3)) = Tern(v100,v2,Tern(v100,v102,v3)) by A27;
hence thesis by A27;
end;
A63: for v103,v101,v100 holds
Tern(v100,v101,v103) = Tern(v100,v103,Tern(v100,v101,v103))
proof let v103,v101,v100;
Tern(v100,v103,v103) = v103 by A34;
hence thesis by A27;
end;
A69: for v103,v102,v100 holds
Tern(v100,v102,v103)=Tern(v100,v102,Tern(v100,Tern(v100,v102,v103),v103))
proof let v103,v102,v100;
Tern(v100,Tern(v100,v102,v103),Tern(v100,v102,v103)) = Tern(v100,v102,v103)
by A34;
hence thesis by A27;
end;
A72: for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v0,v1,Tern(v0,v2,Tern(v0,v1,v2)))
proof let v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),v2) = Tern(v0,v2,Tern(v0,v1,v2)) by A4;
hence thesis by A69;
end;
A74: for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v0,v1,Tern(v0,v1,v2))
proof let v2,v1,v0;
Tern(v0,v2,Tern(v0,v1,v2)) = Tern(v0,v1,v2) by A63;
hence thesis by A72;
end;
A78: for v101,v102,v2,v100 holds
Tern(v100,v101,Tern(v100,v2,v102))=Tern(v100,v102,Tern(v100,v101,Tern(v100,v2
,v102)))
proof let v101,v102,v2,v100;
Tern(v100,v102,Tern(v100,v2,v102)) = Tern(v100,v2,v102) by A63;
hence thesis by A27;
end;
A84: for v102,v101,v2,v100 holds
Tern(v100,v101,Tern(v100,v102,Tern(v100,v2,v101)))=Tern(v100,v102,Tern(v100,v2
,v101))
proof let v102,v101,v2,v100;
Tern(v100,v101,Tern(v100,v2,v101)) = Tern(v100,v2,v101) by A63;
hence thesis by A27;
end;
A87: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v0,v1,v3))) = Tern(v0,v2,Tern(v0,v3,v1))
proof let v2,v3,v1,v0;
Tern(v0,v3,v1) = Tern(v0,v1,v3) by A4;
hence thesis by A84;
end;
A89: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v0,v1,v3))) = Tern(v0,v2,Tern(v0,v1,v3))
proof let v2,v3,v1,v0;
Tern(v0,v3,v1) = Tern(v0,v1,v3) by A4;
hence thesis by A87;
end;
A92: for v100,v3,v102,v2 holds
Tern(v100,Tern(v2,v102,v3),v102)=Tern(v2,v102,Tern(v102,v100,v3))
proof let v100,v3,v102,v2;
Tern(v102,v100,Tern(v2,v102,v3))=Tern(v2,v102,Tern(v102,v100,v3)) by A45;
hence thesis by A3;
end;
A95: for v0,v3,v2,v1 holds
Tern(v0,v2,Tern(v1,v2,v3)) = Tern(v1,v2,Tern(v2,v0,v3))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v2) = Tern(v0,v2,Tern(v1,v2,v3)) by A4;
hence thesis by A92;
end;
A98: for v0,v3,v1,v2 holds
Tern(v0,v1,Tern(v2,v1,v3)) = Tern(v2,v1,Tern(v0,v3,v1))
proof let v0,v3,v1,v2;
Tern(v0,v3,v1) = Tern(v1,v0,v3) by A3;
hence thesis by A95;
end;
A100: for v0,v3,v1,v2 holds
Tern(v0,v1,Tern(v2,v1,v3))=Tern(v2,v1,Tern(v0,v1,v3))
proof let v0,v3,v1,v2;
Tern(v0,v3,v1)=Tern(v0,v1,v3) by A4;
hence thesis by A98;
end;
A103: for v101,v1,v3,v102,v100 holds
Tern(v100,v101,Tern(v102,v1,Tern(v100,v102,v3)))=Tern(v100,v102,Tern(v100,v101
,Tern(v102,v1,v3)))
proof let v101,v1,v3,v102,v100;
Tern(v102,v1,Tern(v100,v102,v3)) = Tern(v100,v102,Tern(v102,v1,v3)) by A45;
hence thesis by A27;
end;
A107: for v100,v3,v1,v102 holds
Tern(v100,Tern(v102,v1,v3),Tern(v102,v1,Tern(v100,v102,v3)))=
Tern(v100,v102,Tern(v102,v1,v3))
proof let v100,v3,v1,v102;
Tern(v102,v1,Tern(v100,v102,v3)) = Tern(v100,v102,Tern(v102,v1,v3)) by A45;
hence thesis by A63;
end;
A111: for v1,v3,v101,v100 holds
Tern(v100,v101,Tern(v101,v1,Tern(v100,v101,v3)))=
Tern(v100,v101,Tern(v101,v1,v3))
proof let v1,v3,v101,v100;
Tern(v101,v1,Tern(v100,v101,v3)) = Tern(v100,v101,Tern(v101,v1,v3)) by A45;
hence thesis by A74;
end;
A115: for v101,v2,v3,v100,v102 holds
Tern(v100,v101,Tern(v2,v102,Tern(v102,v100,v3)))=
Tern(v102,v100,Tern(v100,v101,Tern(v2,v102,v3)))
proof let v101,v2,v3,v100,v102;
Tern(v102,v100,Tern(v2,v102,v3)) = Tern(v2,v102,Tern(v102,v100,v3)) by A45;
hence thesis by A45;
end;
A118: for v1,v2,v3,v4,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v4,v3)))=Tern(v3,v0,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v1,v2,v3,v4,v0;
Tern(v0,v4,v3) = Tern(v3,v0,v4) by A3;
hence thesis by A115;
end;
A120: for v1,v2,v4,v3,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v3,v4)))=Tern(v3,v0,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v1,v2,v4,v3,v0;
Tern(v0,v4,v3) = Tern(v0,v3,v4) by A4;
hence thesis by A118;
end;
A122: for v1,v2,v4,v3,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v3,v4)))=Tern(v0,Tern(v0,v1,Tern(v2,v3,v4)),v3)
proof let v1,v2,v4,v3,v0;
Tern(v0,Tern(v0,v1,Tern(v2,v3,v4)),v3) =
Tern(v3,v0,Tern(v0,v1,Tern(v2,v3,v4))) by A3;
hence thesis by A120;
end;
A124: for v1,v2,v4,v3,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v3,v4)))=Tern(v0,v3,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v1,v2,v4,v3,v0;
Tern(v0,Tern(v0,v1,Tern(v2,v3,v4)),v3) =
Tern(v0,v3,Tern(v0,v1,Tern(v2,v3,v4))) by A4;
hence thesis by A122;
end;
A127: for v100,v3,v2,v102 holds
Tern(v100,Tern(v102,v2,v3),v102)=Tern(v102,v3,Tern(v102,v100,v2))
proof let v100,v3,v2,v102;
Tern(v102,v100,Tern(v102,v2,v3))=Tern(v102,v3,Tern(v102,v100,v2)) by A55;
hence thesis by A3;
end;
A130: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3))=Tern(v1,v3,Tern(v1,v0,v2))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v1)=Tern(v0,v1,Tern(v1,v2,v3)) by A4;
hence thesis by A127;
end;
A132: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3)) = Tern(v1,v3,Tern(v0,v2,v1))
proof let v0,v3,v2,v1;
Tern(v0,v2,v1) = Tern(v1,v0,v2) by A3;
hence thesis by A130;
end;
A134: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3)) = Tern(v1,v3,Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v0,v2,v1) = Tern(v0,v1,v2) by A4;
hence thesis by A132;
end;
A139: for v101,v102,v3,v2,v100 holds
Tern(v100,v101,Tern(v100,v102,Tern(v100,v2,v3)))=
Tern(v100,v102,Tern(v100,v3,Tern(v100,v101,v2)))
proof let v101,v102,v3,v2,v100;
Tern(v100,v101,Tern(v100,v2,v3))=Tern(v100,v3,Tern(v100,v101,v2)) by A55;
hence thesis by A27;
end;
A145: for v101,v1,v102,v2,v100 holds
Tern(v100,v101,Tern(v100,v1,Tern(v100,v2,v102)))=Tern(v100,v102,Tern(v100,v101
,Tern(v100,v1,v2)))
proof let v101,v1,v102,v2,v100;
Tern(v100,v1,Tern(v100,v2,v102))=Tern(v100,v102,Tern(v100,v1,v2)) by A55;
hence thesis by A27;
end;
A149: for v101,v1,v3,v102,v100 holds
Tern(v100,v101,Tern(v102,v1,Tern(v100,v102,v3))) =
Tern(v100,Tern(v102,v1,v3),Tern(v100,v101,v102))
proof let v101,v1,v3,v102,v100;
Tern(v102,v1,Tern(v100,v102,v3)) = Tern(v100,v102,Tern(v102,v1,v3)) by A45;
hence thesis by A55;
end;
A155: for v100,v2,v4,v3,v102 holds
Tern(v100,Tern(v102,v2,Tern(v102,v3,v4)),v102)=
Tern(v102,v3,Tern(v102,v100,Tern(v102,v2,v4)))
proof let v100,v2,v4,v3,v102;
Tern(v102,v100,Tern(v102,v2,Tern(v102,v3,v4)))=
Tern(v102,v3,Tern(v102,v100,Tern(v102,v2,v4))) by A59;
hence thesis by A3;
end;
A158: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))=Tern(v1,v3,Tern(v1,v0,Tern(v1,v2,v4)))
proof let v0,v2,v4,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,v4)),v1)=
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4))) by A4;
hence thesis by A155;
end;
A160: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))=Tern(v1,v3,Tern(v0,Tern(v1,v2,v4),v1))
proof let v0,v2,v4,v3,v1;
Tern(v0,Tern(v1,v2,v4),v1) = Tern(v1,v0,Tern(v1,v2,v4)) by A3;
hence thesis by A158;
end;
A162: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))=Tern(v1,v3,Tern(v0,v1,Tern(v1,v2,v4)))
proof let v0,v2,v4,v3,v1;
Tern(v0,Tern(v1,v2,v4),v1)=Tern(v0,v1,Tern(v1,v2,v4)) by A4;
hence thesis by A160;
end;
A167: for v100,v1,v4,v2,v102 holds
Tern(v100,Tern(v102,v1,Tern(v102,v2,v4)),v102)=
Tern(v102,v1,Tern(v102,v2,Tern(v102,v100,v4)))
proof let v100,v1,v4,v2,v102;
Tern(v102,v1,Tern(v102,v2,Tern(v102,v100,v4)))=
Tern(v102,v100,Tern(v102,v1,Tern(v102,v2,v4))) by A59;
hence thesis by A3;
end;
A170: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))=Tern(v1,v2,Tern(v1,v3,Tern(v1,v0,v4)))
proof let v0,v2,v4,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,v4)),v1)=
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4))) by A4;
hence thesis by A167;
end;
A172: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))=Tern(v1,v2,Tern(v1,v3,Tern(v0,v4,v1)))
proof let v0,v2,v4,v3,v1;
Tern(v0,v4,v1)=Tern(v1,v0,v4) by A3;
hence thesis by A170;
end;
A174: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))=Tern(v1,v2,Tern(v1,v3,Tern(v0,v1,v4)))
proof let v0,v2,v4,v3,v1;
Tern(v0,v4,v1)=Tern(v0,v1,v4) by A4;
hence thesis by A172;
end;
A177: for v101,v3,v100,v4,v2,v102 holds
Tern(v100,v101,Tern(v102,v3,Tern(v102,v100,Tern(v102,v2,v4)))) =
Tern(v102,v100,Tern(v100
,v101,Tern(v102,v2,Tern(v102,v3,v4))))
proof let v101,v3,v100,v4,v2,v102;
Tern(v102,v100,Tern(v102,v2,Tern(v102,v3,v4))) =
Tern(v102,v3,Tern(v102,v100,Tern(v102,v2,v4))) by A59;
hence thesis by A45;
end;
A180: for v1,v3,v0,v5,v4,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,Tern(v2,v4,v5),v2))) =
Tern(v2,v0,Tern(v0,v1,Tern(v2,v4,Tern(v2,v3,v5))))
proof let v1,v3,v0,v5,v4,v2;
Tern(v0,Tern(v2,v4,v5),v2) = Tern(v2,v0,Tern(v2,v4,v5)) by A3;
hence thesis by A177;
end;
A182: for v1,v3,v0,v5,v4,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,Tern(v2,v4,v5)))) =
Tern(v2,v0,Tern(v0,v1,Tern(v2,v4,Tern(v2,v3,v5))))
proof let v1,v3,v0,v5,v4,v2;
Tern(v0,Tern(v2,v4,v5),v2) = Tern(v0,v2,Tern(v2,v4,v5)) by A4;
hence thesis by A180;
end;
A184: for v1,v3,v0,v5,v4,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,Tern(v2,v4,v5))))=
Tern(v0,Tern(v0,v1,Tern(v2,v4,Tern(v2,v3,v5))),v2)
proof let v1,v3,v0,v5,v4,v2;
Tern(v0,Tern(v0,v1,Tern(v2,v4,Tern(v2,v3,v5))),v2)=
Tern(v2,v0,Tern(v0,v1,Tern(v2,v4,Tern(v2,v3,v5)))) by A3;
hence thesis by A182;
end;
A186: for v1,v3,v0,v5,v4,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,Tern(v2,v4,v5)))) =
Tern(v0,v2,Tern(v0,v1,Tern(v2,v4,Tern(v2,v3,v5))))
proof let v1,v3,v0,v5,v4,v2;
Tern(v0,Tern(v0,v1,Tern(v2,v4,Tern(v2,v3,v5))),v2) =
Tern(v0,v2,Tern(v0,v1,Tern(v2,v4,Tern(v2,v3,v5)))) by A4;
hence thesis by A184;
end;
A189: for v101,v102,v1,v3,v103,v100 holds
Tern(v100,v101,Tern(v100,v102,Tern(v103,v1,Tern(v100,v103,v3)))) =
Tern(v100,v103,Tern(v100,v101,Tern(v100,v102,Tern(v103,v1,v3))))
proof let v101,v102,v1,v3,v103,v100;
Tern(v103,v1,Tern(v100,v103,v3)) = Tern(v100,v103,Tern(v103,v1,v3)) by A45;
hence thesis by A59;
end;
A193: for v3,v101,v4,v102,v100 holds
Tern(v100,v3,Tern(v100,v101,Tern(v100,v102,v4))) =
Tern(v100,Tern(v100,v3,v4),Tern(v100,v101,v102))
proof let v3,v101,v4,v102,v100;
Tern(v100,v101,Tern(v100,v102,Tern(v100,v3,v4))) =
Tern(v100,v3,Tern(v100,v101,Tern(v100,v102,v4))) by A59;
hence thesis by A55;
end;
A198: for v1,v2,v4,v3,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v4)))=Tern(v0,v3,Tern(v0,v4,Tern(v0,v1,v2)))
proof let v1,v2,v4,v3,v0;
Tern(v0,v1,Tern(v0,v2,v4))=Tern(v0,v4,Tern(v0,v1,v2)) by A55;
hence thesis by A59;
end;
A201: for v100,v2,v3,v101,v102 holds
Tern(v100,v101,Tern(v102,v2,Tern(v102,v101,v3)))=Tern(v102,v101,Tern(v100,v101
,Tern(v102,v2,v3)))
proof let v100,v2,v3,v101,v102;
Tern(v102,v101,Tern(v102,v2,v3))=Tern(v102,v2,Tern(v102,v101,v3)) by A27;
hence thesis by A100;
end;
A204: for v0,v3,v2,v4,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v4,v2))) =
Tern(v2,v1,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v3,v2,v4,v1;
Tern(v1,v4,v2) = Tern(v2,v1,v4) by A3;
hence thesis by A201;
end;
A206: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4))) =
Tern(v2,v1,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v3,v4,v2,v1;
Tern(v1,v4,v2) = Tern(v1,v2,v4) by A4;
hence thesis by A204;
end;
A208: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))=Tern(v1,Tern(v0,v1,Tern(v2,v3,v4)),v2)
proof let v0,v3,v4,v2,v1;
Tern(v1,Tern(v0,v1,Tern(v2,v3,v4)),v2)=
Tern(v2,v1,Tern(v0,v1,Tern(v2,v3,v4))) by A3;
hence thesis by A206;
end;
A210: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))=Tern(v1,v2,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v3,v4,v2,v1;
Tern(v1,Tern(v0,v1,Tern(v2,v3,v4)),v2)=
Tern(v1,v2,Tern(v0,v1,Tern(v2,v3,v4))) by A4;
hence thesis by A208;
end;
A213: for v100,v101,v2,v102 holds
Tern(v100,v101,Tern(v102,v2,v101))=Tern(v102,v101,Tern(v100,v101,Tern(v102,v2
,v101)))
proof let v100,v101,v2,v102;
Tern(v102,v101,Tern(v102,v2,v101))=Tern(v102,v2,v101) by A63;
hence thesis by A100;
end;
A216: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3)) = Tern(v2,v1,Tern(v0,v1,Tern(v2,v3,v1)))
proof let v0,v3,v2,v1;
Tern(v2,v3,v1) = Tern(v1,v2,v3) by A3;
hence thesis by A213;
end;
A218: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3)) = Tern(v2,v1,Tern(v0,v1,Tern(v1,v2,v3)))
proof let v0,v3,v2,v1;
Tern(v2,v3,v1) = Tern(v1,v2,v3) by A3;
hence thesis by A216;
end;
A220: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3)) = Tern(v1,Tern(v0,v1,Tern(v1,v2,v3)),v2)
proof let v0,v3,v2,v1;
Tern(v1,Tern(v0,v1,Tern(v1,v2,v3)),v2) =
Tern(v2,v1,Tern(v0,v1,Tern(v1,v2,v3))) by A3;
hence thesis by A218;
end;
A222: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3)) = Tern(v1,v2,Tern(v0,v1,Tern(v1,v2,v3)))
proof let v0,v3,v2,v1;
Tern(v1,Tern(v0,v1,Tern(v1,v2,v3)),v2) =
Tern(v1,v2,Tern(v0,v1,Tern(v1,v2,v3))) by A4;
hence thesis by A220;
end;
A227: for v100,v2,v3,v101,v102 holds
Tern(v100,v101,Tern(v2,v102,Tern(v102,v101,v3))) =
Tern(v102,v101,Tern(v100,v101,Tern(v2,v102,v3)))
proof let v100,v2,v3,v101,v102;
Tern(v102,v101,Tern(v2,v102,v3)) = Tern(v2,v102,Tern(v102,v101,v3)) by A45;
hence thesis by A100;
end;
A230: for v0,v2,v3,v4,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v4,v3)))=Tern(v3,v1,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v2,v3,v4,v1;
Tern(v1,v4,v3) = Tern(v3,v1,v4) by A3;
hence thesis by A227;
end;
A232: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v3,v4)))=Tern(v3,v1,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v2,v4,v3,v1;
Tern(v1,v4,v3) = Tern(v1,v3,v4) by A4;
hence thesis by A230;
end;
A234: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v3,v4))) =
Tern(v1,Tern(v0,v1,Tern(v2,v3,v4)),v3)
proof let v0,v2,v4,v3,v1;
Tern(v1,Tern(v0,v1,Tern(v2,v3,v4)),v3) =
Tern(v3,v1,Tern(v0,v1,Tern(v2,v3,v4))) by A3;
hence thesis by A232;
end;
A236: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v3,v4))) =
Tern(v1,v3,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v2,v4,v3,v1;
Tern(v1,Tern(v0,v1,Tern(v2,v3,v4)),v3) =
Tern(v1,v3,Tern(v0,v1,Tern(v2,v3,v4))) by A4;
hence thesis by A234;
end;
A239: for v101,v2,v3,v102,v100 holds
Tern(v100,v101,Tern(v2,v102,Tern(v100,v102,v3))) =
Tern(v100,Tern(v2,v102,v3),Tern(v100,v101,v102))
proof let v101,v2,v3,v102,v100;
Tern(v100,v102,Tern(v2,v102,v3)) = Tern(v2,v102,Tern(v100,v102,v3)) by A100;
hence thesis by A55;
end;
A245: for v101,v2,v100,v3,v102 holds
Tern(v100,v101,Tern(v102,v2,Tern(v102,v3,v100))) =
Tern(v102,v100,Tern(v100,v101,Tern(v102,v2,Tern(v102,v3,v100))))
proof let v101,v2,v100,v3,v102;
Tern(v102,v100,Tern(v102,v2,Tern(v102,v3,v100))) =
Tern(v102,v2,Tern(v102,v3,v100)) by A78;
hence thesis by A45;
end;
A248: for v1,v3,v4,v2,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4)))=
Tern(v2,v0,Tern(v0,v1,Tern(v2,v3,Tern(v2,v4,v0))))
proof let v1,v3,v4,v2,v0;
Tern(v2,v4,v0)=Tern(v0,v2,v4) by A3;
hence thesis by A245;
end;
A250: for v1,v3,v4,v2,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4)))=
Tern(v2,v0,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4))))
proof let v1,v3,v4,v2,v0;
Tern(v2,v4,v0)=Tern(v0,v2,v4) by A3;
hence thesis by A248;
end;
A252: for v1,v3,v4,v2,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4)))=
Tern(v0,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4))),v2)
proof let v1,v3,v4,v2,v0;
Tern(v0,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4))),v2)=
Tern(v2,v0,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4)))) by A3;
hence thesis by A250;
end;
A254: for v1,v3,v4,v2,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4)))=
Tern(v0,v2,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4))))
proof let v1,v3,v4,v2,v0;
Tern(v0,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4))),v2)=
Tern(v0,v2,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2
,v4)))) by A4;
hence thesis by A252;
end;
A259: for v102,v2,v101,v3,v100 holds
Tern(v100,v101,Tern(v102,v101,Tern(v100,v2,Tern(v100,v3,v101))))=
Tern(v102,v101,Tern(v100,v2,Tern(v100,v3,v101)))
proof let v102,v2,v101,v3,v100;
Tern(v100,v101,Tern(v100,v2,Tern(v100,v3,v101)))=
Tern(v100,v2,Tern(v100,v3,v101)) by
A78;
hence thesis by A100;
end;
A262: for v2,v3,v4,v1,v0 holds
Tern(v0,v1,Tern(v2,v1,Tern(v0,v3,Tern(v0,v1,v4))))=
Tern(v2,v1,Tern(v0,v3,Tern(v0,v4,v1)))
proof let v2,v3,v4,v1,v0;
Tern(v0,v4,v1)=Tern(v0,v1,v4) by A4;
hence thesis by A259;
end;
A264: for v2,v3,v4,v1,v0 holds
Tern(v0,v1,Tern(v1,Tern(v0,v3,Tern(v0,v1,v4)),v2))=
Tern(v2,v1,Tern(v0,v3,Tern(v0,v4,v1)))
proof let v2,v3,v4,v1,v0;
Tern(v1,Tern(v0,v3,Tern(v0,v1,v4)),v2)=
Tern(v2,v1,Tern(v0,v3,Tern(v0,v1,v4))) by A3;
hence thesis by A262;
end;
A267: for v4,v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v1,v4,Tern(v0,v2,Tern(v0,v1,v3))))=
Tern(v4,v1,Tern(v0,v2,Tern(v0,v3,v1)))
proof let v4,v2,v3,v1,v0;
Tern(v1,Tern(v0,v2,Tern(v0,v1,v3)),v4)=
Tern(v1,v4,Tern(v0,v2,Tern(v0,v1,v3))) by A4;
hence thesis by A264;
end;
A270: for v2,v3,v4,v1,v0 holds
Tern(v0,v1,Tern(v1,v2,Tern(v0,v3,Tern(v0,v1,v4))))=
Tern(v2,v1,Tern(v0,v3,Tern(v0,v1,v4)))
proof let v2,v3,v4,v1,v0;
Tern(v0,v4,v1)=Tern(v0,v1,v4) by A4;
hence thesis by A267;
end;
A272: for v2,v3,v4,v1,v0 holds
Tern(v0,v1,Tern(v1,v2,Tern(v0,v3,Tern(v0,v1,v4))))=
Tern(v1,Tern(v0,v3,Tern(v0,v1,v4)),v2)
proof let v2,v3,v4,v1,v0;
Tern(v1,Tern(v0,v3,Tern(v0,v1,v4)),v2)=
Tern(v2,v1,Tern(v0,v3,Tern(v0,v1,v4))) by A3;
hence thesis by A270;
end;
A274: for v2,v3,v4,v1,v0 holds
Tern(v0,v1,Tern(v1,v2,Tern(v0,v3,Tern(v0,v1,v4))))=
Tern(v1,v2,Tern(v0,v3,Tern(v0,v1,v4)))
proof let v2,v3,v4,v1,v0;
Tern(v1,Tern(v0,v3,Tern(v0,v1,v4)),v2)=
Tern(v1,v2,Tern(v0,v3,Tern(v0,v1,v4))) by A4;
hence thesis by A272;
end;
A277: for v102,v100,v3,v103,v2 holds
Tern(v100,Tern(v2,v103,v3),Tern(v100,v102,
Tern(v100,v103,Tern(v2,v103,v3))))=Tern(v100
,v102,Tern(v2,v103,Tern(v100,v103,v3)))
proof let v102,v100,v3,v103,v2;
Tern(v100,v103,Tern(v2,v103,v3))=Tern(v2,v103,Tern(v100,v103,v3)) by A100;
hence thesis by A78;
end;
A280: for v4,v0,v3,v2,v1 holds
Tern(v0,v4,Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v4,Tern(v0,v2,Tern(v1,v2,v3))))=
Tern(v0,v4,Tern(v0,v2,Tern(v1
,v2,v3))) by A78;
hence thesis by A277;
end;
A286: for v100,v101,v3,v1,v102 holds
Tern(v100,v101,Tern(v101,v102,Tern(v100,v101,Tern(v102,v1,v3))))=
Tern(v100,v101
,Tern(v102,v1,Tern(v101,v102,v3)))
proof let v100,v101,v3,v1,v102;
Tern(v102,v1,Tern(v101,v102,v3))=Tern(v101,v102,Tern(v102,v1,v3)) by A45;
hence thesis by A111;
end;
A289: for v0,v1,v4,v3,v2 holds
Tern(v0,v1,Tern(v1,v2,Tern(v2,v3,v4)))=Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))
proof let v0,v1,v4,v3,v2;
Tern(v0,v1,Tern(v1,v2,Tern(v0,v1,Tern(v2,v3,v4))))=
Tern(v0,v1,Tern(v1,v2,Tern(v2,v3,v4)))
by A111;
hence thesis by A286;
end;
A293: for v102,v100,v3,v2,v101 holds
Tern(v100,v101,Tern(v101,v102,Tern(v100,v101,Tern(v101,v2,v3))))=
Tern(v100,v101
,Tern(v101,v3,Tern(v101,v102,v2)))
proof let v102,v100,v3,v2,v101;
Tern(v101,v102,Tern(v101,v2,v3))=Tern(v101,v3,Tern(v101,v102,v2)) by A55;
hence thesis by A111;
end;
A296: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))=Tern(v0,v1,Tern(v1,v4,Tern(v1,v2,v3)))
proof let v0,v2,v4,v3,v1;
Tern(v0,v1,Tern(v1,v2,Tern(v0,v1,Tern(v1,v3,v4))))=
Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))
by A111;
hence thesis by A293;
end;
A299: for v2,v3,v100,v102 holds
Tern(v100,Tern(v2,v102,Tern(v102,v100,v3)),v102) =
Tern(v2,v102,Tern(v102,v100,v3))
proof let v2,v3,v100,v102;
Tern(v102,v100,Tern(v2,v102,Tern(v102,v100,v3))) =
Tern(v2,v102,Tern(v102,v100,v3)) by A222;
hence thesis by A3;
end;
A302: for v1,v2,v3,v0 holds
Tern(v0,Tern(v1,v2,Tern(v0,v3,v2)),v2) = Tern(v1,v2,Tern(v2,v0,v3))
proof let v1,v2,v3,v0;
Tern(v0,v3,v2) = Tern(v2,v0,v3) by A3;
hence thesis by A299;
end;
A304: for v1,v3,v2,v0 holds
Tern(v0,Tern(v1,v2,Tern(v0,v2,v3)),v2) = Tern(v1,v2,Tern(v2,v0,v3))
proof let v1,v3,v2,v0;
Tern(v0,v3,v2) = Tern(v0,v2,v3) by A4;
hence thesis by A302;
end;
A306: for v1,v3,v2,v0 holds
Tern(v0,v2,Tern(v1,v2,Tern(v0,v2,v3))) = Tern(v1,v2,Tern(v2,v0,v3))
proof let v1,v3,v2,v0;
Tern(v0,Tern(v1,v2,Tern(v0,v2,v3)),v2) =
Tern(v0,v2,Tern(v1,v2,Tern(v0,v2,v3))) by A4;
hence thesis by A304;
end;
A309: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v2,v1,Tern(v0,v1,v3)))=Tern(v2,v1,Tern(v0,v3,v1))
proof let v2,v3,v1,v0;
Tern(v0,v3,v1)=Tern(v1,v0,v3) by A3;
hence thesis by A306;
end;
A311: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v2,v1,Tern(v0,v1,v3))) = Tern(v2,v1,Tern(v0,v1,v3))
proof let v2,v3,v1,v0;
Tern(v0,v3,v1) = Tern(v0,v1,v3) by A4;
hence thesis by A309;
end;
A314: for v102,v2,v3,v101,v100 holds
Tern(v100,v101,Tern(v102,v101,Tern(v100,v2,Tern(v100,v101,v3)))) =
Tern(v102,v101,Tern(v100,v101,Tern(v100,v2,v3)))
proof let v102,v2,v3,v101,v100;
Tern(v100,v101,Tern(v100,v2,v3)) = Tern(v100,v2,Tern(v100,v101,v3)) by A27;
hence thesis by A311;
end;
A317: for v2,v3,v4,v1,v0 holds
Tern(v0,v1,Tern(v1,Tern(v0,v3,Tern(v0,v1,v4)),v2))=
Tern(v2,v1,Tern(v0,v1,Tern(v0,v3,v4)))
proof let v2,v3,v4,v1,v0;
Tern(v1,Tern(v0,v3,Tern(v0,v1,v4)),v2)=
Tern(v2,v1,Tern(v0,v3,Tern(v0,v1,v4))) by A3;
hence thesis by A314;
end;
A320: for v4,v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v1,v4,Tern(v0,v2,Tern(v0,v1,v3))))=
Tern(v4,v1,Tern(v0,v1,Tern(v0,v2,v3)))
proof let v4,v2,v3,v1,v0;
Tern(v1,Tern(v0,v2,Tern(v0,v1,v3)),v4)=
Tern(v1,v4,Tern(v0,v2,Tern(v0,v1,v3))) by A4;
hence thesis by A317;
end;
A323: for v2,v3,v4,v1,v0 holds
Tern(v1,v2,Tern(v0,v3,Tern(v0,v1,v4)))=
Tern(v2,v1,Tern(v0,v1,Tern(v0,v3,v4)))
proof let v2,v3,v4,v1,v0;
Tern(v0,v1,Tern(v1,v2,Tern(v0,v3,Tern(v0,v1,v4))))=
Tern(v1,v2,Tern(v0,v3,Tern(v0,v1,v4)))
by A274;
hence thesis by A320;
end;
A326: for v1,v3,v4,v0,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v0,v4)))=Tern(v0,Tern(v2,v0,Tern(v2,v3,v4)),v1)
proof let v1,v3,v4,v0,v2;
Tern(v0,Tern(v2,v0,Tern(v2,v3,v4)),v1)=
Tern(v1,v0,Tern(v2,v0,Tern(v2,v3,v4))) by A3;
hence thesis by A323;
end;
A328: for v1,v3,v4,v0,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v0,v4)))=Tern(v0,v1,Tern(v2,v0,Tern(v2,v3,v4)))
proof let v1,v3,v4,v0,v2;
Tern(v0,Tern(v2,v0,Tern(v2,v3,v4)),v1)=
Tern(v0,v1,Tern(v2,v0,Tern(v2,v3,v4))) by A4;
hence thesis by A326;
end;
A331: for v101,v104,v102,v100 holds
Tern(v100,v101,Tern(v100,v102,v104))=
Tern(v100,v102,Tern(v100,v101,Tern(v102,Tern(v100
,v102,v104),v104)))
proof let v101,v104,v102,v100;
Tern(v102,Tern(v100,v102,v104),Tern(v100,v102,v104))=
Tern(v100,v102,v104) by A34;
hence thesis by A103;
end;
A334: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,v3))=Tern(v0,v2,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v3))))
proof let v1,v3,v2,v0;
Tern(v2,Tern(v0,v2,v3),v3)=Tern(v2,v3,Tern(v0,v2,v3)) by A4;
hence thesis by A331;
end;
A336: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,v3))=Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v3)))
proof let v1,v3,v2,v0;
Tern(v0,v2,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v3))))=
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v3)))
by A254;
hence thesis by A334;
end;
A340: for v2,v3,v1,v102 holds
Tern(Tern(v1,v2,v3),Tern(v1,v2,Tern(v102,v1,v3)),v102) =
Tern(v102,v1,Tern(v1,v2,v3))
proof let v2,v3,v1,v102;
Tern(v102,Tern(v1,v2,v3),Tern(v1,v2,Tern(v102,v1,v3))) =
Tern(v102,v1,Tern(v1,v2,v3)) by A107;
hence thesis by A3;
end;
A343: for v1,v0,v3,v2 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,Tern(v2,v3,v0)),v3) =
Tern(v3,v0,Tern(v0,v1,v2))
proof let v1,v0,v3,v2;
Tern(v3,v0,v2) = Tern(v2,v3,v0) by A3;
hence thesis by A340;
end;
A345: for v1,v3,v2,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,Tern(v0,v2,v3)),v3)=Tern(v3,v0,Tern(v0,v1,v2))
proof let v1,v3,v2,v0;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A343;
end;
A347: for v3,v2,v1,v0 holds
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,Tern(v0,v2,v3))) =
Tern(v3,v0,Tern(v0,v1,v2))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v1,Tern(v0,v2,v3)),v3) =
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,Tern(v0,v2,v3))) by A3;
hence thesis by A345;
end;
A350: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,Tern(v1,v3,v0))) =
Tern(v1,Tern(v1,v2,v3),v0)
proof let v0,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v0) = Tern(v0,v1,Tern(v1,v2,v3)) by A3;
hence thesis by A347;
end;
A352: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,Tern(v1,v3,v0))) =
Tern(v1,v0,Tern(v1,v2,v3))
proof let v0,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v0) = Tern(v1,v0,Tern(v1,v2,v3)) by A4;
hence thesis by A350;
end;
A355: for v101,v102,v3,v4,v2,v100 holds
Tern(v100,Tern(v101,v102,Tern(v2,v3,Tern(v100,v2,v4))),
Tern(v101,v102,Tern(v100,v2,Tern(v100,v101,Tern(v2,v3,v4))))) =
Tern(v100,v101,Tern(v101,v102,Tern(v2,v3,Tern(v100,v2,v4))))
proof let v101,v102,v3,v4,v2,v100;
Tern(v100,v101,Tern(v2,v3,Tern(v100,v2,v4))) =
Tern(v100,v2,Tern(v100,v101,Tern(v2,v3,v4))) by A103;
hence thesis by A107;
end;
A359: for v3,v2,v100 holds
Tern(v100,Tern(v2,v3,Tern(v100,v2,v3)),Tern(v100,v2,v3)) =
Tern(v2,v3,Tern(v100,v2,v3))
proof let v3,v2,v100;
Tern(v100,Tern(v2,v3,Tern(v100,v2,v3)),Tern(v2,v3,Tern(v100,v2,v3))) =
Tern(v100,Tern(v2,v3,Tern(v100,v2,v3)),Tern(v100,v2,v3)) by A336;
hence thesis by A34;
end;
A362: for v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v1,v2,Tern(v0,v1,v2))) =
Tern(v1,v2,Tern(v0,v1,v2))
proof let v2,v1,v0;
Tern(v0,Tern(v1,v2,Tern(v0,v1,v2)),Tern(v0,v1,v2)) =
Tern(v0,Tern(v0,v1,v2),Tern(v1,v2,Tern(v0,v1,v2))) by A4;
hence thesis by A359;
end;
A364: for v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2)) = Tern(v1,v2,Tern(v0,v1,v2))
proof let v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v1,v2,Tern(v0,v1,v2))) =
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2))
by A336;
hence thesis by A362;
end;
A366: for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v1,v2,Tern(v0,v1,v2))
proof let v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2)) = Tern(v0,v1,v2) by A34;
hence thesis by A364;
end;
A371: for v100,v2,v4,v3,v102 holds
Tern(v100,Tern(v2,v3,Tern(v102,v3,v4)),v102)=
Tern(v102,v3,Tern(v102,v100,Tern(v2,v3
,v4)))
proof let v100,v2,v4,v3,v102;
Tern(v102,v100,Tern(v2,v3,Tern(v102,v3,v4))) =
Tern(v102,v3,Tern(v102,v100,Tern(v2,v3,v4))) by A124;
hence thesis by A3;
end;
A374: for v0,v1,v3,v4,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v4,v3)),v3) =
Tern(v3,v2,Tern(v3,v0,Tern(v1,v2,v4)))
proof let v0,v1,v3,v4,v2;
Tern(v2,v4,v3) = Tern(v3,v2,v4) by A3;
hence thesis by A371;
end;
A377: for v0,v1,v3,v4,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v4,v3)),v4) =
Tern(v4,v2,Tern(v4,v0,Tern(v1,v2,v3)))
proof let v0,v1,v3,v4,v2;
Tern(v2,v3,v4) = Tern(v2,v4,v3) by A4;
hence thesis by A374;
end;
A380: for v0,v1,v4,v3,v2 holds
Tern(v0,v3,Tern(v1,v2,Tern(v2,v3,v4))) =
Tern(v3,v2,Tern(v3,v0,Tern(v1,v2,v4)))
proof let v0,v1,v4,v3,v2;
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),v3) =
Tern(v0,v3,Tern(v1,v2,Tern(v2,v3,v4))) by A4;
hence thesis by A377;
end;
A383: for v0,v2,v4,v1,v3 holds
Tern(v0,v1,Tern(v2,v3,Tern(v3,v1,v4))) =
Tern(v1,v3,Tern(v0,Tern(v2,v3,v4),v1))
proof let v0,v2,v4,v1,v3;
Tern(v0,Tern(v2,v3,v4),v1) = Tern(v1,v0,Tern(v2,v3,v4)) by A3;
hence thesis by A380;
end;
A385: for v0,v2,v4,v1,v3 holds
Tern(v0,v1,Tern(v2,v3,Tern(v3,v1,v4))) =
Tern(v1,v3,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v2,v4,v1,v3;
Tern(v0,Tern(v2,v3,v4),v1) = Tern(v0,v1,Tern(v2,v3,v4)) by A4;
hence thesis by A383;
end;
A387: for v0,v2,v4,v1,v3 holds
Tern(v0,v1,Tern(v2,v3,Tern(v3,v1,v4))) =
Tern(v3,Tern(v0,v1,Tern(v2,v3,v4)),v1)
proof let v0,v2,v4,v1,v3;
Tern(v3,Tern(v0,v1,Tern(v2,v3,v4)),v1) =
Tern(v1,v3,Tern(v0,v1,Tern(v2,v3,v4))) by A3;
hence thesis by A385;
end;
A389: for v0,v2,v4,v1,v3 holds
Tern(v0,v1,Tern(v2,v3,Tern(v3,v1,v4))) =
Tern(v3,v1,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v2,v4,v1,v3;
Tern(v3,Tern(v0,v1,Tern(v2,v3,v4)),v1) =
Tern(v3,v1,Tern(v0,v1,Tern(v2,v3,v4))) by A4;
hence thesis by A387;
end;
A392: for v102,v4,v3,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v102,v4,v1),v102) =
Tern(v102,v4,Tern(v1,v2,Tern(v102,v1,v3)))
proof let v102,v4,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v102,v4,v1)) =
Tern(v102,v4,Tern(v1,v2,Tern(v102,v1,v3)))
by A149;
hence thesis by A3;
end;
A395: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,v4),v3) =
Tern(v3,v4,Tern(v0,v1,Tern(v3,v0,v2)))
proof let v3,v4,v2,v1,v0;
Tern(v3,v4,v0) = Tern(v0,v3,v4) by A3;
hence thesis by A392;
end;
A397: for v4,v3,v2,v1,v0 holds
Tern(v3,Tern(v0,v1,v2),Tern(v0,v3,v4))=Tern(v3,v4,Tern(v0,v1,Tern(v3,v0,v2)))
proof let v4,v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v3,v4),v3) =
Tern(v3,Tern(v0,v1,v2),Tern(v0,v3,v4)) by A3;
hence thesis by A395;
end;
A400: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v0,v4))=Tern(v0,v4,Tern(v1,v2,Tern(v3,v0,v1)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v1,v3) = Tern(v3,v0,v1) by A3;
hence thesis by A397;
end;
A402: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v0,v4))=Tern(v0,v4,Tern(v1,v2,Tern(v1,v3,v0)))
proof let v4,v0,v3,v2,v1;
Tern(v3,v0,v1) = Tern(v1,v3,v0) by A3;
hence thesis by A400;
end;
A405: for v100,v2,v3,v1,v102 holds
Tern(v100,Tern(v1,v2,Tern(v102,v1,v3)),v102)=
Tern(v102,Tern(v1,v2,v3),Tern(v102,v100
,v1))
proof let v100,v2,v3,v1,v102;
Tern(v102,Tern(v1,v2,v3),Tern(v102,v100,v1))=
Tern(v102,v100,Tern(v1,v2,Tern(v102,v1
,v3))) by A149;
hence thesis by A3;
end;
A408: for v0,v2,v3,v4,v1 holds
Tern(v0,Tern(v1,v2,Tern(v1,v4,v3)),v3)=Tern(v3,Tern(v1,v2,v4),Tern(v3,v0,v1))
proof let v0,v2,v3,v4,v1;
Tern(v1,v4,v3) = Tern(v3,v1,v4) by A3;
hence thesis by A405;
end;
A411: for v0,v2,v3,v4,v1 holds
Tern(v0,Tern(v1,v2,Tern(v1,v4,v3)),v4) =
Tern(v4,Tern(v1,v2,v3),Tern(v4,v0,v1))
proof let v0,v2,v3,v4,v1;
Tern(v1,v3,v4) = Tern(v1,v4,v3) by A4;
hence thesis by A408;
end;
A414: for v0,v2,v4,v3,v1 holds
Tern(v0,v3,Tern(v1,v2,Tern(v1,v3,v4))) =
Tern(v3,Tern(v1,v2,v4),Tern(v3,v0,v1))
proof let v0,v2,v4,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,v4)),v3) =
Tern(v0,v3,Tern(v1,v2,Tern(v1,v3,v4))) by A4;
hence thesis by A411;
end;
A417: for v0,v3,v4,v1,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v1,v4)))=Tern(v1,Tern(v2,v3,v4),Tern(v2,v1,v0))
proof let v0,v3,v4,v1,v2;
Tern(v1,v0,v2)=Tern(v2,v1,v0) by A3;
hence thesis by A414;
end;
A419: for v0,v3,v4,v1,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v1,v4)))=Tern(v1,Tern(v2,v3,v4),Tern(v0,v2,v1))
proof let v0,v3,v4,v1,v2;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A417;
end;
A423: for v4,v0,v1,v3,v2 holds
Tern(v0,Tern(v2,v3,v1),Tern(v0,v4,v1)) =
Tern(v0,v4,Tern(v1,v2,Tern(v0,v1,v3)))
proof let v4,v0,v1,v3,v2;
Tern(v2,v3,v1) = Tern(v1,v2,v3) by A3;
hence thesis by A149;
end;
A426: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,v4))=Tern(v0,v4,Tern(v3,v1,Tern(v0,v3,v2)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v3) = Tern(v0,v3,v4) by A4;
hence thesis by A423;
end;
A428: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,v4))=Tern(v0,v4,Tern(v3,v1,Tern(v0,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v3,v2) = Tern(v0,v2,v3) by A4;
hence thesis by A426;
end;
A430: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,v4))=Tern(v0,v4,Tern(v1,Tern(v0,v2,v3),v3))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v0,v2,v3),v3)=Tern(v3,v1,Tern(v0,v2,v3)) by A3;
hence thesis by A428;
end;
A432: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,v4))=Tern(v0,v4,Tern(v1,v3,Tern(v0,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v0,v2,v3),v3)=Tern(v1,v3,Tern(v0,v2,v3)) by A4;
hence thesis by A430;
end;
A435: for v103,v102,v2,v104,v100 holds
Tern(v100,Tern(Tern(v100,v104,v2),v102,v103),Tern(v100,v104,v2))=
Tern(v100,v104
,Tern(Tern(v100,v104,v2),v102,Tern(v100,Tern(v100,v104,v2),v103)))
proof let v103,v102,v2,v104,v100;
Tern(v100,v104,Tern(v100,v104,v2)) = Tern(v100,v104,v2) by A74;
hence thesis by A149;
end;
A438: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v4,Tern(v0,v1,v2),v3),Tern(v0,v1,v2)) =
Tern(v0,v1,Tern(Tern(v0,v1,v2),v3,Tern(v0
,Tern(v0,v1,v2),v4)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),v3,v4) = Tern(v4,Tern(v0,v1,v2),v3) by A3;
hence thesis by A435;
end;
A441: for v4,v1,v3,v2,v0 holds
Tern(v0,Tern(v4,v1,Tern(v0,v2,v3)),Tern(v0,v2,v3))=
Tern(v0,v2,Tern(Tern(v0,v2,v3),v4,Tern(v0
,Tern(v0,v2,v3),v1)))
proof let v4,v1,v3,v2,v0;
Tern(v1,Tern(v0,v2,v3),v4)=Tern(v4,v1,Tern(v0,v2,v3)) by A3;
hence thesis by A438;
end;
A444: for v1,v2,v4,v3,v0 holds
Tern(v0,Tern(v0,v3,v4),Tern(v1,v2,Tern(v0,v3,v4))) =
Tern(v0,v3,Tern(Tern(v0,v3,v4),v1,Tern(v0,Tern(v0,v3,v4),v2)))
proof let v1,v2,v4,v3,v0;
Tern(v0,Tern(v1,v2,Tern(v0,v3,v4)),Tern(v0,v3,v4)) =
Tern(v0,Tern(v0,v3,v4),Tern(v1,v2,Tern(v0,v3,v4))) by A4;
hence thesis by A441;
end;
A447: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2))) =
Tern(v0,v1,Tern(Tern(v0,v1,v2),v3,Tern(v0,v4,Tern(v0,v1,v2))))
proof let v3,v4,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),v4) = Tern(v0,v4,Tern(v0,v1,v2)) by A4;
hence thesis by A444;
end;
A449: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2))) =
Tern(v0,v1,Tern(v3,Tern(v0,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2)))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2)) =
Tern(Tern(v0,v1,v2),v3,Tern(v0,v4,Tern(v0,v1,v2))) by A3;
hence thesis by A447;
end;
A451: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2))) =
Tern(v0,v1,Tern(v3,Tern(v0,v1,v2),Tern(v0,v4,Tern(v0,v1,v2))))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2)) =
Tern(v3,Tern(v0,v1,v2),Tern(v0,v4,Tern(v0,v1,v2))) by A4;
hence thesis by A449;
end;
A456: for v101,v3,v100,v102 holds
Tern(v100,v101,Tern(v102,v101,Tern(v102,v100,v3))) =
Tern(v102,Tern(v100,v101,v3),Tern(v102,v101,v100))
proof let v101,v3,v100,v102;
Tern(v102,Tern(v100,v101,v3),Tern(v102,v101,v100)) =
Tern(v102,v101,Tern(v100,v101,Tern(v102,v100,v3))) by A149;
hence thesis by A100;
end;
A459: for v1,v2,v3,v0 holds
Tern(v0,v1,Tern(v2,v1,Tern(v0,v3,v2))) =
Tern(v2,Tern(v0,v1,v3),Tern(v2,v1,v0))
proof let v1,v2,v3,v0;
Tern(v0,v3,v2) = Tern(v2,v0,v3) by A3;
hence thesis by A456;
end;
A461: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v2,v1,Tern(v0,v2,v3)))=Tern(v2,Tern(v0,v1,v3),Tern(v2,v1,v0))
proof let v1,v3,v2,v0;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A459;
end;
A463: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v1,Tern(v0,v2,v3),v2))=Tern(v2,Tern(v0,v1,v3),Tern(v2,v1,v0))
proof let v1,v3,v2,v0;
Tern(v1,Tern(v0,v2,v3),v2)=Tern(v2,v1,Tern(v0,v2,v3)) by A3;
hence thesis by A461;
end;
A465: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v1,v2,Tern(v0,v2,v3)))=Tern(v2,Tern(v0,v1,v3),Tern(v2,v1,v0))
proof let v1,v3,v2,v0;
Tern(v1,Tern(v0,v2,v3),v2)=Tern(v1,v2,Tern(v0,v2,v3)) by A4;
hence thesis by A463;
end;
A467: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v1,v2,Tern(v0,v2,v3)))=Tern(v2,Tern(v0,v1,v3),Tern(v0,v2,v1))
proof let v1,v3,v2,v0;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A465;
end;
A469: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v1,v2,Tern(v0,v2,v3)))=Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2))
proof let v1,v3,v2,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A467;
end;
A474: for v102,v3,v101,v100 holds
Tern(v100,v101,Tern(v102,Tern(v100,v101,v3),Tern(v102,v101,v100)))=
Tern(v102,v101
,Tern(v100,v101,Tern(v102,v100,v3)))
proof let v102,v3,v101,v100;
Tern(v102,Tern(v100,v101,v3),Tern(v102,v101,v100))=
Tern(v102,v101,Tern(v100,v101
,Tern(v102,v100,v3))) by A149;
hence thesis by A311;
end;
A477: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v2,Tern(v0,v1,v3),Tern(v0,v2,v1)))=
Tern(v2,v1,Tern(v0,v1,Tern(v2,v0,v3)))
proof let v2,v3,v1,v0;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A474;
end;
A479: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2)))=
Tern(v2,v1,Tern(v0,v1,Tern(v2,v0,v3)))
proof let v2,v3,v1,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A477;
end;
A481: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2)))=
Tern(v2,v1,Tern(v0,v1,Tern(v0,v3,v2)))
proof let v2,v3,v1,v0;
Tern(v0,v3,v2)=Tern(v2,v0,v3) by A3;
hence thesis by A479;
end;
A483: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2)))=
Tern(v2,v1,Tern(v0,v1,Tern(v0,v2,v3)))
proof let v2,v3,v1,v0;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A481;
end;
A485: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2)))=
Tern(v1,Tern(v0,v1,Tern(v0,v2,v3)),v2)
proof let v2,v3,v1,v0;
Tern(v1,Tern(v0,v1,Tern(v0,v2,v3)),v2)=
Tern(v2,v1,Tern(v0,v1,Tern(v0,v2,v3))) by A3;
hence thesis by A483;
end;
A487: for v2,v3,v1,v0 holds
Tern(v0,v1,Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2)))=
Tern(v1,v2,Tern(v0,v1,Tern(v0,v2,v3)))
proof let v2,v3,v1,v0;
Tern(v1,Tern(v0,v1,Tern(v0,v2,v3)),v2)=
Tern(v1,v2,Tern(v0,v1,Tern(v0,v2,v3))) by A4;
hence thesis by A485;
end;
A489: for v1,v0,v4,v3,v2 holds
Tern(v0,Tern(v2,v3,v4),Tern(v0,v1,v2))=Tern(v0,v2,Tern(v0,v1,Tern(v2,v3,v4)))
proof let v1,v0,v4,v3,v2;
Tern(v0,Tern(v2,v3,v4),Tern(v0,v1,v2))=
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4))) by A149;
hence thesis by A103;
end;
A492: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v4))=Tern(v0,v1,Tern(v0,v4,Tern(v1,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v1)=Tern(v0,v1,v4) by A4;
hence thesis by A489;
end;
A495: for v100,v104,v103,v101 holds
Tern(v100,v101,Tern(v101,v103,v104))=
Tern(v101,v104,Tern(v101,v103,Tern(v100,v101
,v104)))
proof let v100,v104,v103,v101;
Tern(v101,v104,Tern(v101,v103,v104))=Tern(v101,v103,v104) by A63;
hence thesis by A174;
end;
A501: for v3,v101,v102,v100 holds
Tern(v3,v100,Tern(v100,v102,v101))=Tern(v100,Tern(v3,v100,v101),Tern(v100,v101
,v102))
proof let v3,v101,v102,v100;
Tern(v100,v101,Tern(v100,v102,Tern(v3,v100,v101)))=Tern(v3,v100,Tern(v100,v102
,v101)) by A495;
hence thesis by A55;
end;
A504: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3))=Tern(v1,Tern(v0,v1,v3),Tern(v1,v2,v3))
proof let v0,v3,v2,v1;
Tern(v1,v3,v2)=Tern(v1,v2,v3) by A4;
hence thesis by A501;
end;
A509: for v3,v2,v102,v1 holds
Tern(Tern(v1,v102,v2),Tern(v102,v3,v2),v102)=Tern(v1,v102,Tern(v102,v3,v2))
proof let v3,v2,v102,v1;
Tern(v102,Tern(v1,v102,v2),Tern(v102,v3,v2))=
Tern(v1,v102,Tern(v102,v3,v2)) by A504;
hence thesis by A3;
end;
A512: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),v1)=Tern(v0,v1,Tern(v1,v3,v2))
proof let v3,v2,v1,v0;
Tern(v1,v3,v2)=Tern(v1,v2,v3) by A4;
hence thesis by A509;
end;
A514: for v3,v2,v1,v0 holds
Tern(v1,Tern(v0,v1,v2),Tern(v1,v2,v3))=Tern(v0,v1,Tern(v1,v3,v2))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),v1)=
Tern(v1,Tern(v0,v1,v2),Tern(v1,v2,v3)) by A3;
hence thesis by A512;
end;
A517: for v3,v2,v0,v1 holds
Tern(v0,Tern(v1,v0,v2),Tern(v0,v2,v3))=Tern(v1,v0,Tern(v0,v2,v3))
proof let v3,v2,v0,v1;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A514;
end;
A520: for v1,v3,v2,v100 holds
Tern(v1,v100,Tern(v100,v2,v3))=Tern(v100,Tern(v100,v2,v3),Tern(v1,v100,v2))
proof let v1,v3,v2,v100;
Tern(v100,Tern(v1,v100,v2),Tern(v100,v2,v3))=
Tern(v1,v100,Tern(v100,v2,v3)) by A517;
hence thesis by A4;
end;
A526: for v104,v103,v101,v100,v1 holds
Tern(v100,v101,Tern(Tern(v1,v100,v101),v103,Tern(v100,Tern(v1,v100,v101)
,v104)))=Tern(v1,v100,Tern(v100,v101,Tern(Tern(v1,v100,v101),v103,v104)))
proof let v104,v103,v101,v100,v1;
Tern(v100,Tern(v1,v100,v101),Tern(v100,v101,
Tern(Tern(v1,v100,v101),v103,v104)))=Tern(v1
,v100,Tern(v100,v101,Tern(Tern(v1,v100,v101),v103,v104))) by A517;
hence thesis by A103;
end;
A529: for v4,v3,v0,v2,v1 holds
Tern(v0,v1,Tern(Tern(v1,v2,v0),v3,Tern(v0,Tern(v2,v0,v1),v4)))=
Tern(v2,v0,Tern(v0,v1
,Tern(Tern(v2,v0,v1),v3,v4)))
proof let v4,v3,v0,v2,v1;
Tern(v2,v0,v1)=Tern(v1,v2,v0) by A3;
hence thesis by A526;
end;
A531: for v4,v3,v2,v1,v0 holds
Tern(v0,v1,Tern(Tern(v0,v1,v2),v3,Tern(v0,Tern(v2,v0,v1),v4)))=
Tern(v2,v0,Tern(v0,v1
,Tern(Tern(v2,v0,v1),v3,v4)))
proof let v4,v3,v2,v1,v0;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A529;
end;
A533: for v4,v3,v2,v1,v0 holds
Tern(v0,v1,Tern(Tern(v0,v1,v2),v3,Tern(v0,Tern(v1,v2,v0),v4)))=
Tern(v2,v0,Tern(v0,v1
,Tern(Tern(v2,v0,v1),v3,v4)))
proof let v4,v3,v2,v1,v0;
Tern(v2,v0,v1)=Tern(v1,v2,v0) by A3;
hence thesis by A531;
end;
A535: for v4,v3,v2,v1,v0 holds
Tern(v0,v1,Tern(Tern(v0,v1,v2),v3,Tern(v0,Tern(v0,v1,v2),v4)))=
Tern(v2,v0,Tern(v0,v1
,Tern(Tern(v2,v0,v1),v3,v4)))
proof let v4,v3,v2,v1,v0;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A533;
end;
A537: for v4,v3,v2,v1,v0 holds
Tern(v0,v1,Tern(Tern(v0,v1,v2),v3,Tern(v0,v4,Tern(v0,v1,v2))))=
Tern(v2,v0,Tern(v0,v1
,Tern(Tern(v2,v0,v1),v3,v4)))
proof let v4,v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),v4)=Tern(v0,v4,Tern(v0,v1,v2)) by A4;
hence thesis by A535;
end;
A539: for v3,v4,v2,v1,v0 holds
Tern(v0,v1,Tern(v3,Tern(v0,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2)))=
Tern(v2,v0,Tern(v0,v1
,Tern(Tern(v2,v0,v1),v3,v4)))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2))=
Tern(Tern(v0,v1,v2),v3,Tern(v0,v4,Tern(v0
,v1,v2))) by A3;
hence thesis by A537;
end;
A542: for v3,v2,v4,v1,v0 holds
Tern(v0,v1,Tern(v2,Tern(v0,v1,v4),Tern(v0,v3,Tern(v0,v1,v4))))=
Tern(v4,v0,Tern(v0,v1
,Tern(Tern(v4,v0,v1),v2,v3)))
proof let v3,v2,v4,v1,v0;
Tern(v2,Tern(v0,v3,Tern(v0,v1,v4)),Tern(v0,v1,v4))=
Tern(v2,Tern(v0,v1,v4),Tern(v0,v3,Tern(v0
,v1,v4))) by A4;
hence thesis by A539;
end;
A545: for v2,v4,v3,v1,v0 holds
Tern(v0,Tern(v0,v1,v3),Tern(v2,v4,Tern(v0,v1,v3)))=
Tern(v3,v0,Tern(v0,v1,Tern(Tern(v3,v0,v1)
,v2,v4)))
proof let v2,v4,v3,v1,v0;
Tern(v0,v1,Tern(v2,Tern(v0,v1,v3),Tern(v0,v4,Tern(v0,v1,v3))))=
Tern(v0,Tern(v0,v1,v3),Tern(v2
,v4,Tern(v0,v1,v3))) by A451;
hence thesis by A542;
end;
A548: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(v2,v0,Tern(v0,v1,Tern(Tern(v1,v2,v0)
,v3,v4)))
proof let v3,v4,v2,v1,v0;
Tern(v2,v0,v1)=Tern(v1,v2,v0) by A3;
hence thesis by A545;
end;
A550: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(v2,v0,Tern(v0,v1,Tern(Tern(v0,v1,v2)
,v3,v4)))
proof let v3,v4,v2,v1,v0;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A548;
end;
A552: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(v2,v0,Tern(v0,v1,Tern(v4,Tern(v0,v1
,v2),v3)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),v3,v4)=Tern(v4,Tern(v0,v1,v2),v3) by A3;
hence thesis by A550;
end;
A554: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(v2,v0,Tern(v0,v1,Tern(v3,v4,Tern(v0
,v1,v2))))
proof let v3,v4,v2,v1,v0;
Tern(v4,Tern(v0,v1,v2),v3)=Tern(v3,v4,Tern(v0,v1,v2)) by A3;
hence thesis by A552;
end;
A556: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(v0,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1
,v2))),v2)
proof let v3,v4,v2,v1,v0;
Tern(v0,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2))),v2)=
Tern(v2,v0,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1
,v2)))) by A3;
hence thesis by A554;
end;
A558: for v3,v4,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0
,v1,v2))))
proof let v3,v4,v2,v1,v0;
Tern(v0,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2))),v2)=
Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1
,v2)))) by A4;
hence thesis by A556;
end;
A561: for v101,v2,v104,v103 holds
Tern(Tern(v103,v104,v2),v101,Tern(Tern(v103,v104,v2),v103,Tern(v103,v104
,v2)))=Tern(v103,Tern(v103,v104,v2),Tern(Tern(v103,v104,v2),v103,
Tern(Tern(v103,v104,v2)
,v101,v104)))
proof let v101,v2,v104,v103;
Tern(v103,Tern(v103,v104,v2),Tern(Tern(v103,v104,v2),v103,v104))=
Tern(Tern(v103,v104,v2)
,v103,Tern(v103,v104,v2)) by A520;
hence thesis by A162;
end;
A564: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2)))=
Tern(v0,Tern(v0,v1,v2)
,Tern(Tern(v0,v1,v2),v0,Tern(Tern(v0,v1,v2),v3,v1)))
proof let v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2))=
Tern(Tern(v0,v1,v2),v0,Tern(v0,v1,v2)) by A3;
hence thesis by A561;
end;
A566: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,v2))=Tern(v0,Tern(v0,v1,v2),
Tern(Tern(v0,v1,v2),v0
,Tern(Tern(v0,v1,v2),v3,v1)))
proof let v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2))=Tern(v0,v1,v2) by A34;
hence thesis by A564;
end;
A568: for v3,v2,v1,v0 holds
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v2))=Tern(v0,Tern(v0,v1,v2),
Tern(Tern(v0,v1,v2),v0
,Tern(Tern(v0,v1,v2),v3,v1)))
proof let v3,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v2))=
Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,v2)) by A3;
hence thesis by A566;
end;
A571: for v0,v3,v2,v1 holds
Tern(v1,v2,v3)=Tern(v1,Tern(v1,v2,v3),Tern(Tern(v1,v2,v3),v1,
Tern(Tern(v1,v2,v3),v0,v2)))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v3))=Tern(v1,v2,v3) by A34;
hence thesis by A568;
end;
A574: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v0,Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v0,
Tern(v1,Tern(v0,v1,v2),v3)))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),v3,v1)=Tern(v1,Tern(v0,v1,v2),v3) by A3;
hence thesis by A571;
end;
A576: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v0,Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v0,
Tern(v1,v3,Tern(v0,v1,v2))))
proof let v3,v2,v1,v0;
Tern(v1,Tern(v0,v1,v2),v3)=Tern(v1,v3,Tern(v0,v1,v2)) by A4;
hence thesis by A574;
end;
A578: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v0,Tern(v0,v1,v2),Tern(v0,Tern(v1,v3,Tern(v0,v1,v2)),
Tern(v0,v1,v2)))
proof let v3,v2,v1,v0;
Tern(v0,Tern(v1,v3,Tern(v0,v1,v2)),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v0,
Tern(v1,v3,Tern(v0
,v1,v2))) by A3;
hence thesis by A576;
end;
A580: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v0,Tern(v0,v1,v2),Tern(v0,Tern(v0,v1,v2),Tern(v1,v3,
Tern(v0,v1,v2))))
proof let v3,v2,v1,v0;
Tern(v0,Tern(v1,v3,Tern(v0,v1,v2)),Tern(v0,v1,v2))=
Tern(v0,Tern(v0,v1,v2),Tern(v1,v3,Tern(v0
,v1,v2))) by A4;
hence thesis by A578;
end;
A582: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v0,Tern(v0,v1,v2),Tern(v0,v2,
Tern(v0,v1,Tern(v1,v3,Tern(v0,v1,v2)))))
proof let v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v1,v3,Tern(v0,v1,v2)))=
Tern(v0,v2,Tern(v0,v1,Tern(v1,v3,Tern(v0,v1
,v2)))) by A558;
hence thesis by A580;
end;
A584: for v0,v2,v3,v1 holds
Tern(v0,v1,v2)=Tern(v0,Tern(v0,v1,v2),Tern(v0,v2,Tern(v0,v1,Tern(v1,v3,v2))))
proof let v0,v2,v3,v1;
Tern(v0,v1,Tern(v1,v3,Tern(v0,v1,v2)))=Tern(v0,v1,Tern(v1,v3,v2)) by A111;
hence thesis by A582;
end;
A586: for v0,v3,v2,v1 holds
Tern(v0,v1,v2)=Tern(v0,Tern(v0,v1,v2),Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3))))
proof let v0,v3,v2,v1;
Tern(v1,v3,v2)=Tern(v1,v2,v3) by A4;
hence thesis by A584;
end;
A588: for v0,v3,v2,v1 holds
Tern(v0,v1,v2)=Tern(v0,v1,Tern(v0,v2,Tern(v0,Tern(v0,v1,Tern(v1,v2,v3)),v2)))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v0,v1,v2),Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3))))=
Tern(v0,v1,Tern(v0,v2,Tern(v0
,Tern(v0,v1,Tern(v1,v2,v3)),v2))) by A193;
hence thesis by A586;
end;
A590: for v0,v3,v2,v1 holds
Tern(v0,v1,v2)=Tern(v0,v1,Tern(v0,v2,Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3)))))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v0,v1,Tern(v1,v2,v3)),v2)=
Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3))) by A4;
hence thesis by A588;
end;
A592: for v0,v3,v2,v1 holds
Tern(v0,v1,v2)=Tern(v0,v1,Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3))))
proof let v0,v3,v2,v1;
Tern(v0,v2,Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3))))=
Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3)))
by A74;
hence thesis by A590;
end;
A594: for v0,v3,v2,v1 holds
Tern(v0,v1,v2)=Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3)))
proof let v0,v3,v2,v1;
Tern(v0,v1,Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3))))=
Tern(v0,v2,Tern(v0,v1,Tern(v1,v2,v3)))
by A89;
hence thesis by A592;
end;
A599: for v102,v3,v100,v2 holds
Tern(v100,Tern(v102,v2,Tern(v2,v100,v3)),v102)=Tern(v102,v2,v100)
proof let v102,v3,v100,v2;
Tern(v102,v100,Tern(v102,v2,Tern(v2,v100,v3)))=Tern(v102,v2,v100) by A594;
hence thesis by A3;
end;
A602: for v1,v2,v3,v0 holds
Tern(v0,Tern(v1,v2,Tern(v0,v3,v2)),v1)=Tern(v1,v2,v0)
proof let v1,v2,v3,v0;
Tern(v0,v3,v2)=Tern(v2,v0,v3) by A3;
hence thesis by A599;
end;
A604: for v1,v3,v2,v0 holds
Tern(v0,Tern(v1,v2,Tern(v0,v2,v3)),v1)=Tern(v1,v2,v0)
proof let v1,v3,v2,v0;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A602;
end;
A606: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v1,v2,Tern(v0,v2,v3)))=Tern(v1,v2,v0)
proof let v1,v3,v2,v0;
Tern(v0,Tern(v1,v2,Tern(v0,v2,v3)),v1)=
Tern(v0,v1,Tern(v1,v2,Tern(v0,v2,v3))) by A4;
hence thesis by A604;
end;
A608: for v1,v3,v2,v0 holds
Tern(v0,v1,Tern(v1,v2,Tern(v0,v2,v3)))=Tern(v0,v1,v2)
proof let v1,v3,v2,v0;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A606;
end;
A610: for v0,v1,v2,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v2,v1)))=Tern(v0,v2,v1)
proof let v0,v1,v2,v3;
Tern(v2,v1,v3)=Tern(v3,v2,v1) by A3;
hence thesis by A594;
end;
A612: for v0,v2,v3,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v3,v2)))=Tern(v0,v2,v1)
proof let v0,v2,v3,v1;
Tern(v3,v2,v1)=Tern(v1,v3,v2) by A3;
hence thesis by A610;
end;
A614: for v0,v3,v2,v1 holds Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,v3)))=
Tern(v0,v2,v1)
proof let v0,v3,v2,v1;
Tern(v1,v3,v2)=Tern(v1,v2,v3) by A4;
hence thesis by A612;
end;
A616: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v0,v1,v2)
proof let v0,v3,v2,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A614;
end;
A619: for v101,v100,v3,v102,v2 holds
Tern(v100,v101,Tern(v100,v2,v102))=
Tern(v100,v102,Tern(v100,v101,Tern(v100,v2,Tern(v2
,v102,v3))))
proof let v101,v100,v3,v102,v2;
Tern(v100,v102,Tern(v100,v2,Tern(v2,v102,v3)))=Tern(v100,v2,v102) by A594;
hence thesis by A27;
end;
A625: for v100,v2,v3,v101,v102 holds
Tern(v100,v101,Tern(v100,v102,Tern(v102,v2,Tern(v102,v101,v3))))=
Tern(v100,v102
,v101)
proof let v100,v2,v3,v101,v102;
Tern(v102,v101,Tern(v102,v2,v3))=Tern(v102,v2,Tern(v102,v101,v3)) by A27;
hence thesis by A594;
end;
A628: for v0,v3,v2,v4,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v2,v3,Tern(v1,v4,v2))))=Tern(v0,v2,v1)
proof let v0,v3,v2,v4,v1;
Tern(v1,v4,v2)=Tern(v2,v1,v4) by A3;
hence thesis by A625;
end;
A630: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v2,v3,Tern(v1,v2,v4))))=Tern(v0,v2,v1)
proof let v0,v3,v4,v2,v1;
Tern(v1,v4,v2)=Tern(v1,v2,v4) by A4;
hence thesis by A628;
end;
A632: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v2,v3,Tern(v1,v2,v4))))=Tern(v0,v1,v2)
proof let v0,v3,v4,v2,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A630;
end;
A635: for v100,v103,v3,v1,v102 holds
Tern(v100,Tern(v102,v1,v3),Tern(v100,v102,Tern(v102,
Tern(v102,v1,v3),v103)))=Tern(v102
,v1,Tern(v100,v102,v3))
proof let v100,v103,v3,v1,v102;
Tern(v102,v1,Tern(v100,v102,v3))=Tern(v100,v102,Tern(v102,v1,v3)) by A45;
hence thesis by A594;
end;
A638: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v1,v4,Tern(v1,v2,v3))))=
Tern(v1,v2,Tern(v0,v1,v3))
proof let v0,v4,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v4)=Tern(v1,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A635;
end;
A640: for v0,v4,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v4,Tern(v1,v2,v3)),Tern(v1,v2,v3)))=
Tern(v1,v2,Tern(v0,v1,v3))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v1,v4,Tern(v1,v2,v3))))=
Tern(v0,v1,Tern(v0,Tern(v1,v4
,Tern(v1,v2,v3)),Tern(v1,v2,v3))) by A492;
hence thesis by A638;
end;
A643: for v2,v0,v4,v3,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v3,v4),Tern(v1,v2,Tern(v1,v3,v4))))=
Tern(v1,v3,Tern(v0,v1,v4))
proof let v2,v0,v4,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,v4)),Tern(v1,v3,v4))=
Tern(v0,Tern(v1,v3,v4),Tern(v1,v2,Tern(v1
,v3,v4))) by A4;
hence thesis by A640;
end;
A647: for v100,v103,v3,v102,v2 holds
Tern(v100,Tern(v2,v102,v3),Tern(v100,v102,Tern(v102,Tern(v2,v102,v3),v103)))
=Tern(v2
,v102,Tern(v100,v102,v3))
proof let v100,v103,v3,v102,v2;
Tern(v100,v102,Tern(v2,v102,v3))=Tern(v2,v102,Tern(v100,v102,v3)) by A100;
hence thesis by A594;
end;
A650: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v2,v4,Tern(v1,v2,v3))))=
Tern(v1,v2,Tern(v0,v2,v3))
proof let v0,v4,v3,v2,v1;
Tern(v2,Tern(v1,v2,v3),v4)=Tern(v2,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A647;
end;
A652: for v3,v1,v2,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v1)))=Tern(v0,v2,v1)
proof let v3,v1,v2,v0;
Tern(v2,v3,Tern(v0,v2,v1))=Tern(v0,v2,Tern(v2,v1,v3)) by A134;
hence thesis by A594;
end;
A654: for v3,v2,v1,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v1,v2)))=Tern(v0,v2,v1)
proof let v3,v2,v1,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A652;
end;
A656: for v3,v2,v1,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v1,v2)))=Tern(v0,v1,v2)
proof let v3,v2,v1,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A654;
end;
A659: for v100,v103,v1,v3,v102 holds
Tern(v100,Tern(v102,v3,v1),Tern(v100,v102,Tern(v102,Tern(v102,v3,v1),v103)))
=Tern(v102
,v1,Tern(v100,v102,v3))
proof let v100,v103,v1,v3,v102;
Tern(v102,v1,Tern(v100,v102,v3))=Tern(v100,v102,Tern(v102,v3,v1)) by A134;
hence thesis by A594;
end;
A662: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v1,v4,Tern(v1,v2,v3))))=
Tern(v1,v3,Tern(v0,v1,v2))
proof let v0,v4,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v4)=Tern(v1,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A659;
end;
A664: for v0,v4,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v4,Tern(v1,v2,v3)),Tern(v1,v2,v3)))=
Tern(v1,v3,Tern(v0,v1,v2))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v1,v4,Tern(v1,v2,v3))))=
Tern(v0,v1,Tern(v0,Tern(v1,v4
,Tern(v1,v2,v3)),Tern(v1,v2,v3))) by A492;
hence thesis by A662;
end;
A667: for v2,v0,v4,v3,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v3,v4),Tern(v1,v2,Tern(v1,v3,v4))))=
Tern(v1,v4,Tern(v0,v1,v3))
proof let v2,v0,v4,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,v4)),Tern(v1,v3,v4))=
Tern(v0,Tern(v1,v3,v4),Tern(v1,v2,Tern(v1
,v3,v4))) by A4;
hence thesis by A664;
end;
A670: for v2,v3,v1,v0 holds
Tern(v1,v2,Tern(v0,v1,v3))=Tern(v1,v3,Tern(v0,v1,v2))
proof
now let v4,v0,v3,v2,v1;
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3))))=
Tern(v1,v2,Tern(v0,v1,v3))
by A643;
hence Tern(v1,v2,Tern(v0,v1,v3))=Tern(v1,v3,Tern(v0,v1,v2)) by A667;
end;
hence thesis;
end;
A674: for v101,v100,v3,v102,v103 holds
Tern(v100,v101,Tern(v100,v103,v102))=
Tern(v100,Tern(v103,v102,v3),Tern(v100,v101
,Tern(v100,v102,v103)))
proof let v101,v100,v3,v102,v103;
Tern(v100,v102,Tern(v100,v103,Tern(v103,v102,v3)))=
Tern(v100,v103,v102) by A594;
hence thesis by A145;
end;
A677: for v1,v0,v4,v3,v2 holds
Tern(v0,v1,Tern(v0,v2,v3))=Tern(v0,Tern(v2,v3,v4),Tern(v0,v1,Tern(v0,v2,v3)))
proof let v1,v0,v4,v3,v2;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A674;
end;
A681: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v2))=Tern(v1,v2,Tern(v2,v0,Tern(v1,v0,v3)))
proof let v0,v3,v2,v1;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A469;
end;
A683: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v1,v2,Tern(v2,v0,Tern(v1,v0,v3)))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v2))=
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,v3))) by A492;
hence thesis by A681;
end;
A685: for v2,v3,v0,v1 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v2,v0,Tern(v1,v0,v3)))
proof let v2,v3,v0,v1;
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v0,v1,v2) by A616;
hence thesis by A683;
end;
A687: for v2,v1,v3,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v2,v0,Tern(v0,v3,v1)))
proof let v2,v1,v3,v0;
Tern(v0,v3,v1)=Tern(v1,v0,v3) by A3;
hence thesis by A685;
end;
A689: for v2,v3,v1,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v2,v0,Tern(v0,v1,v3)))
proof let v2,v3,v1,v0;
Tern(v0,v3,v1)=Tern(v0,v1,v3) by A4;
hence thesis by A687;
end;
A691: for v2,v3,v1,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v0,Tern(v0,v1,v3),v2))
proof let v2,v3,v1,v0;
Tern(v0,Tern(v0,v1,v3),v2)=Tern(v2,v0,Tern(v0,v1,v3)) by A3;
hence thesis by A689;
end;
A693: for v2,v3,v1,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v0,v2,Tern(v0,v1,v3)))
proof let v2,v3,v1,v0;
Tern(v0,Tern(v0,v1,v3),v2)=Tern(v0,v2,Tern(v0,v1,v3)) by A4;
hence thesis by A691;
end;
A697: for v1,v3,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v0,v1,Tern(v0,v2,v3)))
proof let v1,v3,v2,v0;
Tern(v0,v1,Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2)))=Tern(v0,v1,v2) by A656;
hence thesis by A487;
end;
A702: for v100,v3,v102,v2 holds
Tern(v100,Tern(v2,v102,v3),v102)=Tern(v102,v3,Tern(v2,v102,v100))
proof let v100,v3,v102,v2;
Tern(v102,v100,Tern(v2,v102,v3))=Tern(v102,v3,Tern(v2,v102,v100)) by A670;
hence thesis by A3;
end;
A705: for v0,v3,v2,v1 holds
Tern(v0,v2,Tern(v1,v2,v3))=Tern(v2,v3,Tern(v1,v2,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v2)=Tern(v0,v2,Tern(v1,v2,v3)) by A4;
hence thesis by A702;
end;
A708: for v0,v3,v1,v2 holds
Tern(v0,v1,Tern(v2,v1,v3))=Tern(v1,v3,Tern(v0,v2,v1))
proof let v0,v3,v1,v2;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A705;
end;
A713: for v100,v102,v3,v2 holds
Tern(v100,Tern(v2,v3,v102),v102)=Tern(v2,v102,Tern(v3,v102,v100))
proof let v100,v102,v3,v2;
Tern(v102,v100,Tern(v2,v3,v102))=Tern(v2,v102,Tern(v3,v102,v100)) by A708;
hence thesis by A3;
end;
A716: for v0,v3,v2,v1 holds
Tern(v0,v3,Tern(v1,v2,v3))=Tern(v1,v3,Tern(v2,v3,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v3)=Tern(v0,v3,Tern(v1,v2,v3)) by A4;
hence thesis by A713;
end;
A719: for v0,v1,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v1))=Tern(v2,v1,Tern(v0,v3,v1))
proof let v0,v1,v3,v2;
Tern(v3,v1,v0)=Tern(v0,v3,v1) by A3;
hence thesis by A716;
end;
A722: for v100,v103,v102,v101 holds
Tern(v100,Tern(v101,v102,v103),Tern(v100,v102,v101))=
Tern(v102,Tern(v100,v101,v103)
,Tern(v100,v101,v102))
proof let v100,v103,v102,v101;
Tern(v102,Tern(v100,v101,v103),Tern(v100,v101,v102))=
Tern(v100,v102,Tern(v101,v102
,Tern(v100,v101,v103))) by A708;
hence thesis by A149;
end;
A725: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v2))=
Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A722;
end;
A727: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v2))=
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,v3))) by A492;
hence thesis by A725;
end;
A729: for v2,v3,v1,v0 holds
Tern(v0,v1,v2)=Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,v2))
proof let v2,v3,v1,v0;
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v0,v1,v2) by A616;
hence thesis by A727;
end;
A734: for v100,v103,v1,v102,v3 holds
Tern(v100,Tern(v3,v102,v1),Tern(v100,v102,Tern(v102,Tern(v3,v102,v1),v103)))
=Tern(v102
,v1,Tern(v100,v3,v102))
proof let v100,v103,v1,v102,v3;
Tern(v102,v1,Tern(v100,v3,v102))=Tern(v100,v102,Tern(v3,v102,v1)) by A708;
hence thesis by A594;
end;
A737: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v2,v4,Tern(v1,v2,v3))))=
Tern(v2,v3,Tern(v0,v1,v2))
proof let v0,v4,v3,v2,v1;
Tern(v2,Tern(v1,v2,v3),v4)=Tern(v2,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A734;
end;
A739: for v1,v3,v2,v0 holds
Tern(v1,v2,Tern(v0,v2,v3))=Tern(v2,v3,Tern(v0,v1,v2))
proof
now let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v2,v4,Tern(v1,v2,v3))))=
Tern(v1,v2,Tern(v0,v2,v3))
by A650;
hence Tern(v1,v2,Tern(v0,v2,v3))=Tern(v2,v3,Tern(v0,v1,v2)) by A737;
end;
hence thesis;
end;
A745: for v100,v2,v103,v102 holds
Tern(v100,Tern(v102,v103,v2),Tern(v102,v103,v2))=
Tern(v102,Tern(v102,v103,v2),Tern(v100
,v103,Tern(v102,v103,v2)))
proof let v100,v2,v103,v102;
Tern(v102,v103,Tern(v102,v103,v2))=Tern(v102,v103,v2) by A74;
hence thesis by A719;
end;
A748: for v0,v3,v2,v1 holds
Tern(v1,v2,v3)=Tern(v1,Tern(v1,v2,v3),Tern(v0,v2,Tern(v1,v2,v3)))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v3))=Tern(v1,v2,v3) by A34;
hence thesis by A745;
end;
A751: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v0,v2,Tern(v0,v1,Tern(v3,v1,Tern(v0,v1,v2))))
proof let v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v3,v1,Tern(v0,v1,v2)))=
Tern(v0,v2,Tern(v0,v1,Tern(v3,v1,Tern(v0,v1
,v2)))) by A558;
hence thesis by A748;
end;
A753: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v0,v2,Tern(v3,v1,Tern(v0,v1,v2)))
proof let v3,v2,v1,v0;
Tern(v0,v1,Tern(v3,v1,Tern(v0,v1,v2)))=Tern(v3,v1,Tern(v0,v1,v2)) by A311;
hence thesis by A751;
end;
A758: for v102,v100,v1,v3,v103 holds
Tern(v100,Tern(v103,v3,v1),Tern(v102,v103,Tern(v103,v3,v1)))=
Tern(v102,Tern(v103,v3,v1)
,Tern(v103,v1,Tern(v100,v103,v3)))
proof let v102,v100,v1,v3,v103;
Tern(v103,v1,Tern(v100,v103,v3))=Tern(v100,v103,Tern(v103,v3,v1)) by A134;
hence thesis by A719;
end;
A761: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,Tern(v1,v2,v3),v4))=
Tern(v4,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0
,v1,v2)))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v4)=Tern(v4,v1,Tern(v1,v2,v3)) by A3;
hence thesis by A758;
end;
A763: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=
Tern(v4,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0
,v1,v2)))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v4)=Tern(v1,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A761;
end;
A766: for v102,v104,v103,v100 holds
Tern(v102,Tern(v100,v103,v104),Tern(v100,v103,Tern(v100,v103,v104)))=
Tern(v100,v103
,Tern(v100,Tern(v100,v103,v104),Tern(v102,v103,v104)))
proof let v102,v104,v103,v100;
Tern(v100,Tern(v100,v103,v104),Tern(v102,v103,Tern(v100,v103,v104)))=
Tern(v102,Tern(v100
,v103,v104),Tern(v100,v103,Tern(v100,v103,v104))) by A719;
hence thesis by A124;
end;
A769: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v3))=
Tern(v1,v2,Tern(v1,Tern(v1,v2,v3),Tern(v0,v2,v3)))
proof let v0,v3,v2,v1;
Tern(v1,v2,Tern(v1,v2,v3))=Tern(v1,v2,v3) by A74;
hence thesis by A766;
end;
A771: for v0,v3,v2,v1 holds
Tern(v1,v2,v3)=Tern(v1,v2,Tern(v1,Tern(v1,v2,v3),Tern(v0,v2,v3)))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v3))=Tern(v1,v2,v3) by A34;
hence thesis by A769;
end;
A776: for v103,v3,v100,v102 holds
Tern(v100,Tern(v102,v100,v3),Tern(v102,v103,Tern(v102,v100,v3)))=
Tern(v102,Tern(v100
,v103,v3),Tern(v102,Tern(v102,v100,v3),v100))
proof let v103,v3,v100,v102;
Tern(v102,Tern(v100,v103,v3),Tern(v102,Tern(v102,v100,v3),v100))=
Tern(v102,Tern(v102
,v100,v3),Tern(v100,v103,Tern(v102,v100,v3))) by A149;
hence thesis by A719;
end;
A779: for v3,v2,v0,v1 holds
Tern(v0,Tern(v0,v2,v1),Tern(v1,v3,Tern(v1,v0,v2)))=
Tern(v1,Tern(v0,v3,v2),Tern(v1,Tern(v1,v0
,v2),v0))
proof let v3,v2,v0,v1;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A776;
end;
A782: for v3,v1,v0,v2 holds
Tern(v0,Tern(v0,v2,v1),Tern(v2,v3,Tern(v2,v0,v1)))=
Tern(v2,Tern(v0,v3,v1),Tern(v2,Tern(v2,v0
,v1),v0))
proof let v3,v1,v0,v2;
Tern(v0,v1,v2)=Tern(v0,v2,v1) by A4;
hence thesis by A779;
end;
A785: for v3,v1,v2,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v1,v3,Tern(v0,v2,v1)))=
Tern(v1,Tern(v0,v3,v2),Tern(v1,Tern(v1,v0
,v2),v0))
proof let v3,v1,v2,v0;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A782;
end;
A787: for v3,v2,v1,v0 holds
Tern(v0,Tern(v0,v1,v2),Tern(v1,v3,Tern(v0,v1,v2)))=
Tern(v1,Tern(v0,v3,v2),Tern(v1,Tern(v1,v0
,v2),v0))
proof let v3,v2,v1,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A785;
end;
A789: for v3,v2,v1,v0 holds
Tern(v0,v2,Tern(v0,v1,Tern(v1,v3,Tern(v0,v1,v2))))=
Tern(v1,Tern(v0,v3,v2),Tern(v1,Tern(v1,v0
,v2),v0))
proof let v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v1,v3,Tern(v0,v1,v2)))=
Tern(v0,v2,Tern(v0,v1,Tern(v1,v3,Tern(v0,v1
,v2)))) by A558;
hence thesis by A787;
end;
A792: for v0,v1,v3,v2 holds
Tern(v0,v1,Tern(v0,v2,Tern(v2,v3,v1)))=
Tern(v2,Tern(v0,v3,v1),Tern(v2,Tern(v2,v0,v1),v0))
proof let v0,v1,v3,v2;
Tern(v0,v2,Tern(v2,v3,Tern(v0,v2,v1)))=Tern(v0,v2,Tern(v2,v3,v1)) by A111;
hence thesis by A789;
end;
A794: for v0,v3,v1,v2 holds
Tern(v0,v1,Tern(v0,v2,Tern(v2,v1,v3)))=
Tern(v2,Tern(v0,v3,v1),Tern(v2,Tern(v2,v0,v1),v0))
proof let v0,v3,v1,v2;
Tern(v2,v3,v1)=Tern(v2,v1,v3) by A4;
hence thesis by A792;
end;
A796: for v2,v1,v3,v0 holds
Tern(v0,v2,v1)=Tern(v2,Tern(v0,v3,v1),Tern(v2,Tern(v2,v0,v1),v0))
proof let v2,v1,v3,v0;
Tern(v0,v1,Tern(v0,v2,Tern(v2,v1,v3)))=Tern(v0,v2,v1) by A594;
hence thesis by A794;
end;
A799: for v1,v3,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v2,v3),Tern(v1,Tern(v1,v0,v2),v0))
proof let v1,v3,v2,v0;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A796;
end;
A801: for v1,v3,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v2,v3),Tern(v1,Tern(v0,v2,v1),v0))
proof let v1,v3,v2,v0;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A799;
end;
A803: for v1,v3,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v2,v3),Tern(v1,Tern(v0,v1,v2),v0))
proof let v1,v3,v2,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A801;
end;
A805: for v1,v3,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v2,v3),Tern(v0,v1,Tern(v0,v1,v2)))
proof let v1,v3,v2,v0;
Tern(v1,Tern(v0,v1,v2),v0)=Tern(v0,v1,Tern(v0,v1,v2)) by A3;
hence thesis by A803;
end;
A807: for v1,v3,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v2,v3),Tern(v0,v1,v2))
proof let v1,v3,v2,v0;
Tern(v0,v1,Tern(v0,v1,v2))=Tern(v0,v1,v2) by A74;
hence thesis by A805;
end;
A812: for v100,v103,v102,v3,v2 holds
Tern(v100,Tern(v2,v3,v102),Tern(v100,v102,Tern(v102,Tern(v2,v3,v102),v103)))
=Tern(v2
,v102,Tern(v100,v3,v102))
proof let v100,v103,v102,v3,v2;
Tern(v100,v102,Tern(v2,v3,v102))=Tern(v2,v102,Tern(v100,v3,v102)) by A719;
hence thesis by A594;
end;
A815: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v3,v4,Tern(v1,v2,v3))))=
Tern(v1,v3,Tern(v0,v2,v3))
proof let v0,v4,v3,v2,v1;
Tern(v3,Tern(v1,v2,v3),v4)=Tern(v3,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A812;
end;
A817: for v0,v2,v1,v3 holds
Tern(v0,Tern(v3,v1,v2),Tern(v1,v2,v0))=Tern(v1,v2,v0)
proof let v0,v2,v1,v3;
Tern(v1,v2,v3)=Tern(v3,v1,v2) by A3;
hence thesis by A729;
end;
A820: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,v3))=Tern(v2,v3,v0)
proof let v0,v3,v2,v1;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A817;
end;
A822: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,v3))=Tern(v0,v2,v3)
proof let v0,v3,v2,v1;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A820;
end;
A824: for v0,v1,v3,v2 holds
Tern(v0,Tern(v2,v3,v1),Tern(v1,v2,v0))=Tern(v1,v2,v0)
proof let v0,v1,v3,v2;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A729;
end;
A827: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,v1))=Tern(v3,v1,v0)
proof let v0,v3,v2,v1;
Tern(v3,v1,v0)=Tern(v0,v3,v1) by A3;
hence thesis by A824;
end;
A829: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v3))=Tern(v3,v1,v0)
proof let v0,v3,v2,v1;
Tern(v0,v3,v1)=Tern(v0,v1,v3) by A4;
hence thesis by A827;
end;
A831: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,v3,Tern(v1,v2,v3)))=Tern(v3,v1,v0)
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v3))=
Tern(v0,v1,Tern(v0,v3,Tern(v1,v2,v3))) by A492;
hence thesis by A829;
end;
A834: for v0,v2,v3,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v3,v2)))=Tern(v0,v2,v1)
proof let v0,v2,v3,v1;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A831;
end;
A836: for v0,v2,v3,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v3,v2)))=Tern(v0,v1,v2)
proof let v0,v2,v3,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A834;
end;
A839: for v3,v100,v2,v1 holds
Tern(v1,v2,v100)=Tern(v100,Tern(v1,v2,v100),Tern(v1,v2,v3))
proof let v3,v100,v2,v1;
Tern(v100,Tern(v1,v2,v3),Tern(v1,v2,v100))=Tern(v1,v2,v100) by A729;
hence thesis by A4;
end;
A845: for v100,v2,v3,v102,v101 holds
Tern(v100,Tern(v2,v101,Tern(v101,v102,v3)),Tern(v101,v102,v100))=
Tern(v101,v102
,v100)
proof let v100,v2,v3,v102,v101;
Tern(v101,v102,Tern(v2,v101,v3))=Tern(v2,v101,Tern(v101,v102,v3)) by A45;
hence thesis by A729;
end;
A848: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v3))=Tern(v2,v3,v0)
proof let v0,v1,v4,v3,v2;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A845;
end;
A850: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v3))=Tern(v0,v2,v3)
proof let v0,v1,v4,v3,v2;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A848;
end;
A853: for v100,v1,v102,v2,v101 holds
Tern(v100,Tern(v101,v1,Tern(v101,v2,v102)),Tern(v101,v102,v100))=
Tern(v101,v102
,v100)
proof let v100,v1,v102,v2,v101;
Tern(v101,v1,Tern(v101,v2,v102))=Tern(v101,v102,Tern(v101,v1,v2)) by A55;
hence thesis by A729;
end;
A856: for v0,v2,v4,v3,v1 holds
Tern(v0,Tern(v1,v2,Tern(v1,v3,v4)),Tern(v0,v1,v4))=Tern(v1,v4,v0)
proof let v0,v2,v4,v3,v1;
Tern(v1,v4,v0)=Tern(v0,v1,v4) by A3;
hence thesis by A853;
end;
A858: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v0,v4,Tern(v1,v2,Tern(v1,v3,v4))))=Tern(v1,v4,v0)
proof let v0,v2,v4,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,v4)),Tern(v0,v1,v4))=
Tern(v0,v1,Tern(v0,v4,Tern(v1,v2,Tern(v1,v3
,v4)))) by A492;
hence thesis by A856;
end;
A861: for v0,v3,v2,v4,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v3,Tern(v1,v4,v2))))=Tern(v0,v1,v2)
proof let v0,v3,v2,v4,v1;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A858;
end;
A864: for v100,v2,v102,v3,v101 holds
Tern(v100,Tern(v2,v101,Tern(v101,v3,v102)),Tern(v101,v102,v100))=
Tern(v101,v102
,v100)
proof let v100,v2,v102,v3,v101;
Tern(v101,v102,Tern(v2,v101,v3))=Tern(v2,v101,Tern(v101,v3,v102)) by A134;
hence thesis by A729;
end;
A867: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4))=Tern(v2,v4,v0)
proof let v0,v1,v4,v3,v2;
Tern(v2,v4,v0)=Tern(v0,v2,v4) by A3;
hence thesis by A864;
end;
A869: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4))=Tern(v0,v2,v4)
proof let v0,v1,v4,v3,v2;
Tern(v2,v4,v0)=Tern(v0,v2,v4) by A3;
hence thesis by A867;
end;
A872: for v102,v100,v3,v2,v1 holds
Tern(v100,Tern(v1,v2,v3),Tern(v100,v102,Tern(v1,v2,v102)))=
Tern(v100,v102,Tern(v1,v2
,v3))
proof let v102,v100,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v1,v2,v102))=Tern(v1,v2,v102) by A729;
hence thesis by A594;
end;
A876: for v103,v102,v3,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v1,v2,v102),Tern(v102,Tern(v1,v2,v3),v103))=
Tern(Tern(v1,v2,v3)
,v103,Tern(v1,v2,v102))
proof let v103,v102,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v1,v2,v102))=Tern(v1,v2,v102) by A729;
hence thesis by A670;
end;
A879: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(Tern(v0,v1,v2),v4,Tern(v0
,v1,v3))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),v4)=Tern(v3,v4,Tern(v0,v1,v2)) by A4;
hence thesis by A876;
end;
A881: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(v4,Tern(v0,v1,v3),Tern(v0
,v1,v2))
proof let v3,v4,v2,v1,v0;
Tern(v4,Tern(v0,v1,v3),Tern(v0,v1,v2))=
Tern(Tern(v0,v1,v2),v4,Tern(v0,v1,v3)) by A3;
hence thesis by A879;
end;
A884: for v100,v101,v3,v2,v1 holds
Tern(v100,Tern(v1,v2,v101),Tern(v101,Tern(v1,v2,v3),v100))=
Tern(v101,Tern(v1,v2,v3)
,v100)
proof let v100,v101,v3,v2,v1;
Tern(v101,Tern(v1,v2,v3),Tern(v1,v2,v101))=Tern(v1,v2,v101) by A729;
hence thesis by A729;
end;
A887: for v0,v3,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v1,v2,v4)))=Tern(v3,Tern(v1,v2,v4),v0)
proof let v0,v3,v4,v2,v1;
Tern(v3,Tern(v1,v2,v4),v0)=Tern(v0,v3,Tern(v1,v2,v4)) by A3;
hence thesis by A884;
end;
A889: for v0,v3,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v1,v2,v4)))=Tern(v0,v3,Tern(v1,v2,v4))
proof let v0,v3,v4,v2,v1;
Tern(v3,Tern(v1,v2,v4),v0)=Tern(v0,v3,Tern(v1,v2,v4)) by A3;
hence thesis by A887;
end;
A892: for v100,v102,v3,v2 holds
Tern(v100,Tern(v2,v3,v102),v102)=Tern(v3,v102,Tern(v2,v102,v100))
proof let v100,v102,v3,v2;
Tern(v102,v100,Tern(v2,v3,v102))=Tern(v3,v102,Tern(v2,v102,v100)) by A739;
hence thesis by A3;
end;
A895: for v0,v3,v2,v1 holds
Tern(v0,v3,Tern(v1,v2,v3))=Tern(v2,v3,Tern(v1,v3,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v3)=Tern(v0,v3,Tern(v1,v2,v3)) by A4;
hence thesis by A892;
end;
A898: for v0,v1,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v1))=Tern(v3,v1,Tern(v0,v2,v1))
proof let v0,v1,v3,v2;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A895;
end;
A901: for v101,v103,v2,v102 holds
Tern(Tern(v102,v2,v103),v101,Tern(v102,v2,v103))=
Tern(v103,Tern(v102,v2,v103),Tern(v102
,Tern(v102,v2,v103),v101))
proof let v101,v103,v2,v102;
Tern(v102,v103,Tern(v102,v2,v103))=Tern(v102,v2,v103) by A63;
hence thesis by A739;
end;
A904: for v3,v2,v1,v0 holds
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v2))=
Tern(v2,Tern(v0,v1,v2),Tern(v0,Tern(v0,v1,v2),v3))
proof let v3,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v2))=
Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,v2)) by A3;
hence thesis by A901;
end;
A907: for v0,v3,v2,v1 holds
Tern(v1,v2,v3)=Tern(v3,Tern(v1,v2,v3),Tern(v1,Tern(v1,v2,v3),v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v3))=Tern(v1,v2,v3) by A34;
hence thesis by A904;
end;
A910: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v2,Tern(v0,v1,v2),Tern(v0,v3,Tern(v0,v1,v2)))
proof let v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),v3)=Tern(v0,v3,Tern(v0,v1,v2)) by A4;
hence thesis by A907;
end;
A915: for v103,v100,v102,v3,v2 holds
Tern(v100,Tern(v2,v3,v102),Tern(v102,v100,v103))=
Tern(v100,v103,Tern(v3,v102,Tern(v2
,v102,v100)))
proof let v103,v100,v102,v3,v2;
Tern(v102,v100,Tern(v2,v3,v102))=Tern(v3,v102,Tern(v2,v102,v100)) by A739;
hence thesis by A670;
end;
A918: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v4,v3))=Tern(v0,v4,Tern(v2,v3,Tern(v1,v3,v0)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v3)=Tern(v3,v0,v4) by A3;
hence thesis by A915;
end;
A920: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,v4))=Tern(v0,v4,Tern(v2,v3,Tern(v1,v3,v0)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v3)=Tern(v0,v3,v4) by A4;
hence thesis by A918;
end;
A922: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,v4))=Tern(v0,v4,Tern(v2,v3,Tern(v0,v1,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v1,v3,v0)=Tern(v0,v1,v3) by A3;
hence thesis by A920;
end;
A925: for v3,v2,v100,v1 holds
Tern(v1,v100,v2)=Tern(v100,Tern(v1,v100,v2),Tern(v1,v2,v3))
proof let v3,v2,v100,v1;
Tern(v100,Tern(v1,v2,v3),Tern(v1,v100,v2))=Tern(v1,v100,v2) by A807;
hence thesis by A4;
end;
A931: for v100,v103,v2,v3,v1,v101 holds
Tern(v100,Tern(v101,Tern(v1,v2,Tern(v101,v1,v3)),v103),
Tern(v101,v100,Tern(v1,v2,Tern(v101
,v1,v3))))=Tern(v101,Tern(v1,v2,v3),Tern(v101,v100,v1))
proof let v100,v103,v2,v3,v1,v101;
Tern(v101,Tern(v1,v2,v3),Tern(v101,v100,v1))=
Tern(v101,v100,Tern(v1,v2,Tern(v101,v1
,v3))) by A149;
hence thesis by A807;
end;
A934: for v0,v5,v3,v4,v2,v1 holds
Tern(v0,Tern(v1,v5,Tern(v2,v3,Tern(v1,v2,v4))),
Tern(v1,v0,Tern(v2,v3,Tern(v1,v2
,v4))))=Tern(v1,Tern(v2,v3,v4),Tern(v1,v0,v2))
proof let v0,v5,v3,v4,v2,v1;
Tern(v1,Tern(v2,v3,Tern(v1,v2,v4)),v5)=
Tern(v1,v5,Tern(v2,v3,Tern(v1,v2,v4))) by A4;
hence thesis by A931;
end;
A937: for v0,v2,v4,v5,v3,v1 holds
Tern(v0,Tern(v1,v2,Tern(v3,v4,Tern(v1,v3,v5))),
Tern(v0,Tern(v3,v4,Tern(v1,v3,v5))
,v1))=Tern(v1,Tern(v3,v4,v5),Tern(v1,v0,v3))
proof let v0,v2,v4,v5,v3,v1;
Tern(v0,Tern(v3,v4,Tern(v1,v3,v5)),v1)=
Tern(v1,v0,Tern(v3,v4,Tern(v1,v3,v5))) by A3;
hence thesis by A934;
end;
A939: for v0,v2,v4,v5,v3,v1 holds
Tern(v0,Tern(v1,v2,Tern(v3,v4,Tern(v1,v3,v5))),
Tern(v0,v1,Tern(v3,v4,Tern(v1,v3
,v5))))=Tern(v1,Tern(v3,v4,v5),Tern(v1,v0,v3))
proof let v0,v2,v4,v5,v3,v1;
Tern(v0,Tern(v3,v4,Tern(v1,v3,v5)),v1)=
Tern(v0,v1,Tern(v3,v4,Tern(v1,v3,v5))) by A4;
hence thesis by A937;
end;
A941: for v2,v0,v4,v5,v3,v1 holds
Tern(v0,v1,Tern(v0,Tern(v3,v4,Tern(v1,v3,v5)),Tern(v1,v2,Tern(v3,v4,Tern(v1,v3
,v5)))))=Tern(v1,Tern(v3,v4,v5),Tern(v1,v0,v3))
proof let v2,v0,v4,v5,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v3,v4,Tern(v1,v3,v5))),
Tern(v0,v1,Tern(v3,v4,Tern(v1,v3,v5))))=Tern(v0
,v1,Tern(v0,Tern(v3,v4,Tern(v1,v3,v5)),Tern(v1,v2,Tern(v3,v4,
Tern(v1,v3,v5))))) by A492;
hence thesis by A939;
end;
A944: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))=Tern(v1,Tern(v2,v3,v4),Tern(v1,v0,v2))
proof
now let v5,v0,v3,v4,v2,v1;
Tern(v0,v1,Tern(v0,Tern(v2,v3,Tern(v1,v2,v4)),
Tern(v1,v5,Tern(v2,v3,Tern(v1,v2,v4)))))=Tern(v0
,v1,Tern(v2,v3,Tern(v1,v2,v4))) by A836;
hence Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))=
Tern(v1,Tern(v2,v3,v4),Tern(v1,v0,v2)) by
A941;
end;
hence thesis;
end;
A946: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))=Tern(v1,Tern(v2,v3,v4),Tern(v0,v2,v1))
proof let v0,v3,v4,v2,v1;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A944;
end;
A948: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))=Tern(v1,Tern(v2,v3,v4),Tern(v0,v1,v2))
proof let v0,v3,v4,v2,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A946;
end;
A953: for v102,v3,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v102,v2,v3),v102)=Tern(v102,v2,v3)
proof let v102,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v102,v2,v3))=Tern(v102,v2,v3) by A822;
hence thesis by A3;
end;
A956: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v2,v3,v1),v3)=Tern(v3,v1,v2)
proof let v3,v2,v1,v0;
Tern(v3,v1,v2)=Tern(v2,v3,v1) by A3;
hence thesis by A953;
end;
A958: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),v3)=Tern(v3,v1,v2)
proof let v3,v2,v1,v0;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A956;
end;
A960: for v3,v2,v1,v0 holds
Tern(v3,Tern(v0,v1,v2),Tern(v1,v2,v3))=Tern(v3,v1,v2)
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),v3)=
Tern(v3,Tern(v0,v1,v2),Tern(v1,v2,v3)) by A3;
hence thesis by A958;
end;
A963: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,v0))=Tern(v3,v0,v2)
proof let v0,v3,v2,v1;
Tern(v0,v2,v3)=Tern(v3,v0,v2) by A3;
hence thesis by A960;
end;
A965: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,v0))=Tern(v2,v3,v0)
proof let v0,v3,v2,v1;
Tern(v3,v0,v2)=Tern(v2,v3,v0) by A3;
hence thesis by A963;
end;
A968: for v103,v100,v102,v104,v1 holds
Tern(v100,Tern(v1,v104,v102),Tern(v100,v102,Tern(v100,v103,v104)))=
Tern(v100,v103
,Tern(v100,v104,v102))
proof let v103,v100,v102,v104,v1;
Tern(v100,Tern(v1,v104,v102),Tern(v100,v104,v102))=
Tern(v100,v104,v102) by A822;
hence thesis by A139;
end;
A971: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v0,v2,v4)))=Tern(v0,v4,Tern(v0,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v2)=Tern(v0,v2,v4) by A4;
hence thesis by A968;
end;
A974: for v100,v1,v3,v2,v101 holds
Tern(v100,Tern(v1,v101,Tern(v101,v2,v3)),Tern(v100,Tern(v1,v101,v2),
Tern(v101,v2
,v3)))=Tern(v100,Tern(v1,v101,v2),Tern(v101,v2,v3))
proof let v100,v1,v3,v2,v101;
Tern(v101,Tern(v1,v101,v2),Tern(v101,v2,v3))=
Tern(v1,v101,Tern(v101,v2,v3)) by A517;
hence thesis by A822;
end;
A978: for v102,v100,v3,v2,v1 holds
Tern(v100,Tern(v1,v2,v3),Tern(v100,v102,Tern(v102,v2,v3)))=
Tern(v100,v102,Tern(v1,v2
,v3))
proof let v102,v100,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v102,v2,v3))=Tern(v102,v2,v3) by A822;
hence thesis by A594;
end;
A981: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v4,Tern(v3,v4,v2)))=Tern(v0,v4,Tern(v1,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v4,v2,v3)=Tern(v3,v4,v2) by A3;
hence thesis by A978;
end;
A983: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v4,Tern(v2,v3,v4)))=Tern(v0,v4,Tern(v1,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v3,v4,v2)=Tern(v2,v3,v4) by A3;
hence thesis by A981;
end;
A986: for v103,v102,v3,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v102,v2,v3),Tern(v102,Tern(v1,v2,v3),v103))=
Tern(Tern(v1,v2,v3)
,v103,Tern(v102,v2,v3))
proof let v103,v102,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v102,v2,v3))=Tern(v102,v2,v3) by A822;
hence thesis by A670;
end;
A989: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v2,v3,v1),Tern(v3,Tern(v0,v1,v2),v4))=
Tern(Tern(v0,v1,v2),v4,Tern(v3
,v1,v2))
proof let v4,v3,v2,v1,v0;
Tern(v3,v1,v2)=Tern(v2,v3,v1) by A3;
hence thesis by A986;
end;
A991: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v3,Tern(v0,v1,v2),v4))=
Tern(Tern(v0,v1,v2),v4,Tern(v3
,v1,v2))
proof let v4,v3,v2,v1,v0;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A989;
end;
A993: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(Tern(v0,v1,v2),v4,Tern(v3
,v1,v2))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),v4)=Tern(v3,v4,Tern(v0,v1,v2)) by A4;
hence thesis by A991;
end;
A995: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(Tern(v0,v1,v2),v4,Tern(v2
,v3,v1))
proof let v3,v4,v2,v1,v0;
Tern(v3,v1,v2)=Tern(v2,v3,v1) by A3;
hence thesis by A993;
end;
A997: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(Tern(v0,v1,v2),v4,Tern(v1
,v2,v3))
proof let v3,v4,v2,v1,v0;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A995;
end;
A999: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v3,v4,Tern(v0,v1,v2)))=
Tern(v4,Tern(v1,v2,v3),Tern(v0
,v1,v2))
proof let v3,v4,v2,v1,v0;
Tern(v4,Tern(v1,v2,v3),Tern(v0,v1,v2))=
Tern(Tern(v0,v1,v2),v4,Tern(v1,v2,v3)) by A3;
hence thesis by A997;
end;
A1002: for v100,v101,v3,v2,v1 holds
Tern(v100,Tern(v101,v2,v3),Tern(v101,Tern(v1,v2,v3),v100))=
Tern(v101,Tern(v1,v2,v3)
,v100)
proof let v100,v101,v3,v2,v1;
Tern(v101,Tern(v1,v2,v3),Tern(v101,v2,v3))=Tern(v101,v2,v3) by A822;
hence thesis by A729;
end;
A1005: for v0,v1,v2,v4,v3 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,Tern(v3,v4,v2),v0))=Tern(v1,Tern(v4,v2,v3),v0)
proof let v0,v1,v2,v4,v3;
Tern(v4,v2,v3)=Tern(v3,v4,v2) by A3;
hence thesis by A1002;
end;
A1007: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,Tern(v2,v3,v4),v0))=Tern(v1,Tern(v4,v2,v3),v0)
proof let v0,v1,v4,v3,v2;
Tern(v3,v4,v2)=Tern(v2,v3,v4) by A3;
hence thesis by A1005;
end;
A1009: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,v4)))=Tern(v1,Tern(v4,v2,v3),v0)
proof let v0,v1,v4,v3,v2;
Tern(v1,Tern(v2,v3,v4),v0)=Tern(v0,v1,Tern(v2,v3,v4)) by A3;
hence thesis by A1007;
end;
A1011: for v1,v0,v4,v3,v2 holds
Tern(v0,v1,Tern(v0,Tern(v2,v3,v4),Tern(v1,v2,v3)))=Tern(v1,Tern(v4,v2,v3),v0)
proof let v1,v0,v4,v3,v2;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,v4)))=
Tern(v0,v1,Tern(v0,Tern(v2,v3,v4),Tern(v1
,v2,v3))) by A492;
hence thesis by A1009;
end;
A1013: for v1,v0,v4,v3,v2 holds
Tern(v0,v1,Tern(v0,Tern(v2,v3,v4),Tern(v1,v2,v3)))=Tern(v1,Tern(v3,v4,v2),v0)
proof let v1,v0,v4,v3,v2;
Tern(v4,v2,v3)=Tern(v3,v4,v2) by A3;
hence thesis by A1011;
end;
A1015: for v1,v0,v4,v3,v2 holds
Tern(v0,v1,Tern(v0,Tern(v2,v3,v4),Tern(v1,v2,v3)))=Tern(v1,Tern(v2,v3,v4),v0)
proof let v1,v0,v4,v3,v2;
Tern(v3,v4,v2)=Tern(v2,v3,v4) by A3;
hence thesis by A1013;
end;
A1017: for v1,v0,v4,v3,v2 holds
Tern(v0,v1,Tern(v0,Tern(v2,v3,v4),Tern(v1,v2,v3)))=Tern(v0,v1,Tern(v2,v3,v4))
proof let v1,v0,v4,v3,v2;
Tern(v1,Tern(v2,v3,v4),v0)=Tern(v0,v1,Tern(v2,v3,v4)) by A3;
hence thesis by A1015;
end;
A1020: for v100,v2,v3,v102,v101 holds
Tern(v100,Tern(v101,v102,v100),Tern(v101,v2,Tern(v101,v102,v3)))=
Tern(v101,v102
,v100)
proof let v100,v2,v3,v102,v101;
Tern(v101,v102,Tern(v101,v2,v3))=Tern(v101,v2,Tern(v101,v102,v3)) by A27;
hence thesis by A839;
end;
A1023: for v0,v3,v4,v2,v1 holds
Tern(v0,Tern(v0,v1,v2),Tern(v1,v3,Tern(v1,v2,v4)))=Tern(v1,v2,v0)
proof let v0,v3,v4,v2,v1;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A1020;
end;
A1025: for v0,v3,v4,v2,v1 holds
Tern(v0,Tern(v0,v1,v2),Tern(v1,v3,Tern(v1,v2,v4)))=Tern(v0,v1,v2)
proof let v0,v3,v4,v2,v1;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A1023;
end;
A1028: for v100,v103,v102,v3,v2 holds
Tern(v100,Tern(v2,v3,v102),Tern(v100,v102,Tern(v102,Tern(v2,v3,v102),v103)))
=Tern(v3
,v102,Tern(v100,v2,v102))
proof let v100,v103,v102,v3,v2;
Tern(v100,v102,Tern(v2,v3,v102))=Tern(v3,v102,Tern(v100,v2,v102)) by A898;
hence thesis by A594;
end;
A1031: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v3,v4,Tern(v1,v2,v3))))=
Tern(v2,v3,Tern(v0,v1,v3))
proof let v0,v4,v3,v2,v1;
Tern(v3,Tern(v1,v2,v3),v4)=Tern(v3,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A1028;
end;
A1033: for v1,v3,v2,v0 holds Tern(v1,v3,Tern(v0,v2,v3))=Tern(v2,v3,Tern(v0,v1,
v3))
proof
now let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v3,v4,Tern(v1,v2,v3))))=
Tern(v1,v3,Tern(v0,v2,v3))
by A815;
hence Tern(v1,v3,Tern(v0,v2,v3))=Tern(v2,v3,Tern(v0,v1,v3)) by A1031;
end;
hence thesis;
end;
A1037: for v100,v101,v3,v2,v1 holds
Tern(v100,v101,Tern(v101,Tern(v1,v2,v3),Tern(v1,v2,v100)))=
Tern(v100,v101,Tern(v1,v2
,v3))
proof let v100,v101,v3,v2,v1;
Tern(v100,Tern(v1,v2,v3),Tern(v1,v2,v100))=Tern(v1,v2,v100) by A729;
hence thesis by A608;
end;
A1040: for v0,v1,v4,v3,v2 holds
Tern(v0,v1,Tern(v1,Tern(v2,v3,v4),Tern(v0,v2,v3)))=Tern(v0,v1,Tern(v2,v3,v4))
proof let v0,v1,v4,v3,v2;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A1037;
end;
A1043: for v100,v102,v5,v4,v103 holds
Tern(v100,Tern(v102,v103,Tern(v103,v4,v5)),Tern(v102,v103,v100))=Tern(v102,
v103
,Tern(v102,v100,Tern(v103,v4,Tern(v103,v100,v5))))
proof let v100,v102,v5,v4,v103;
Tern(v102,v100,Tern(v103,v100,Tern(v102,v103,Tern(v103,v4,v5))))=Tern(v102,v103
,Tern(v102,v100,Tern(v103,v4,Tern(v103,v100,v5)))) by A186;
hence thesis by A708;
end;
A1046: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v1,v2))=Tern(v1,v2,Tern(v1,v0,Tern(
v2,v3,Tern(v2
,v0,v4))))
proof let v0,v1,v4,v3,v2;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A1043;
end;
A1048: for v0,v1,v4,v3,v2 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,Tern(v2,v3,v4))))=Tern(v1,v2,Tern(v1,v0,Tern(
v2,v3,Tern(v2
,v0,v4))))
proof let v0,v1,v4,v3,v2;
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v1,v2))=Tern(v0,v1,Tern(v0,v2,Tern(
v1,v2,Tern(v2,v3
,v4)))) by A492;
hence thesis by A1046;
end;
A1050: for v1,v3,v4,v0,v2 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v1,v0,Tern(v2,v3,Tern(v2,v0,v4))))
proof let v1,v3,v4,v0,v2;
Tern(v0,v1,Tern(v0,v2,Tern(v1,v2,Tern(v2,v3,v4))))=Tern(v0,v1,v2) by A616;
hence thesis by A1048;
end;
A1052: for v1,v3,v2,v4,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v1,v0,Tern(v2,v3,Tern(v0,v4,v2))))
proof let v1,v3,v2,v4,v0;
Tern(v0,v4,v2)=Tern(v2,v0,v4) by A3;
hence thesis by A1050;
end;
A1054: for v1,v3,v4,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v1,v0,Tern(v2,v3,Tern(v0,v2,v4))))
proof let v1,v3,v4,v2,v0;
Tern(v0,v4,v2)=Tern(v0,v2,v4) by A4;
hence thesis by A1052;
end;
A1056: for v1,v3,v4,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v0,Tern(v2,v3,Tern(v0,v2,v4)),v1))
proof let v1,v3,v4,v2,v0;
Tern(v0,Tern(v2,v3,Tern(v0,v2,v4)),v1)=Tern(v1,v0,Tern(v2,v3,Tern(v0,v2,v4)))
by A3;
hence thesis by A1054;
end;
A1058: for v1,v3,v4,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,v2,Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4))))
proof let v1,v3,v4,v2,v0;
Tern(v0,Tern(v2,v3,Tern(v0,v2,v4)),v1)=Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4)))
by A4;
hence thesis by A1056;
end;
A1063: for v101,v103,v102,v1 holds
Tern(Tern(v1,v102,v103),v101,Tern(v1,v102,Tern(v102,v101,v103)))=
Tern(v102,Tern(v1,v102
,v103),v101)
proof let v101,v103,v102,v1;
Tern(v102,Tern(v1,v102,v103),Tern(v102,v101,v103))=Tern(v1,v102,Tern(v102,v101
,v103)) by A504;
hence thesis by A697;
end;
A1066: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,Tern(v1,v2,v3)))=Tern(v1,Tern(v0,v1,v2),v3)
proof let v3,v2,v1,v0;
Tern(v1,v3,v2)=Tern(v1,v2,v3) by A4;
hence thesis by A1063;
end;
A1068: for v0,v3,v2,v1 holds
Tern(v3,Tern(v0,v1,Tern(v1,v2,v3)),Tern(v0,v1,v2))=Tern(v1,Tern(v0,v1,v2),v3)
proof let v0,v3,v2,v1;
Tern(v3,Tern(v0,v1,Tern(v1,v2,v3)),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v3,Tern(
v0,v1,Tern(v1
,v2,v3))) by A3;
hence thesis by A1066;
end;
A1071: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,Tern(v2,v3,v0)))=Tern(v2,Tern(v1,v2,v3),v0)
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,Tern(v2,v3,v0)),Tern(v1,v2,v3))=Tern(v0,Tern(v1,v2,v3),Tern(
v1,v2,Tern(v2
,v3,v0))) by A4;
hence thesis by A1068;
end;
A1073: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,Tern(v2,v3,v0)))=Tern(v2,v0,Tern(v1,v2,v3))
proof let v0,v3,v2,v1;
Tern(v2,Tern(v1,v2,v3),v0)=Tern(v2,v0,Tern(v1,v2,v3)) by A4;
hence thesis by A1071;
end;
A1076: for v101,v100,v102,v5,v4,v3 holds
Tern(v100,v3,Tern(v100,v101,Tern(v100,v102,Tern(v3,v4,v5))))=Tern(v100,Tern(v3
,v4
,Tern(v100,v3,v5)),Tern(v100,v101,v102))
proof let v101,v100,v102,v5,v4,v3;
Tern(v100,v101,Tern(v100,v102,Tern(v3,v4,Tern(v100,v3,v5))))=Tern(v100,v3,Tern(
v100,v101
,Tern(v100,v102,Tern(v3,v4,v5)))) by A189;
hence thesis by A55;
end;
A1082: for v100,v1,v4,v101,v103 holds
Tern(v100,v101,Tern(v100,Tern(v1,v103,Tern(v103,v101,v4)),Tern(v100,v103
,v101)))=Tern(v100,v103,v101)
proof let v100,v1,v4,v101,v103;
Tern(v100,Tern(v1,v103,Tern(v103,v101,v4)),Tern(v100,v103,v101))=Tern(v100,v103
,v101) by A850;
hence thesis by A78;
end;
A1085: for v0,v2,v3,v4,v1 holds
Tern(v0,v1,Tern(v0,Tern(v2,v3,Tern(v1,v4,v3)),Tern(v0,v3,v1)))=Tern(v0,v3,v1)
proof let v0,v2,v3,v4,v1;
Tern(v1,v4,v3)=Tern(v3,v1,v4) by A3;
hence thesis by A1082;
end;
A1087: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v0,Tern(v2,v3,Tern(v1,v3,v4)),Tern(v0,v3,v1)))=Tern(v0,v3,v1)
proof let v0,v2,v4,v3,v1;
Tern(v1,v4,v3)=Tern(v1,v3,v4) by A4;
hence thesis by A1085;
end;
A1089: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v0,Tern(v2,v3,Tern(v1,v3,v4)),Tern(v0,v1,v3)))=Tern(v0,v3,v1)
proof let v0,v2,v4,v3,v1;
Tern(v0,v3,v1)=Tern(v0,v1,v3) by A4;
hence thesis by A1087;
end;
A1091: for v0,v2,v4,v3,v1 holds
Tern(v0,Tern(v2,v3,Tern(v1,v3,v4)),Tern(v0,v1,v3))=Tern(v0,v3,v1)
proof let v0,v2,v4,v3,v1;
Tern(v0,v1,Tern(v0,Tern(v2,v3,Tern(v1,v3,v4)),Tern(v0,v1,v3)))=Tern(v0,Tern(v2,
v3,Tern(v1,v3
,v4)),Tern(v0,v1,v3)) by A89;
hence thesis by A1089;
end;
A1094: for v0,v1,v4,v2,v3 holds
Tern(v0,Tern(v1,v2,Tern(v3,v2,v4)),Tern(v0,v3,v2))=Tern(v0,v3,v2)
proof let v0,v1,v4,v2,v3;
Tern(v0,v2,v3)=Tern(v0,v3,v2) by A4;
hence thesis by A1091;
end;
A1097: for v103,v104,v2,v3,v101,v100 holds
Tern(v100,Tern(v2,v101,Tern(v100,v101,v3)),Tern(v100,v103,v104))=Tern(v100,
v101
,Tern(v100,v103,Tern(v100,v104,Tern(v2,v101,v3))))
proof let v103,v104,v2,v3,v101,v100;
Tern(v100,v101,Tern(v2,v101,v3))=Tern(v2,v101,Tern(v100,v101,v3)) by A100;
hence thesis by A193;
end;
A1101: for v3,v2,v103,v101 holds
Tern(Tern(v3,v103,v2),Tern(v101,Tern(v101,v103,v2),Tern(v3,v103,v2)),Tern(v101
,v103
,v2))=Tern(v101,Tern(v101,v103,v2),Tern(v3,v103,v2))
proof let v3,v2,v103,v101;
Tern(v101,v103,Tern(v101,Tern(v101,v103,v2),Tern(v3,v103,v2)))=Tern(v101,v103,
v2) by
A771;
hence thesis by A910;
end;
A1104: for v0,v1,v3,v2 holds
Tern(Tern(v0,v1,v2),Tern(v3,Tern(v2,v3,v1),Tern(v0,v1,v2)),Tern(v3,v1,v2))=
Tern(v3,Tern(v3,v1
,v2),Tern(v0,v1,v2))
proof let v0,v1,v3,v2;
Tern(v3,v1,v2)=Tern(v2,v3,v1) by A3;
hence thesis by A1101;
end;
A1106: for v0,v3,v2,v1 holds
Tern(Tern(v0,v1,v2),Tern(v3,Tern(v1,v2,v3),Tern(v0,v1,v2)),Tern(v3,v1,v2))=
Tern(v3,Tern(v3,v1
,v2),Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A1104;
end;
A1108: for v0,v3,v2,v1 holds
Tern(Tern(v0,v1,v2),Tern(v3,Tern(v1,v2,v3),Tern(v0,v1,v2)),Tern(v2,v3,v1))=
Tern(v3,Tern(v3,v1
,v2),Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v3,v1,v2)=Tern(v2,v3,v1) by A3;
hence thesis by A1106;
end;
A1110: for v0,v3,v2,v1 holds
Tern(Tern(v0,v1,v2),Tern(v3,Tern(v1,v2,v3),Tern(v0,v1,v2)),Tern(v1,v2,v3))=
Tern(v3,Tern(v3,v1
,v2),Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A1108;
end;
A1112: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v3,Tern(v1,v2,v3),Tern(v0,v1,v2)))=
Tern(v3,Tern(v3,v1
,v2),Tern(v0,v1,v2))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v3,Tern(v1,v2,v3),Tern(v0,v1,v2)),Tern(v1,v2,v3))=Tern
(Tern(v0,v1,v2)
,Tern(v1,v2,v3),Tern(v3,Tern(v1,v2,v3),Tern(v0,v1,v2))) by A4;
hence thesis by A1110;
end;
A1114: for v0,v3,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v1,v2,v3),Tern(v0,v1,v2))=Tern(v3,Tern(v3,v1,v2),Tern
(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v3,Tern(v1,v2,v3),Tern(v0,v1,v2)))=Tern
(Tern(v1,v2,v3)
,Tern(v1,v2,v3),Tern(v0,v1,v2)) by A999;
hence thesis by A1112;
end;
A1117: for v3,v1,v0,v2 holds Tern(v0,v1,v2)=Tern(v2,Tern(v2,v0,v1),Tern(v3,v0,
v1))
proof let v3,v1,v0,v2;
Tern(Tern(v0,v1,v2),Tern(v0,v1,v2),Tern(v3,v0,v1))=Tern(v0,v1,v2) by A2;
hence thesis by A1114;
end;
A1119: for v3,v0,v2,v1 holds Tern(v0,v1,v2)=Tern(v2,Tern(v1,v2,v0),Tern(v3,v0,
v1))
proof let v3,v0,v2,v1;
Tern(v2,v0,v1)=Tern(v1,v2,v0) by A3;
hence thesis by A1117;
end;
A1121: for v3,v2,v1,v0 holds Tern(v0,v1,v2)=Tern(v2,Tern(v0,v1,v2),Tern(v3,v0,
v1))
proof let v3,v2,v1,v0;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A1119;
end;
A1126: for v4,v2,v100,v102 holds
Tern(v100,Tern(v102,v100,v2),Tern(v102,v100,v2))=Tern(v102,Tern(v102,v100,v2),
Tern(v100
,Tern(v102,v100,v2),Tern(v100,v2,v4)))
proof let v4,v2,v100,v102;
Tern(v102,Tern(v102,v100,v2),Tern(v100,Tern(v102,v100,v2),Tern(v100,v2,v4)))=
Tern(v102
,v100,v2) by A1025;
hence thesis by A311;
end;
A1129: for v3,v2,v0,v1 holds
Tern(v0,Tern(v0,v2,v1),Tern(v1,v0,v2))=Tern(v1,Tern(v1,v0,v2),Tern(v0,Tern(v1,
v0,v2),Tern(v0
,v2,v3)))
proof let v3,v2,v0,v1;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A1126;
end;
A1132: for v3,v1,v0,v2 holds
Tern(v0,Tern(v0,v2,v1),Tern(v2,v0,v1))=Tern(v2,Tern(v2,v0,v1),Tern(v0,Tern(v2,
v0,v1),Tern(v0
,v1,v3)))
proof let v3,v1,v0,v2;
Tern(v0,v1,v2)=Tern(v0,v2,v1) by A4;
hence thesis by A1129;
end;
A1135: for v3,v2,v0,v1 holds
Tern(v0,Tern(v0,v1,v2),Tern(v0,v2,v1))=Tern(v1,Tern(v1,v0,v2),Tern(v0,Tern(v1,
v0,v2),Tern(v0
,v2,v3)))
proof let v3,v2,v0,v1;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A1132;
end;
A1137: for v3,v2,v0,v1 holds
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2))=Tern(v1,Tern(v1,v0,v2),Tern(v0,Tern(v1,
v0,v2),Tern(v0
,v2,v3)))
proof let v3,v2,v0,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A1135;
end;
A1139: for v3,v2,v0,v1 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v1,v0,v2),Tern(v0,Tern(v1,v0,v2),Tern(v0,v2,v3)))
proof let v3,v2,v0,v1;
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2))=Tern(v0,v1,v2) by A34;
hence thesis by A1137;
end;
A1141: for v3,v2,v0,v1 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v2,v1),Tern(v0,Tern(v1,v0,v2),Tern(v0,v2,v3)))
proof let v3,v2,v0,v1;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A1139;
end;
A1143: for v3,v2,v0,v1 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v1,v2),Tern(v0,Tern(v1,v0,v2),Tern(v0,v2,v3)))
proof let v3,v2,v0,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A1141;
end;
A1145: for v3,v1,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v1,v2),Tern(v0,Tern(v0,v2,v1),Tern(v0,v2,v3)))
proof let v3,v1,v2,v0;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A1143;
end;
A1147: for v3,v2,v1,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v1,v2),Tern(v0,Tern(v0,v1,v2),Tern(v0,v2,v3)))
proof let v3,v2,v1,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A1145;
end;
A1149: for v1,v2,v3,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v1,v2),Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v2))))
proof let v1,v2,v3,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v0,v2,v3))=Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v2)))
by A193;
hence thesis by A1147;
end;
A1151: for v1,v3,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v1,v2),Tern(v0,v1,Tern(v0,v2,Tern(v0,v2,v3))))
proof let v1,v3,v2,v0;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A1149;
end;
A1153: for v1,v3,v2,v0 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v1,v2),Tern(v0,v1,Tern(v0,v2,v3)))
proof let v1,v3,v2,v0;
Tern(v0,v2,Tern(v0,v2,v3))=Tern(v0,v2,v3) by A74;
hence thesis by A1151;
end;
A1158: for v101,v100,v3,v2,v1 holds
Tern(v100,Tern(v101,v100,Tern(v1,v2,v3)),Tern(v101,v100,Tern(v101,v2,v3)))=
Tern(v101
,v100,Tern(v1,v2,v3))
proof let v101,v100,v3,v2,v1;
Tern(v101,Tern(v1,v2,v3),Tern(v101,v2,v3))=Tern(v101,v2,v3) by A822;
hence thesis by A1153;
end;
A1161: for v1,v0,v4,v3,v2 holds
Tern(v0,Tern(v0,Tern(v2,v3,v4),v1),Tern(v1,v0,Tern(v1,v3,v4)))=Tern(v1,v0,Tern
(v2,v3,v4))
proof let v1,v0,v4,v3,v2;
Tern(v0,Tern(v2,v3,v4),v1)=Tern(v1,v0,Tern(v2,v3,v4)) by A3;
hence thesis by A1158;
end;
A1164: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v0,v4,Tern(v1,v2,v3)),Tern(v4,v0,Tern(v4,v2,v3)))=Tern(v4,v0,Tern
(v1,v2,v3))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v4)=Tern(v0,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A1161;
end;
A1167: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v0,v1,Tern(v2,v3,v4)),Tern(v0,Tern(v1,v3,v4),v1))=Tern(v1,v0,Tern
(v2,v3,v4))
proof let v0,v1,v4,v3,v2;
Tern(v0,Tern(v1,v3,v4),v1)=Tern(v1,v0,Tern(v1,v3,v4)) by A3;
hence thesis by A1164;
end;
A1169: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v0,v1,Tern(v2,v3,v4)),Tern(v0,v1,Tern(v1,v3,v4)))=Tern(v1,v0,Tern
(v2,v3,v4))
proof let v0,v1,v4,v3,v2;
Tern(v0,Tern(v1,v3,v4),v1)=Tern(v0,v1,Tern(v1,v3,v4)) by A4;
hence thesis by A1167;
end;
A1171: for v2,v0,v4,v3,v1 holds
Tern(v0,v1,Tern(v0,v1,Tern(v0,Tern(v1,v3,v4),Tern(v2,v3,v4))))=Tern(v1,v0,Tern
(v2,v3,v4))
proof let v2,v0,v4,v3,v1;
Tern(v0,Tern(v0,v1,Tern(v2,v3,v4)),Tern(v0,v1,Tern(v1,v3,v4)))=Tern(v0,v1,Tern(
v0,v1,Tern(v0
,Tern(v1,v3,v4),Tern(v2,v3,v4)))) by A193;
hence thesis by A1169;
end;
A1174: for v4,v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v4,v2,v3)))=Tern(v1,v0,Tern(v4,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v0,v1,Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v4,v2,v3))))=Tern(v0,v1,Tern(
v0,Tern(v1,v2
,v3),Tern(v4,v2,v3))) by A74;
hence thesis by A1171;
end;
A1176: for v4,v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v4,v2,v3)))=Tern(v0,Tern(v4,v2,v3),v1)
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v4,v2,v3),v1)=Tern(v1,v0,Tern(v4,v2,v3)) by A3;
hence thesis by A1174;
end;
A1178: for v4,v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v4,v2,v3)))=Tern(v0,v1,Tern(v4,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v4,v2,v3),v1)=Tern(v0,v1,Tern(v4,v2,v3)) by A4;
hence thesis by A1176;
end;
A1181: for v3,v4,v100,v101,v102 holds
Tern(v100,v101,Tern(v102,v3,Tern(v102,v4,Tern(v102,v101,v100))))=Tern(v102,
v100
,v101)
proof let v3,v4,v100,v101,v102;
Tern(v102,v101,Tern(v102,v100,Tern(v102,v3,v4)))=Tern(v102,v3,Tern(v102,v4,Tern
(v102
,v101,v100))) by A198;
hence thesis by A693;
end;
A1184: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v4,Tern(v0,v2,v1))))=Tern(v2,v0,v1)
proof let v3,v4,v1,v2,v0;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A1181;
end;
A1186: for v3,v4,v2,v1,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v4,Tern(v0,v1,v2))))=Tern(v2,v0,v1)
proof let v3,v4,v2,v1,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A1184;
end;
A1188: for v3,v4,v2,v1,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v4,Tern(v0,v1,v2))))=Tern(v1,v2,v0)
proof let v3,v4,v2,v1,v0;
Tern(v2,v0,v1)=Tern(v1,v2,v0) by A3;
hence thesis by A1186;
end;
A1190: for v3,v4,v2,v1,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v4,Tern(v0,v1,v2))))=Tern(v0,v1,v2)
proof let v3,v4,v2,v1,v0;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A1188;
end;
A1193: for v103,v104,v100,v1,v4,v3,v2 holds
Tern(v100,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v100,Tern(v100,v2,v4),Tern(Tern(v100
,v2,v4),v103
,Tern(Tern(v1,v2,Tern(v2,v3,v4)),Tern(v100,v2,v4),v104))))=Tern(v100,v2,v4)
proof let v103,v104,v100,v1,v4,v3,v2;
Tern(v100,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v100,v2,v4))=Tern(v100,v2,v4) by A869
;
hence thesis by A632;
end;
A1196: for v5,v0,v6,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,Tern(v0,v2,v4),Tern(Tern(v0,v2,v4),
v5,Tern(v6,Tern(v1
,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4)))))=Tern(v0,v2,v4)
proof let v5,v0,v6,v1,v4,v3,v2;
Tern(Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4),v6)=Tern(v6,Tern(v1,v2,Tern(v2,
v3,v4)),Tern(v0
,v2,v4)) by A3;
hence thesis by A1193;
end;
A1198: for v5,v0,v6,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,Tern(v0,v2,v4),Tern(v5,Tern(v6,Tern
(v1,v2,Tern(v2,v3
,v4)),Tern(v0,v2,v4)),Tern(v0,v2,v4))))=Tern(v0,v2,v4)
proof let v5,v0,v6,v1,v4,v3,v2;
Tern(v5,Tern(v6,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4)),Tern(v0,v2,v4))=Tern
(Tern(v0,v2,v4)
,v5,Tern(v6,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4))) by A3;
hence thesis by A1196;
end;
A1200: for v5,v0,v6,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,Tern(v0,v2,v4),Tern(v5,Tern(v0,v2,
v4),Tern(v6,Tern(v1
,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4)))))=Tern(v0,v2,v4)
proof let v5,v0,v6,v1,v4,v3,v2;
Tern(v5,Tern(v6,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4)),Tern(v0,v2,v4))=Tern
(v5,Tern(v0,v2
,v4),Tern(v6,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4))) by A4;
hence thesis by A1198;
end;
A1203: for v100,v3,v4,v101,v102 holds
Tern(v102,v100,v101)=Tern(v100,Tern(v101,v3,Tern(v102,v101,v4)),Tern(v102,v100
,v101))
proof let v100,v3,v4,v101,v102;
Tern(v100,v101,Tern(v102,v100,Tern(v101,v3,Tern(v102,v101,v4))))=Tern(v102,v100
,v101) by A1058;
hence thesis by A670;
end;
A1209: for v103,v3,v4,v2,v102,v101 holds
Tern(Tern(v2,v3,Tern(v2,v4,Tern(v101,v102,v2))),Tern(v101,v102,v103),Tern(v101
,v102
,Tern(v2,v3,Tern(v2,v4,Tern(v101,v102,v2)))))=Tern(v101,v102,v2)
proof let v103,v3,v4,v2,v102,v101;
Tern(v101,v102,Tern(v2,v3,Tern(v2,v4,Tern(v101,v102,v2))))=Tern(v101,v102,v2)
by
A1190;
hence thesis by A729;
end;
A1212: for v5,v1,v2,v4,v3,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v4))),Tern(v3,v4,v5),Tern(v3,v4,Tern(v0,
v1,Tern(v0,v2
,Tern(v3,v4,v0)))))=Tern(v3,v4,v0)
proof let v5,v1,v2,v4,v3,v0;
Tern(v3,v4,v0)=Tern(v0,v3,v4) by A3;
hence thesis by A1209;
end;
A1214: for v5,v1,v2,v4,v3,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v4))),Tern(v3,v4,v5),Tern(v3,v4,Tern(v0,
v1,Tern(v0,v2
,Tern(v0,v3,v4)))))=Tern(v3,v4,v0)
proof let v5,v1,v2,v4,v3,v0;
Tern(v3,v4,v0)=Tern(v0,v3,v4) by A3;
hence thesis by A1212;
end;
A1216: for v1,v2,v4,v3,v0 holds
Tern(v3,v4,Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v4))))=Tern(v3,v4,v0)
proof
now let v5,v1,v2,v4,v3,v0;
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v4))),Tern(v3,v4,v5),Tern(v3,v4,Tern(v0,
v1,Tern(v0,v2
,Tern(v0,v3,v4)))))=Tern(v3,v4,Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v4)))) by A729;
hence Tern(v3,v4,Tern(v0,v1,Tern(v0,v2,Tern(v0,v3,v4))))=Tern(v3,v4,v0) by
A1214;
end;
hence thesis;
end;
A1219: for v3,v4,v1,v0,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v4,Tern(v2,v0,v1))))=Tern(v2,v0,v1)
proof let v3,v4,v1,v0,v2;
Tern(v0,v1,v2)=Tern(v2,v0,v1) by A3;
hence thesis by A1216;
end;
A1222: for v101,v4,v102,v100 holds
Tern(v101,v100,Tern(v100,v101,Tern(v100,v102,v4)))=Tern(v100,Tern(v101,v100,v4
)
,Tern(v100,v101,v102))
proof let v101,v4,v102,v100;
Tern(v100,v101,Tern(v100,v102,Tern(v101,v100,v4)))=Tern(v101,v100,Tern(v100,
v101
,Tern(v100,v102,v4))) by A210;
hence thesis by A55;
end;
A1225: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),v1))=Tern(v1,Tern(v0,v1,v3),Tern(v1,v0,v2))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v1)=Tern(v1,v0,Tern(v1,v2,v3)) by A3;
hence thesis by A1222;
end;
A1227: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,v1,Tern(v1,v2,v3)))=Tern(v1,Tern(v0,v1,v3),Tern(v1,v0,v2))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v1)=Tern(v0,v1,Tern(v1,v2,v3)) by A4;
hence thesis by A1225;
end;
A1229: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3))=Tern(v1,Tern(v0,v1,v3),Tern(v1,v0,v2))
proof let v0,v3,v2,v1;
Tern(v0,v1,Tern(v0,v1,Tern(v1,v2,v3)))=Tern(v0,v1,Tern(v1,v2,v3)) by A74;
hence thesis by A1227;
end;
A1231: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3))=Tern(v1,Tern(v0,v1,v3),Tern(v0,v2,v1))
proof let v0,v3,v2,v1;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A1229;
end;
A1233: for v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v1,v2,v3))=Tern(v1,Tern(v0,v1,v3),Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A1231;
end;
A1238: for v104,v3,v103,v102 holds
Tern(v104,Tern(v102,v103,v3),Tern(v102,v103,Tern(Tern(v102,v103,v3),v103
,v104)))=Tern(Tern(v102,v103,v3),v103,Tern(v102,v103,v104))
proof let v104,v3,v103,v102;
Tern(v104,Tern(v102,v103,v3),Tern(v102,v103,v104))=Tern(v102,v103,v104) by A729
;
hence thesis by A236;
end;
A1241: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,Tern(v1,v2,v3),v2)))=Tern(Tern(v1,v2
,v3),v2,Tern(v1
,v2,v0))
proof let v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),v2,v0)=Tern(v0,Tern(v1,v2,v3),v2) by A3;
hence thesis by A1238;
end;
A1243: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,v2,Tern(v1,v2,v3))))=Tern(Tern(v1,v2
,v3),v2,Tern(v1
,v2,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v2)=Tern(v0,v2,Tern(v1,v2,v3)) by A4;
hence thesis by A1241;
end;
A1245: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v1,v2,v3)))=Tern(Tern(v1,v2,v3),v2,Tern
(v1,v2,v0))
proof let v0,v3,v2,v1;
Tern(v1,v2,Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v0,v2,Tern(v1,v2,v3)) by A311;
hence thesis by A1243;
end;
A1247: for v0,v3,v2,v1 holds
Tern(v0,v2,Tern(v1,v2,v3))=Tern(Tern(v1,v2,v3),v2,Tern(v1,v2,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v0,v2,Tern(v1,v2,v3))
by A63;
hence thesis by A1245;
end;
A1250: for v0,v3,v1,v2 holds
Tern(v0,v1,Tern(v2,v1,v3))=Tern(Tern(v2,v1,v3),v1,Tern(v0,v2,v1))
proof let v0,v3,v1,v2;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A1247;
end;
A1252: for v0,v3,v1,v2 holds
Tern(v0,v1,Tern(v2,v1,v3))=Tern(v1,Tern(v0,v2,v1),Tern(v2,v1,v3))
proof let v0,v3,v1,v2;
Tern(v1,Tern(v0,v2,v1),Tern(v2,v1,v3))=Tern(Tern(v2,v1,v3),v1,Tern(v0,v2,v1))
by A3;
hence thesis by A1250;
end;
A1257: for v104,v103,v102,v1 holds
Tern(v104,Tern(v1,v102,v103),Tern(v102,v103,Tern(Tern(v1,v102,v103),v103
,v104)))=Tern(Tern(v1,v102,v103),v103,Tern(v102,v103,v104))
proof let v104,v103,v102,v1;
Tern(v104,Tern(v1,v102,v103),Tern(v102,v103,v104))=Tern(v102,v103,v104) by A965
;
hence thesis by A236;
end;
A1260: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,Tern(v1,v2,v3),v3)))=Tern(Tern(v1,v2
,v3),v3,Tern(v2
,v3,v0))
proof let v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),v3,v0)=Tern(v0,Tern(v1,v2,v3),v3) by A3;
hence thesis by A1257;
end;
A1262: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v3,Tern(v1,v2,v3))))=Tern(Tern(v1,v2
,v3),v3,Tern(v2
,v3,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v3)=Tern(v0,v3,Tern(v1,v2,v3)) by A4;
hence thesis by A1260;
end;
A1264: for v0,v3,v2,v1 holds
Tern(v0,v3,Tern(v1,v2,v3))=Tern(Tern(v1,v2,v3),v3,Tern(v2,v3,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v3,Tern(v1,v2,v3))))=Tern(v0,v3,Tern(
v1,v2,v3))
by A753;
hence thesis by A1262;
end;
A1267: for v0,v1,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v1))=Tern(Tern(v2,v3,v1),v1,Tern(v0,v3,v1))
proof let v0,v1,v3,v2;
Tern(v3,v1,v0)=Tern(v0,v3,v1) by A3;
hence thesis by A1264;
end;
A1269: for v0,v1,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v1))=Tern(v1,Tern(v0,v3,v1),Tern(v2,v3,v1))
proof let v0,v1,v3,v2;
Tern(v1,Tern(v0,v3,v1),Tern(v2,v3,v1))=Tern(Tern(v2,v3,v1),v1,Tern(v0,v3,v1))
by A3;
hence thesis by A1267;
end;
A1274: for v103,v101,v1,v3,v102 holds
Tern(Tern(v102,v3,v1),Tern(v101,v102,Tern(v102,v3,v1)),Tern(v102,v1,Tern(v103,
v102
,v3)))=Tern(v101,Tern(v102,v3,v1),Tern(v103,v102,Tern(v102,v3,v1)))
proof let v103,v101,v1,v3,v102;
Tern(v102,v1,Tern(v103,v102,v3))=Tern(v103,v102,Tern(v102,v3,v1)) by A134;
hence thesis by A1269;
end;
A1277: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,Tern(v0,v1,v2),v3),Tern(v0,v2,Tern(v4,v0,v1)))=
Tern(v3,Tern(v0,v1
,v2),Tern(v4,v0,Tern(v0,v1,v2)))
proof let v4,v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),v3)=Tern(v3,v0,Tern(v0,v1,v2)) by A3;
hence thesis by A1274;
end;
A1279: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,Tern(v0,v1,v2)),Tern(v0,v2,Tern(v4,v0,v1)))=
Tern(v3,Tern(v0,v1
,v2),Tern(v4,v0,Tern(v0,v1,v2)))
proof let v4,v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),v3)=Tern(v0,v3,Tern(v0,v1,v2)) by A4;
hence thesis by A1277;
end;
A1281: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,Tern(v0,v1,v2)),Tern(v0,v2,Tern(v1,v4,v0)))=
Tern(v3,Tern(v0,v1
,v2),Tern(v4,v0,Tern(v0,v1,v2)))
proof let v4,v3,v2,v1,v0;
Tern(v4,v0,v1)=Tern(v1,v4,v0) by A3;
hence thesis by A1279;
end;
A1283: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,Tern(v0,v1,v2)),Tern(v0,v2,Tern(v0,v1,v4)))=
Tern(v3,Tern(v0,v1
,v2),Tern(v4,v0,Tern(v0,v1,v2)))
proof let v4,v3,v2,v1,v0;
Tern(v1,v4,v0)=Tern(v0,v1,v4) by A3;
hence thesis by A1281;
end;
A1285: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,Tern(v0,v1,v2)),Tern(v0,v2,Tern(v0,v1,v4)))=
Tern(v3,Tern(v0,v1
,v2),Tern(v0,Tern(v0,v1,v2),v4))
proof let v4,v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),v4)=Tern(v4,v0,Tern(v0,v1,v2)) by A3;
hence thesis by A1283;
end;
A1287: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,Tern(v0,v1,v2)),Tern(v0,v2,Tern(v0,v1,v4)))=
Tern(v3,Tern(v0,v1
,v2),Tern(v0,v4,Tern(v0,v1,v2)))
proof let v4,v3,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),v4)=Tern(v0,v4,Tern(v0,v1,v2)) by A4;
hence thesis by A1285;
end;
A1290: for v103,v104,v100,v4,v3,v2,v1 holds
Tern(v100,Tern(v1,v2,v3),Tern(v100,Tern(v100,v4,v2),Tern(Tern(v100,v4,v2),v103
,Tern(Tern(v1
,v2,v3),Tern(v100,v4,v2),v104))))=Tern(v100,v4,Tern(v1,v2,Tern(v100,v2,v3)))
proof let v103,v104,v100,v4,v3,v2,v1;
Tern(v100,Tern(v1,v2,v3),Tern(v100,v4,v2))=Tern(v100,v4,Tern(v1,v2,Tern(v100,v2
,v3)))
by A239;
hence thesis by A632;
end;
A1293: for v5,v6,v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v2,v4),Tern(Tern(v0,v4,v2),v5,Tern(Tern
(v1,v2,v3),Tern(v0
,v4,v2),v6))))=Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,v3)))
proof let v5,v6,v0,v4,v3,v2,v1;
Tern(v0,v4,v2)=Tern(v0,v2,v4) by A4;
hence thesis by A1290;
end;
A1295: for v5,v6,v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v2,v4),Tern(Tern(v0,v2,v4),v5,Tern(Tern
(v1,v2,v3),Tern(v0
,v4,v2),v6))))=Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,v3)))
proof let v5,v6,v0,v4,v3,v2,v1;
Tern(v0,v4,v2)=Tern(v0,v2,v4) by A4;
hence thesis by A1293;
end;
A1297: for v5,v6,v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v2,v4),Tern(Tern(v0,v2,v4),v5,Tern(Tern
(v1,v2,v3),Tern(v0
,v2,v4),v6))))=Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,v3)))
proof let v5,v6,v0,v4,v3,v2,v1;
Tern(v0,v4,v2)=Tern(v0,v2,v4) by A4;
hence thesis by A1295;
end;
A1299: for v5,v0,v4,v6,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v2,v4),Tern(Tern(v0,v2,v4),v5,Tern(v6,
Tern(v1,v2,v3)
,Tern(v0,v2,v4)))))=Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,v3)))
proof let v5,v0,v4,v6,v3,v2,v1;
Tern(Tern(v1,v2,v3),Tern(v0,v2,v4),v6)=Tern(v6,Tern(v1,v2,v3),Tern(v0,v2,v4))
by A3;
hence thesis by A1297;
end;
A1301: for v5,v0,v4,v6,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v2,v4),Tern(v5,Tern(v6,Tern(v1,v2,v3),
Tern(v0,v2,v4))
,Tern(v0,v2,v4))))=Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,v3)))
proof let v5,v0,v4,v6,v3,v2,v1;
Tern(v5,Tern(v6,Tern(v1,v2,v3),Tern(v0,v2,v4)),Tern(v0,v2,v4))=Tern(Tern(v0,v2,
v4),v5,Tern(v6
,Tern(v1,v2,v3),Tern(v0,v2,v4))) by A3;
hence thesis by A1299;
end;
A1303: for v5,v0,v4,v6,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v2,v4),Tern(v5,Tern(v0,v2,v4),Tern(v6,
Tern(v1,v2,v3)
,Tern(v0,v2,v4)))))=Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,v3)))
proof let v5,v0,v4,v6,v3,v2,v1;
Tern(v5,Tern(v6,Tern(v1,v2,v3),Tern(v0,v2,v4)),Tern(v0,v2,v4))=Tern(v5,Tern(v0,
v2,v4),Tern(v6
,Tern(v1,v2,v3),Tern(v0,v2,v4))) by A4;
hence thesis by A1301;
end;
A1305: for v1,v0,v4,v3,v2 holds
Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,Tern(v2,v3,v4))))=Tern(v0,v2,v4)
proof
now let v5,v0,v6,v1,v4,v3,v2;
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,Tern(v0,v2,v4),Tern(v5,Tern(v0,v2,v4
),Tern(v6,Tern(v1
,v2,Tern(v2,v3,v4)),Tern(v0,v2,v4)))))=Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,Tern(v2
,v3
,v4)))) by A1303;
hence Tern(v0,v4,Tern(v1,v2,Tern(v0,v2,Tern(v2,v3,v4))))=Tern(v0,v2,v4) by
A1200;
end;
hence thesis;
end;
A1309: for v3,v103,v104,v2,v102,v1 holds
Tern(Tern(v1,v102,v2),Tern(v1,v2,v3),Tern(v102,v103,Tern(v102,v104,Tern(v1,
v102
,v2))))=Tern(v102,Tern(v1,v102,v2),Tern(v1,v2,v3))
proof let v3,v103,v104,v2,v102,v1;
Tern(v102,Tern(v1,v102,v2),Tern(v1,v2,v3))=Tern(v1,v102,v2) by A925;
hence thesis by A1219;
end;
A1312: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v1,v4,Tern(v1,v5,Tern(v0,v1,v2))))=
Tern(v0,v1,v2)
proof let v3,v4,v5,v2,v1,v0;
Tern(v1,Tern(v0,v1,v2),Tern(v0,v2,v3))=Tern(v0,v1,v2) by A925;
hence thesis by A1309;
end;
A1315: for v103,v2,v101,v102,v4,v3 holds
Tern(Tern(v2,v3,Tern(v101,v3,Tern(v3,v4,v102))),Tern(v101,v102,v103),Tern(v101
,v102
,Tern(v2,v3,Tern(v101,v3,Tern(v3,v4,v102)))))=Tern(v101,v3,v102)
proof let v103,v2,v101,v102,v4,v3;
Tern(v101,v102,Tern(v2,v3,Tern(v101,v3,Tern(v3,v4,v102))))=Tern(v101,v3,v102)
by
A1305;
hence thesis by A729;
end;
A1318: for v5,v0,v2,v4,v3,v1 holds
Tern(Tern(v0,v1,Tern(v1,Tern(v1,v3,v4),v2)),Tern(v2,v4,v5),Tern(v2,v4,Tern(v0,
v1,Tern(v2,v1
,Tern(v1,v3,v4)))))=Tern(v2,v1,v4)
proof let v5,v0,v2,v4,v3,v1;
Tern(v1,Tern(v1,v3,v4),v2)=Tern(v2,v1,Tern(v1,v3,v4)) by A3;
hence thesis by A1315;
end;
A1321: for v5,v0,v4,v3,v2,v1 holds
Tern(Tern(v0,v1,Tern(v1,v4,Tern(v1,v2,v3))),Tern(v4,v3,v5),Tern(v4,v3,Tern(v0,
v1,Tern(v4,v1
,Tern(v1,v2,v3)))))=Tern(v4,v1,v3)
proof let v5,v0,v4,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v4)=Tern(v1,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A1318;
end;
A1324: for v5,v0,v2,v4,v3,v1 holds
Tern(Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4))),Tern(v2,v4,v5),Tern(v2,v4,Tern(v0,
v1,Tern(v1,Tern(v1
,v3,v4),v2))))=Tern(v2,v1,v4)
proof let v5,v0,v2,v4,v3,v1;
Tern(v1,Tern(v1,v3,v4),v2)=Tern(v2,v1,Tern(v1,v3,v4)) by A3;
hence thesis by A1321;
end;
A1326: for v5,v0,v2,v4,v3,v1 holds
Tern(Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4))),Tern(v2,v4,v5),Tern(v2,v4,Tern(v0,
v1,Tern(v1,v2
,Tern(v1,v3,v4)))))=Tern(v2,v1,v4)
proof let v5,v0,v2,v4,v3,v1;
Tern(v1,Tern(v1,v3,v4),v2)=Tern(v1,v2,Tern(v1,v3,v4)) by A4;
hence thesis by A1324;
end;
A1328: for v0,v2,v4,v3,v1 holds
Tern(v2,v4,Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4))))=Tern(v2,v1,v4)
proof
now let v5,v0,v2,v4,v3,v1;
Tern(Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4))),Tern(v2,v4,v5),Tern(v2,v4,Tern(v0,
v1,Tern(v1,v2
,Tern(v1,v3,v4)))))=Tern(v2,v4,Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4)))) by A729;
hence Tern(v2,v4,Tern(v0,v1,Tern(v1,v2,Tern(v1,v3,v4))))=Tern(v2,v1,v4) by
A1326;
end;
hence thesis;
end;
A1331: for v2,v0,v1,v4,v3 holds
Tern(v0,v1,Tern(v2,v3,Tern(v3,v0,Tern(v3,v4,v1))))=Tern(v3,v1,v0)
proof let v2,v0,v1,v4,v3;
Tern(v3,v1,v0)=Tern(v0,v3,v1) by A3;
hence thesis by A1328;
end;
A1333: for v2,v0,v1,v4,v3 holds
Tern(v0,v1,Tern(v2,v3,Tern(v3,v0,Tern(v3,v4,v1))))=Tern(v3,v0,v1)
proof let v2,v0,v1,v4,v3;
Tern(v3,v1,v0)=Tern(v3,v0,v1) by A4;
hence thesis by A1331;
end;
A1335: for v1,v2,v4,v3,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v3,v4)))=Tern(v0,v1,Tern(v3,v4,Tern(v0,v2,v3)))
proof let v1,v2,v4,v3,v0;
Tern(v3,v4,Tern(v0,v2,v3))=Tern(v0,v3,Tern(v2,v3,v4)) by A708;
hence thesis by A280;
end;
A1340: for v100,v4,v103,v102 holds
Tern(v100,Tern(v102,v103,v4),Tern(v102,v103,Tern(v102,v103,v4)))=Tern(v103,
Tern(v102
,v103,v4),Tern(v102,v103,Tern(v102,v100,v4)))
proof let v100,v4,v103,v102;
Tern(v103,Tern(v102,v103,v4),Tern(v102,v100,Tern(v102,v103,v4)))=Tern(v103,Tern
(v102
,v103,v4),Tern(v102,v103,Tern(v102,v100,v4))) by A328;
hence thesis by A1033;
end;
A1343: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v3))=Tern(v2,Tern(v1,v2,v3),Tern(v1,v2,Tern(
v1,v0,v3)))
proof let v0,v3,v2,v1;
Tern(v1,v2,Tern(v1,v2,v3))=Tern(v1,v2,v3) by A74;
hence thesis by A1340;
end;
A1345: for v2,v3,v0,v1 holds
Tern(v1,v2,v3)=Tern(v2,Tern(v1,v2,v3),Tern(v1,v2,Tern(v1,v0,v3)))
proof let v2,v3,v0,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v3))=Tern(v1,v2,v3) by A34;
hence thesis by A1343;
end;
A1348: for v1,v0,v2,v3 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v1,v2),Tern(v0,v1,Tern(v3,v2,v0)))
proof let v1,v0,v2,v3;
Tern(v3,v2,v0)=Tern(v0,v3,v2) by A3;
hence thesis by A1345;
end;
A1350: for v1,v2,v0,v3 holds
Tern(v0,v1,v2)=Tern(v1,Tern(v0,v1,v2),Tern(v0,v1,Tern(v3,v0,v2)))
proof let v1,v2,v0,v3;
Tern(v3,v2,v0)=Tern(v3,v0,v2) by A4;
hence thesis by A1348;
end;
A1352: for v1,v2,v0,v3 holds Tern(v0,v1,v2)=Tern(v0,v1,Tern(v1,Tern(v3,v0,v2),
v2))
proof let v1,v2,v0,v3;
Tern(v1,Tern(v0,v1,v2),Tern(v0,v1,Tern(v3,v0,v2)))=Tern(v0,v1,Tern(v1,Tern(v3,
v0,v2),v2))
by A1233;
hence thesis by A1350;
end;
A1354: for v1,v2,v0,v3 holds Tern(v0,v1,v2)=Tern(v0,v1,Tern(v1,v2,Tern(v3,v0,v2
)))
proof let v1,v2,v0,v3;
Tern(v1,Tern(v3,v0,v2),v2)=Tern(v1,v2,Tern(v3,v0,v2)) by A4;
hence thesis by A1352;
end;
A1358: for v100,v102,v103,v3 holds
Tern(v100,Tern(v3,v103,v102),Tern(v100,v102,Tern(v103,v100,Tern(v3,v103
,v102))))=Tern(v103,v100,v102)
proof let v100,v102,v103,v3;
Tern(v103,v100,Tern(v100,v102,Tern(v3,v103,v102)))=Tern(v103,v100,v102) by
A1354;
hence thesis by A495;
end;
A1361: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v0,Tern(v1,v2,v3),v2)))=Tern(v2,v0,v3)
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v2)=Tern(v2,v0,Tern(v1,v2,v3)) by A3;
hence thesis by A1358;
end;
A1363: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v0,v2,Tern(v1,v2,v3))))=Tern(v2,v0,v3)
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v2)=Tern(v0,v2,Tern(v1,v2,v3)) by A4;
hence thesis by A1361;
end;
A1365: for v0,v3,v2,v1 holds Tern(v0,v3,Tern(v0,v2,Tern(v1,v2,v3)))=Tern(v2,v0,
v3)
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v0,v2,Tern(v1,v2,v3))))=Tern(v0,v3,Tern(
v0,v2,Tern(v1
,v2,v3))) by A78;
hence thesis by A1363;
end;
A1368: for v0,v1,v2,v3 holds Tern(v0,v1,Tern(v0,v2,Tern(v3,v2,v1)))=Tern(v0,v1,
v2)
proof let v0,v1,v2,v3;
Tern(v0,v1,v2)=Tern(v2,v0,v1) by A3;
hence thesis by A1365;
end;
A1370: for v0,v1,v2,v3 holds Tern(v0,v1,Tern(v0,v2,Tern(v3,v2,v1)))=Tern(v0,v2,
v1)
proof let v0,v1,v2,v3;
Tern(v0,v1,v2)=Tern(v0,v2,v1) by A4;
hence thesis by A1368;
end;
A1373: for v101,v103,v3,v102 holds
Tern(Tern(v102,v3,v103),Tern(v101,v102,v103),Tern(v101,v102,v103))=Tern(v101,
Tern(v102
,v3,v103),Tern(v101,v102,v103))
proof let v101,v103,v3,v102;
Tern(v101,v102,Tern(v101,v103,Tern(v102,v3,v103)))=Tern(v101,v102,v103) by A836
;
hence thesis by A352;
end;
A1376: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v2,v3,v0),Tern(v3,v0,v2))=Tern(v3,Tern(v0,v1,v2),Tern
(v3,v0,v2))
proof let v3,v2,v1,v0;
Tern(v3,v0,v2)=Tern(v2,v3,v0) by A3;
hence thesis by A1373;
end;
A1378: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v3,v0,v2))=Tern(v3,Tern(v0,v1,v2),Tern
(v3,v0,v2))
proof let v3,v2,v1,v0;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A1376;
end;
A1380: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v2,v3,v0))=Tern(v3,Tern(v0,v1,v2),Tern
(v3,v0,v2))
proof let v3,v2,v1,v0;
Tern(v3,v0,v2)=Tern(v2,v3,v0) by A3;
hence thesis by A1378;
end;
A1382: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v0,v2,v3))=Tern(v3,Tern(v0,v1,v2),Tern
(v3,v0,v2))
proof let v3,v2,v1,v0;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A1380;
end;
A1384: for v3,v2,v1,v0 holds Tern(v0,v2,v3)=Tern(v3,Tern(v0,v1,v2),Tern(v3,v0,
v2))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v0,v2,v3))=Tern(v0,v2,v3) by A34;
hence thesis by A1382;
end;
A1387: for v2,v1,v3,v0 holds Tern(v0,v1,v2)=Tern(v2,Tern(v0,v3,v1),Tern(v1,v2,
v0))
proof let v2,v1,v3,v0;
Tern(v2,v0,v1)=Tern(v1,v2,v0) by A3;
hence thesis by A1384;
end;
A1389: for v2,v1,v3,v0 holds Tern(v0,v1,v2)=Tern(v2,Tern(v0,v3,v1),Tern(v0,v1,
v2))
proof let v2,v1,v3,v0;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A1387;
end;
A1394: for v3,v102,v101,v2,v1 holds
Tern(Tern(v3,v1,v2),Tern(v101,v102,Tern(v1,v2,v101)),Tern(v101,v102,Tern(v1,v2
,v101)))=Tern(v101,Tern(v3,v1,v2),Tern(v101,v102,Tern(v1,v2,v101)))
proof let v3,v102,v101,v2,v1;
Tern(v101,Tern(v1,v2,v101),Tern(v3,v1,v2))=Tern(v1,v2,v101) by A1121;
hence thesis by A352;
end;
A1397: for v4,v3,v2,v1,v0 holds
Tern(v3,v4,Tern(v1,v2,v3))=Tern(v3,Tern(v0,v1,v2),Tern(v3,v4,Tern(v1,v2,v3)))
proof let v4,v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v3,v4,Tern(v1,v2,v3)),Tern(v3,v4,Tern(v1,v2,v3)))=Tern
(v3,v4,Tern(v1
,v2,v3)) by A34;
hence thesis by A1394;
end;
A1403: for v101,v3,v103,v4,v102 holds
Tern(Tern(v102,v3,Tern(v102,v4,v103)),Tern(v101,v102,v103),Tern(v101,v102
,v103))=Tern(v101,Tern(v102,v3,Tern(v102,v4,v103)),Tern(v101,v102,v103))
proof let v101,v3,v103,v4,v102;
Tern(v101,v102,Tern(v101,v103,Tern(v102,v3,Tern(v102,v4,v103))))=Tern(v101,v102
,v103) by A861;
hence thesis by A352;
end;
A1406: for v4,v1,v3,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,v3)),Tern(v3,v4,v0),Tern(v4,v0,v3))=Tern(v4,Tern(v0
,v1,Tern(v0,v2
,v3)),Tern(v4,v0,v3))
proof let v4,v1,v3,v2,v0;
Tern(v4,v0,v3)=Tern(v3,v4,v0) by A3;
hence thesis by A1403;
end;
A1408: for v4,v1,v3,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,v3)),Tern(v0,v3,v4),Tern(v4,v0,v3))=Tern(v4,Tern(v0
,v1,Tern(v0,v2
,v3)),Tern(v4,v0,v3))
proof let v4,v1,v3,v2,v0;
Tern(v3,v4,v0)=Tern(v0,v3,v4) by A3;
hence thesis by A1406;
end;
A1410: for v4,v1,v3,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,v3)),Tern(v0,v3,v4),Tern(v3,v4,v0))=Tern(v4,Tern(v0
,v1,Tern(v0,v2
,v3)),Tern(v4,v0,v3))
proof let v4,v1,v3,v2,v0;
Tern(v4,v0,v3)=Tern(v3,v4,v0) by A3;
hence thesis by A1408;
end;
A1412: for v4,v1,v3,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,v3)),Tern(v0,v3,v4),Tern(v0,v3,v4))=Tern(v4,Tern(v0
,v1,Tern(v0,v2
,v3)),Tern(v4,v0,v3))
proof let v4,v1,v3,v2,v0;
Tern(v3,v4,v0)=Tern(v0,v3,v4) by A3;
hence thesis by A1410;
end;
A1414: for v4,v1,v3,v2,v0 holds
Tern(v0,v3,v4)=Tern(v4,Tern(v0,v1,Tern(v0,v2,v3)),Tern(v4,v0,v3))
proof let v4,v1,v3,v2,v0;
Tern(Tern(v0,v1,Tern(v0,v2,v3)),Tern(v0,v3,v4),Tern(v0,v3,v4))=Tern(v0,v3,v4)
by A34;
hence thesis by A1412;
end;
A1417: for v2,v3,v1,v4,v0 holds
Tern(v0,v1,v2)=Tern(v2,Tern(v0,v3,Tern(v0,v4,v1)),Tern(v1,v2,v0))
proof let v2,v3,v1,v4,v0;
Tern(v2,v0,v1)=Tern(v1,v2,v0) by A3;
hence thesis by A1414;
end;
A1419: for v2,v3,v1,v4,v0 holds
Tern(v0,v1,v2)=Tern(v2,Tern(v0,v3,Tern(v0,v4,v1)),Tern(v0,v1,v2))
proof let v2,v3,v1,v4,v0;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A1417;
end;
A1424: for v104,v103,v2,v102 holds
Tern(v104,Tern(v102,v2,v103),Tern(v102,v103,Tern(Tern(v102,v2,v103),v103
,v104)))=Tern(Tern(v102,v2,v103),v103,Tern(v102,v103,v104))
proof let v104,v103,v2,v102;
Tern(v104,Tern(v102,v2,v103),Tern(v102,v103,v104))=Tern(v102,v103,v104) by
A1389;
hence thesis by A236;
end;
A1427: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,Tern(v1,v2,v3),v3)))=Tern(Tern(v1,v2
,v3),v3,Tern(v1
,v3,v0))
proof let v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),v3,v0)=Tern(v0,Tern(v1,v2,v3),v3) by A3;
hence thesis by A1424;
end;
A1429: for v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,v3,Tern(v1,v2,v3))))=Tern(Tern(v1,v2
,v3),v3,Tern(v1
,v3,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v3)=Tern(v0,v3,Tern(v1,v2,v3)) by A4;
hence thesis by A1427;
end;
A1431: for v0,v3,v2,v1 holds
Tern(v0,v3,Tern(v1,v2,v3))=Tern(Tern(v1,v2,v3),v3,Tern(v1,v3,v0))
proof let v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,v3,Tern(v1,v2,v3))))=Tern(v0,v3,Tern(
v1,v2,v3))
by A753;
hence thesis by A1429;
end;
A1434: for v0,v1,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v1))=Tern(Tern(v2,v3,v1),v1,Tern(v0,v2,v1))
proof let v0,v1,v3,v2;
Tern(v2,v1,v0)=Tern(v0,v2,v1) by A3;
hence thesis by A1431;
end;
A1436: for v0,v1,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v1))=Tern(v1,Tern(v0,v2,v1),Tern(v2,v3,v1))
proof let v0,v1,v3,v2;
Tern(v1,Tern(v0,v2,v1),Tern(v2,v3,v1))=Tern(Tern(v2,v3,v1),v1,Tern(v0,v2,v1))
by A3;
hence thesis by A1434;
end;
A1441: for v3,v103,v101,v2,v1 holds
Tern(Tern(v2,v3,v101),Tern(v101,Tern(v1,v2,v101),v103),Tern(v101,Tern(v1,v2,
v101),Tern(v2
,v3,v101)))=Tern(v1,v101,Tern(v2,v3,v101))
proof let v3,v103,v101,v2,v1;
Tern(v101,Tern(v1,v2,v101),Tern(v2,v3,v101))=Tern(v1,v101,Tern(v2,v3,v101)) by
A1436;
hence thesis by A729;
end;
A1444: for v1,v4,v0,v3,v2 holds
Tern(Tern(v0,v1,v2),Tern(v2,Tern(v2,v3,v0),v4),Tern(v2,Tern(v3,v0,v2),Tern(v0,
v1
,v2)))=Tern(v3,v2,Tern(v0,v1,v2))
proof let v1,v4,v0,v3,v2;
Tern(v3,v0,v2)=Tern(v2,v3,v0) by A3;
hence thesis by A1441;
end;
A1446: for v1,v4,v3,v2,v0 holds
Tern(Tern(v0,v1,v2),Tern(v2,Tern(v0,v2,v3),v4),Tern(v2,Tern(v3,v0,v2),Tern(v0,
v1
,v2)))=Tern(v3,v2,Tern(v0,v1,v2))
proof let v1,v4,v3,v2,v0;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A1444;
end;
A1448: for v1,v4,v3,v2,v0 holds
Tern(Tern(v0,v1,v2),Tern(v2,v4,Tern(v0,v2,v3)),Tern(v2,Tern(v3,v0,v2),Tern(v0,
v1
,v2)))=Tern(v3,v2,Tern(v0,v1,v2))
proof let v1,v4,v3,v2,v0;
Tern(v2,Tern(v0,v2,v3),v4)=Tern(v2,v4,Tern(v0,v2,v3)) by A4;
hence thesis by A1446;
end;
A1451: for v1,v3,v4,v2,v0 holds
Tern(Tern(v0,v1,v2),Tern(v2,v3,Tern(v0,v2,v4)),Tern(v2,Tern(v2,v4,v0),Tern(v0,
v1
,v2)))=Tern(v4,v2,Tern(v0,v1,v2))
proof let v1,v3,v4,v2,v0;
Tern(v4,v0,v2)=Tern(v2,v4,v0) by A3;
hence thesis by A1448;
end;
A1453: for v1,v3,v4,v2,v0 holds
Tern(Tern(v0,v1,v2),Tern(v2,v3,Tern(v0,v2,v4)),Tern(v2,Tern(v0,v2,v4),Tern(v0,
v1
,v2)))=Tern(v4,v2,Tern(v0,v1,v2))
proof let v1,v3,v4,v2,v0;
Tern(v2,v4,v0)=Tern(v0,v2,v4) by A3;
hence thesis by A1451;
end;
A1455: for v1,v4,v2,v0 holds
Tern(v2,Tern(v0,v2,v4),Tern(v0,v1,v2))=Tern(v4,v2,Tern(v0,v1,v2))
proof
now let v1,v3,v4,v2,v0;
Tern(Tern(v0,v1,v2),Tern(v2,v3,Tern(v0,v2,v4)),Tern(v2,Tern(v0,v2,v4),Tern(v0,
v1,v2)))=Tern(v2
,Tern(v0,v2,v4),Tern(v0,v1,v2)) by A1389;
hence Tern(v2,Tern(v0,v2,v4),Tern(v0,v1,v2))=Tern(v4,v2,Tern(v0,v1,v2)) by
A1453;
end;
hence thesis;
end;
A1458: for v3,v2,v0,v1 holds
Tern(v0,Tern(v1,v0,v2),Tern(v1,v3,v0))=Tern(v0,Tern(v1,v3,v0),v2)
proof let v3,v2,v0,v1;
Tern(v0,Tern(v1,v3,v0),v2)=Tern(v2,v0,Tern(v1,v3,v0)) by A3;
hence thesis by A1455;
end;
A1460: for v3,v2,v0,v1 holds
Tern(v0,Tern(v1,v0,v2),Tern(v1,v3,v0))=Tern(v0,v2,Tern(v1,v3,v0))
proof let v3,v2,v0,v1;
Tern(v0,Tern(v1,v3,v0),v2)=Tern(v0,v2,Tern(v1,v3,v0)) by A4;
hence thesis by A1458;
end;
A1463: for v103,v102,v2,v4,v3,v1 holds
Tern(Tern(v1,v2,Tern(v1,v3,v4)),Tern(v1,v4,v102),Tern(v102,Tern(v1,v4,v102),
Tern(v102,Tern(v1
,v2,Tern(v1,v3,v4)),v103)))=Tern(v1,v4,v102)
proof let v103,v102,v2,v4,v3,v1;
Tern(v102,Tern(v1,v2,Tern(v1,v3,v4)),Tern(v1,v4,v102))=Tern(v1,v4,v102) by
A1419;
hence thesis by A693;
end;
A1466: for v4,v5,v1,v3,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,v3)),Tern(v0,v3,v4),Tern(v4,Tern(v0,v3,v4),Tern(v4,
v5,Tern(v0,v1
,Tern(v0,v2,v3)))))=Tern(v0,v3,v4)
proof let v4,v5,v1,v3,v2,v0;
Tern(v4,Tern(v0,v1,Tern(v0,v2,v3)),v5)=Tern(v4,v5,Tern(v0,v1,Tern(v0,v2,v3)))
by A4;
hence thesis by A1463;
end;
A1469: for v3,v102,v103,v2,v101,v1 holds
Tern(Tern(v1,v101,v2),Tern(v101,v102,v103),Tern(v1,v101,v2))=Tern(Tern(v1,v101
,v2),Tern(v1
,v2,v3),Tern(v101,v102,Tern(v101,v103,Tern(v1,v101,v2))))
proof let v3,v102,v103,v2,v101,v1;
Tern(v101,Tern(v1,v101,v2),Tern(v1,v2,v3))=Tern(v1,v101,v2) by A925;
hence thesis by A402;
end;
A1472: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v3,v4),Tern(v0,v1,v2))=Tern(v0,v1,v2)
proof
now let v5,v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v2,v5),Tern(v1,v3,Tern(v1,v4,Tern(v0,v1,v2))))=Tern
(v0,v1,v2)
by A1312;
hence Tern(Tern(v0,v1,v2),Tern(v1,v3,v4),Tern(v0,v1,v2))=Tern(v0,v1,v2) by
A1469;
end;
hence thesis;
end;
A1475: for v104,v101,v4,v3,v103 holds
Tern(Tern(v103,v3,v4),v101,Tern(Tern(v103,v3,v4),v103,v104))=Tern(Tern(Tern(
v103,v3,v4)
,v103,v104),Tern(v103,v3,v4),Tern(Tern(v103,v3,v4),v103,Tern(Tern(v103,v3,v4),
v101
,v104)))
proof let v104,v101,v4,v3,v103;
Tern(Tern(Tern(v103,v3,v4),v103,v104),Tern(v103,v3,v4),Tern(Tern(v103,v3,v4),
v103
,v104))=Tern(Tern(v103,v3,v4),v103,v104) by A1472;
hence thesis by A162;
end;
A1478: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v4,Tern(v0,v1,v2),v0))=Tern(Tern(Tern(v0,v1,v2),v0
,v4),Tern(v0,v1
,v2),Tern(Tern(v0,v1,v2),v0,Tern(Tern(v0,v1,v2),v3,v4)))
proof let v4,v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),v0,v4)=Tern(v4,Tern(v0,v1,v2),v0) by A3;
hence thesis by A1475;
end;
A1480: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,v4,Tern(v0,v1,v2)))=Tern(Tern(Tern(v0,v1,v2),v0
,v4),Tern(v0,v1
,v2),Tern(Tern(v0,v1,v2),v0,Tern(Tern(v0,v1,v2),v3,v4)))
proof let v4,v3,v2,v1,v0;
Tern(v4,Tern(v0,v1,v2),v0)=Tern(v0,v4,Tern(v0,v1,v2)) by A3;
hence thesis by A1478;
end;
A1482: for v3,v4,v2,v1,v0 holds
Tern(v3,Tern(v0,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2))=Tern(Tern(Tern(v0,v1,v2),v0
,v4),Tern(v0,v1
,v2),Tern(Tern(v0,v1,v2),v0,Tern(Tern(v0,v1,v2),v3,v4)))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v3,Tern(
v0,v4,Tern(v0
,v1,v2))) by A3;
hence thesis by A1480;
end;
A1485: for v2,v0,v4,v3,v1 holds
Tern(v0,Tern(v1,v3,v4),Tern(v1,v2,Tern(v1,v3,v4)))=Tern(Tern(Tern(v1,v3,v4),v1
,v2),Tern(v1,v3
,v4),Tern(Tern(v1,v3,v4),v1,Tern(Tern(v1,v3,v4),v0,v2)))
proof let v2,v0,v4,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,v4)),Tern(v1,v3,v4))=Tern(v0,Tern(v1,v3,v4),Tern(
v1,v2,Tern(v1
,v3,v4))) by A4;
hence thesis by A1482;
end;
A1488: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v4,Tern(v1,v2,v3)
,v1),Tern(v1,v2
,v3),Tern(Tern(v1,v2,v3),v1,Tern(Tern(v1,v2,v3),v0,v4)))
proof let v4,v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),v1,v4)=Tern(v4,Tern(v1,v2,v3),v1) by A3;
hence thesis by A1485;
end;
A1490: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v1,v4,Tern(v1,v2,
v3)),Tern(v1,v2
,v3),Tern(Tern(v1,v2,v3),v1,Tern(Tern(v1,v2,v3),v0,v4)))
proof let v4,v0,v3,v2,v1;
Tern(v4,Tern(v1,v2,v3),v1)=Tern(v1,v4,Tern(v1,v2,v3)) by A3;
hence thesis by A1488;
end;
A1492: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v1,v4,Tern(v1,v2,
v3)),Tern(v1,v2
,v3),Tern(Tern(v1,v2,v3),v1,Tern(v4,Tern(v1,v2,v3),v0)))
proof let v4,v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),v0,v4)=Tern(v4,Tern(v1,v2,v3),v0) by A3;
hence thesis by A1490;
end;
A1494: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v1,v4,Tern(v1,v2,
v3)),Tern(v1,v2
,v3),Tern(Tern(v1,v2,v3),v1,Tern(v0,v4,Tern(v1,v2,v3))))
proof let v4,v0,v3,v2,v1;
Tern(v4,Tern(v1,v2,v3),v0)=Tern(v0,v4,Tern(v1,v2,v3)) by A3;
hence thesis by A1492;
end;
A1496: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v1,v4,Tern(v1,v2,
v3)),Tern(v1,v2
,v3),Tern(v1,Tern(v0,v4,Tern(v1,v2,v3)),Tern(v1,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v0,v4,Tern(v1,v2,v3)),Tern(v1,v2,v3))=Tern(Tern(v1,v2,v3),v1,Tern(
v0,v4,Tern(v1
,v2,v3))) by A3;
hence thesis by A1494;
end;
A1498: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v1,v4,Tern(v1,v2,
v3)),Tern(v1,v2
,v3),Tern(v1,Tern(v1,v2,v3),Tern(v0,v4,Tern(v1,v2,v3))))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v0,v4,Tern(v1,v2,v3)),Tern(v1,v2,v3))=Tern(v1,Tern(v1,v2,v3),Tern(
v0,v4,Tern(v1
,v2,v3))) by A4;
hence thesis by A1496;
end;
A1500: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v1,v4,Tern(v1,v2,
v3)),Tern(v1,v2
,v3),Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3)))))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),Tern(v0,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v1,v2,Tern(
v0,v4,Tern(v1,v2
,v3)))) by A558;
hence thesis by A1498;
end;
A1502: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v1,v2,v3),Tern(v1
,v3,Tern(v1,v2
,Tern(v0,v4,Tern(v1,v2,v3)))),Tern(v1,v4,Tern(v1,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3)))),Tern(v1,
v4,Tern(v1,v2
,v3)))=Tern(Tern(v1,v4,Tern(v1,v2,v3)),Tern(v1,v2,v3),Tern(v1,v3,Tern(v1,v2,
Tern(v0,v4,Tern(v1
,v2,v3))))) by A3;
hence thesis by A1500;
end;
A1504: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(Tern(v1,v2,v3),Tern(v1
,v4,Tern(v1,v2
,v3)),Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3)))))
proof let v4,v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3)))),Tern(v1,
v4,Tern(v1,v2
,v3)))=Tern(Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)),Tern(v1,v3,Tern(v1,v2,
Tern(v0,v4,Tern(v1
,v2,v3))))) by A4;
hence thesis by A1502;
end;
A1506: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v4,Tern(v1,v2,v3),Tern
(v1,Tern(v0,v4
,Tern(v1,v2,v3)),Tern(v1,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)),Tern(v1,v3,Tern(v1,v2,Tern(v0,v4
,Tern(v1,v2
,v3)))))=Tern(v4,Tern(v1,v2,v3),Tern(v1,Tern(v0,v4,Tern(v1,v2,v3)),Tern(v1,v2,
v3))) by
A1287;
hence thesis by A1504;
end;
A1508: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v4,Tern(v1,v2,v3),Tern
(v1,Tern(v1,v2
,v3),Tern(v0,v4,Tern(v1,v2,v3))))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v0,v4,Tern(v1,v2,v3)),Tern(v1,v2,v3))=Tern(v1,Tern(v1,v2,v3),Tern(
v0,v4,Tern(v1
,v2,v3))) by A4;
hence thesis by A1506;
end;
A1510: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v4,Tern(v1,v2,v3),Tern
(v1,v3,Tern(v1
,v2,Tern(v0,v4,Tern(v1,v2,v3)))))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),Tern(v0,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v1,v2,Tern(
v0,v4,Tern(v1,v2
,v3)))) by A558;
hence thesis by A1508;
end;
A1515: for v104,v101,v4,v3,v103 holds
Tern(Tern(Tern(v103,v3,v4),v103,Tern(v101,Tern(v103,v3,v4),v104)),v101,Tern(
Tern(v103,v3
,v4),v103,Tern(v101,Tern(v103,v3,v4),v104)))=Tern(Tern(Tern(v103,v3,v4),v103,
Tern(v101
,Tern(v103,v3,v4),v104)),v101,Tern(v103,v3,v4))
proof let v104,v101,v4,v3,v103;
Tern(Tern(Tern(v103,v3,v4),v103,Tern(v101,Tern(v103,v3,v4),v104)),Tern(v103,v3,
v4)
,Tern(Tern(v103,v3,v4),v103,Tern(v101,Tern(v103,v3,v4),v104)))=Tern(Tern(v103,
v3,v4)
,v103,Tern(v101,Tern(v103,v3,v4),v104)) by A1472;
hence thesis by A632;
end;
A1518: for v3,v4,v2,v1,v0 holds
Tern(Tern(Tern(v0,v1,v2),v0,Tern(v3,v4,Tern(v0,v1,v2))),v3,Tern(Tern(v0,v1,v2)
,v0,Tern(v3
,Tern(v0,v1,v2),v4)))=Tern(Tern(Tern(v0,v1,v2),v0,Tern(v3,Tern(v0,v1,v2),v4)),
v3,Tern(v0,v1
,v2))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),v4)=Tern(v3,v4,Tern(v0,v1,v2)) by A4;
hence thesis by A1515;
end;
A1520: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2)),v3,Tern(Tern(v0,v1,v2)
,v0,Tern(v3
,Tern(v0,v1,v2),v4)))=Tern(Tern(Tern(v0,v1,v2),v0,Tern(v3,Tern(v0,v1,v2),v4)),
v3,Tern(v0,v1
,v2))
proof let v3,v4,v2,v1,v0;
Tern(v0,Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v0,Tern(
v3,v4,Tern(v0
,v1,v2))) by A3;
hence thesis by A1518;
end;
A1523: for v1,v2,v4,v3,v0 holds
Tern(Tern(v0,Tern(v0,v3,v4),Tern(v1,v2,Tern(v0,v3,v4))),v1,Tern(Tern(v0,v3,v4)
,v0,Tern(v1
,Tern(v0,v3,v4),v2)))=Tern(Tern(Tern(v0,v3,v4),v0,Tern(v1,Tern(v0,v3,v4),v2)),
v1,Tern(v0,v3
,v4))
proof let v1,v2,v4,v3,v0;
Tern(v0,Tern(v1,v2,Tern(v0,v3,v4)),Tern(v0,v3,v4))=Tern(v0,Tern(v0,v3,v4),Tern(
v1,v2,Tern(v0
,v3,v4))) by A4;
hence thesis by A1520;
end;
A1526: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2)))),v3,Tern(Tern(v0,v1,v2)
,v0,Tern(v3
,Tern(v0,v1,v2),v4)))=Tern(Tern(Tern(v0,v1,v2),v0,Tern(v3,Tern(v0,v1,v2),v4)),
v3,Tern(v0,v1
,v2))
proof let v3,v4,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)))=Tern(v0,v2,Tern(v0,v1,Tern(
v3,v4,Tern(v0,v1
,v2)))) by A558;
hence thesis by A1523;
end;
A1529: for v3,v4,v1,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),v3,Tern(Tern(v0,v2,v1)
,v0,Tern(v3,v4
,Tern(v0,v2,v1))))=Tern(Tern(Tern(v0,v2,v1),v0,Tern(v3,Tern(v0,v2,v1),v4)),v3,
Tern(v0,v2
,v1))
proof let v3,v4,v1,v2,v0;
Tern(v3,Tern(v0,v2,v1),v4)=Tern(v3,v4,Tern(v0,v2,v1)) by A4;
hence thesis by A1526;
end;
A1531: for v3,v4,v1,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),v3,Tern(v0,Tern(v3,v4,
Tern(v0,v2,v1))
,Tern(v0,v2,v1)))=Tern(Tern(Tern(v0,v2,v1),v0,Tern(v3,Tern(v0,v2,v1),v4)),v3,
Tern(v0,v2
,v1))
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v3,v4,Tern(v0,v2,v1)),Tern(v0,v2,v1))=Tern(Tern(v0,v2,v1),v0,Tern(
v3,v4,Tern(v0
,v2,v1))) by A3;
hence thesis by A1529;
end;
A1533: for v3,v4,v1,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),v3,Tern(v0,Tern(v0,v2,
v1),Tern(v3,v4
,Tern(v0,v2,v1))))=Tern(Tern(Tern(v0,v2,v1),v0,Tern(v3,Tern(v0,v2,v1),v4)),v3,
Tern(v0,v2
,v1))
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v3,v4,Tern(v0,v2,v1)),Tern(v0,v2,v1))=Tern(v0,Tern(v0,v2,v1),Tern(
v3,v4,Tern(v0
,v2,v1))) by A4;
hence thesis by A1531;
end;
A1535: for v3,v4,v1,v2,v0 holds
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),v3,Tern(v0,v1,Tern(v0,
v2,Tern(v3,v4
,Tern(v0,v2,v1)))))=Tern(Tern(Tern(v0,v2,v1),v0,Tern(v3,Tern(v0,v2,v1),v4)),v3,
Tern(v0,v2
,v1))
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v0,v2,v1),Tern(v3,v4,Tern(v0,v2,v1)))=Tern(v0,v1,Tern(v0,v2,Tern(
v3,v4,Tern(v0,v2
,v1)))) by A558;
hence thesis by A1533;
end;
A1537: for v3,v4,v1,v2,v0 holds
Tern(v3,Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),Tern(v0,v1,Tern(v0,
v2,Tern(v3,v4
,Tern(v0,v2,v1)))))=Tern(Tern(Tern(v0,v2,v1),v0,Tern(v3,Tern(v0,v2,v1),v4)),v3,
Tern(v0,v2
,v1))
proof let v3,v4,v1,v2,v0;
Tern(v3,Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),Tern(v0,v1,Tern(v0,
v2,Tern(v3,v4
,Tern(v0,v2,v1)))))=Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),v3,
Tern(v0,v1
,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))) by A3;
hence thesis by A1535;
end;
A1540: for v0,v4,v2,v3,v1 holds
Tern(v1,v2,Tern(v1,v3,Tern(v0,v4,Tern(v1,v3,v2))))=Tern(Tern(Tern(v1,v3,v2),v1
,Tern(v0,Tern(v1
,v3,v2),v4)),v0,Tern(v1,v3,v2))
proof let v0,v4,v2,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,Tern(v0,v4,Tern(v1,v3,v2)))),Tern(v1,v2,Tern(v1,
v3,Tern(v0,v4
,Tern(v1,v3,v2)))))=Tern(v1,v2,Tern(v1,v3,Tern(v0,v4,Tern(v1,v3,v2)))) by A34;
hence thesis by A1537;
end;
A1543: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(Tern(v0,v2,v1),v0
,Tern(v3,v4
,Tern(v0,v2,v1))),v3,Tern(v0,v2,v1))
proof let v3,v4,v1,v2,v0;
Tern(v3,Tern(v0,v2,v1),v4)=Tern(v3,v4,Tern(v0,v2,v1)) by A4;
hence thesis by A1540;
end;
A1545: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,Tern(v3,v4,
Tern(v0,v2,v1))
,Tern(v0,v2,v1)),v3,Tern(v0,v2,v1))
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v3,v4,Tern(v0,v2,v1)),Tern(v0,v2,v1))=Tern(Tern(v0,v2,v1),v0,Tern(
v3,v4,Tern(v0
,v2,v1))) by A3;
hence thesis by A1543;
end;
A1547: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,Tern(v0,v2,v1)
,Tern(v3,v4
,Tern(v0,v2,v1))),v3,Tern(v0,v2,v1))
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v3,v4,Tern(v0,v2,v1)),Tern(v0,v2,v1))=Tern(v0,Tern(v0,v2,v1),Tern(
v3,v4,Tern(v0
,v2,v1))) by A4;
hence thesis by A1545;
end;
A1549: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v1,Tern(v0,v2,
Tern(v3,v4,Tern(v0
,v2,v1)))),v3,Tern(v0,v2,v1))
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v0,v2,v1),Tern(v3,v4,Tern(v0,v2,v1)))=Tern(v0,v1,Tern(v0,v2,Tern(
v3,v4,Tern(v0,v2
,v1)))) by A558;
hence thesis by A1547;
end;
A1551: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v2,v1),Tern(v0
,v1,Tern(v0,v2
,Tern(v3,v4,Tern(v0,v2,v1)))),v3)
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),v3,Tern(v0,v2,v1))=Tern
(Tern(v0,v2,v1)
,Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),v3) by A3;
hence thesis by A1549;
end;
A1553: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(v3,Tern(v0,v2,v1),Tern
(v0,v1,Tern(v0
,v2,Tern(v3,v4,Tern(v0,v2,v1)))))
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v2,v1),Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1)))),v3)=Tern
(v3,Tern(v0,v2
,v1),Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))) by A3;
hence thesis by A1551;
end;
A1558: for v4,v2,v3,v100,v1 holds
Tern(v4,v100,Tern(v1,v2,Tern(v1,v100,v3)))=Tern(v100,Tern(v4,v1,v100),Tern(v1,
v2,v3))
proof let v4,v2,v3,v100,v1;
Tern(v100,Tern(v1,v2,v3),Tern(v4,v1,v100))=Tern(v4,v100,Tern(v1,v2,Tern(v1,v100
,v3)))
by A419;
hence thesis by A4;
end;
A1561: for v0,v3,v2,v4,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v4,v2)))=Tern(v1,Tern(v0,v2,v1),Tern(v2,v3,v4))
proof let v0,v3,v2,v4,v1;
Tern(v1,v4,v2)=Tern(v2,v1,v4) by A3;
hence thesis by A1558;
end;
A1563: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))=Tern(v1,Tern(v0,v2,v1),Tern(v2,v3,v4))
proof let v0,v3,v4,v2,v1;
Tern(v1,v4,v2)=Tern(v1,v2,v4) by A4;
hence thesis by A1561;
end;
A1565: for v0,v3,v4,v2,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v2,v4)))=Tern(v1,Tern(v0,v1,v2),Tern(v2,v3,v4))
proof let v0,v3,v4,v2,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A1563;
end;
A1570: for v104,v101,v3,v2,v103 holds
Tern(Tern(v103,v2,v3),v101,Tern(Tern(Tern(v103,v2,v3),v101,v104),Tern(v103,v2,
v3)
,Tern(Tern(v103,v2,v3),v103,v104)))=Tern(Tern(v103,v2,v3),Tern(Tern(v103,v2,v3)
,v101
,v104),Tern(v103,v2,Tern(v103,Tern(Tern(v103,v2,v3),v101,v104),v3)))
proof let v104,v101,v3,v2,v103;
Tern(Tern(Tern(v103,v2,v3),v101,v104),Tern(v103,v2,v3),Tern(Tern(v103,v2,v3),
v103
,Tern(Tern(v103,v2,v3),v101,v104)))=Tern(Tern(v103,v2,v3),Tern(Tern(v103,v2,v3)
,v101
,v104),Tern(v103,v2,Tern(v103,Tern(Tern(v103,v2,v3),v101,v104),v3))) by A419;
hence thesis by A162;
end;
A1573: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(Tern(v4,Tern(v0,v1,v2),v3),Tern(v0,v1,v2),Tern(
Tern(v0,v1,v2),v0
,v4)))=Tern(Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,Tern(v0,Tern(
Tern(v0,v1,v2)
,v3,v4),v2)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),v3,v4)=Tern(v4,Tern(v0,v1,v2),v3) by A3;
hence thesis by A1570;
end;
A1575: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2),Tern(
Tern(v0,v1,v2),v0
,v4)))=Tern(Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,Tern(v0,Tern(
Tern(v0,v1,v2)
,v3,v4),v2)))
proof let v3,v4,v2,v1,v0;
Tern(v4,Tern(v0,v1,v2),v3)=Tern(v3,v4,Tern(v0,v1,v2)) by A3;
hence thesis by A1573;
end;
A1577: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2),Tern(v4,
Tern(v0,v1,v2)
,v0)))=Tern(Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,Tern(v0,Tern(
Tern(v0,v1,v2)
,v3,v4),v2)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),v0,v4)=Tern(v4,Tern(v0,v1,v2),v0) by A3;
hence thesis by A1575;
end;
A1579: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,v2),Tern(v0,
v4,Tern(v0,v1
,v2))))=Tern(Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,Tern(v0,Tern(
Tern(v0,v1,v2)
,v3,v4),v2)))
proof let v3,v4,v2,v1,v0;
Tern(v4,Tern(v0,v1,v2),v0)=Tern(v0,v4,Tern(v0,v1,v2)) by A3;
hence thesis by A1577;
end;
A1581: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(Tern(v0,v1,v2),Tern(v0,v4,Tern(v0,v1,v2)),Tern(v3,
v4,Tern(v0,v1
,v2))))=Tern(Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,Tern(v0,Tern(
Tern(v0,v1,v2)
,v3,v4),v2)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v4,Tern(v0,v1,v2)),Tern(v3,v4,Tern(v0,v1,v2)))=Tern
(Tern(v3,v4
,Tern(v0,v1,v2)),Tern(v0,v1,v2),Tern(v0,v4,Tern(v0,v1,v2))) by A3;
hence thesis by A1579;
end;
A1583: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2))))=
Tern(Tern(v0,v1
,v2),Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,Tern(v0,Tern(Tern(v0,v1,v2),v3,v4),
v2)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v4,Tern(v0,v1,v2)),Tern(v3,v4,Tern(v0,v1,v2)))=Tern
(v0,Tern(v0,v1
,v2),Tern(v3,v4,Tern(v0,v1,v2))) by A1269;
hence thesis by A1581;
end;
A1585: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2)))))=
Tern(Tern(v0,v1
,v2),Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,Tern(v0,Tern(Tern(v0,v1,v2),v3,v4),
v2)))
proof let v3,v4,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)))=Tern(v0,v2,Tern(v0,v1,Tern(
v3,v4,Tern(v0,v1
,v2)))) by A558;
hence thesis by A1583;
end;
A1587: for v3,v4,v2,v1,v0 holds
Tern(v3,Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2)))),Tern(v0,v1,v2))=
Tern(Tern(v0,v1
,v2),Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,Tern(v0,Tern(Tern(v0,v1,v2),v3,v4),
v2)))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2)))),Tern(v0,v1,v2))=Tern
(Tern(v0,v1,v2)
,v3,Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2))))) by A3;
hence thesis by A1585;
end;
A1590: for v0,v4,v2,v3,v1 holds
Tern(v0,Tern(v1,v3,v2),Tern(v1,v2,Tern(v1,v3,Tern(v0,v4,Tern(v1,v3,v2)))))=
Tern(Tern(v1,v3
,v2),Tern(Tern(v1,v3,v2),v0,v4),Tern(v1,v3,Tern(v1,Tern(Tern(v1,v3,v2),v0,v4),
v2)))
proof let v0,v4,v2,v3,v1;
Tern(v0,Tern(v1,v2,Tern(v1,v3,Tern(v0,v4,Tern(v1,v3,v2)))),Tern(v1,v3,v2))=Tern
(v0,Tern(v1,v3
,v2),Tern(v1,v2,Tern(v1,v3,Tern(v0,v4,Tern(v1,v3,v2))))) by A4;
hence thesis by A1587;
end;
A1593: for v0,v4,v3,v2,v1 holds
Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3))))=Tern(Tern(v1,v2,v3),Tern(
Tern(v1,v2,v3),v0
,v4),Tern(v1,v2,Tern(v1,Tern(Tern(v1,v2,v3),v0,v4),v3)))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3)))))=Tern
(v1,v3,Tern(v1
,v2,Tern(v0,v4,Tern(v1,v2,v3)))) by A1553;
hence thesis by A1590;
end;
A1596: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v2,v1),Tern(v4
,Tern(v0,v2,v1)
,v3),Tern(v0,v2,Tern(v0,Tern(Tern(v0,v2,v1),v3,v4),v1)))
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v2,v1),v3,v4)=Tern(v4,Tern(v0,v2,v1),v3) by A3;
hence thesis by A1593;
end;
A1598: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v2,v1),Tern(v3
,v4,Tern(v0,v2
,v1)),Tern(v0,v2,Tern(v0,Tern(Tern(v0,v2,v1),v3,v4),v1)))
proof let v3,v4,v1,v2,v0;
Tern(v4,Tern(v0,v2,v1),v3)=Tern(v3,v4,Tern(v0,v2,v1)) by A3;
hence thesis by A1596;
end;
A1600: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v2,v1),Tern(v3
,v4,Tern(v0,v2
,v1)),Tern(v0,v2,Tern(v0,Tern(v4,Tern(v0,v2,v1),v3),v1)))
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v2,v1),v3,v4)=Tern(v4,Tern(v0,v2,v1),v3) by A3;
hence thesis by A1598;
end;
A1602: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v2,v1),Tern(v3
,v4,Tern(v0,v2
,v1)),Tern(v0,v2,Tern(v0,Tern(v3,v4,Tern(v0,v2,v1)),v1)))
proof let v3,v4,v1,v2,v0;
Tern(v4,Tern(v0,v2,v1),v3)=Tern(v3,v4,Tern(v0,v2,v1)) by A3;
hence thesis by A1600;
end;
A1604: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v2,v1),Tern(v3
,v4,Tern(v0,v2
,v1)),Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v2,v1)))))
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v3,v4,Tern(v0,v2,v1)),v1)=Tern(v0,v1,Tern(v3,v4,Tern(v0,v2,v1)))
by A4;
hence thesis by A1602;
end;
A1609: for v4,v103,v102,v3,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v4,v1,v102),Tern(v102,Tern(v4,v1,v102),Tern(v102,Tern
(v1,v2,v3)
,v103)))=Tern(v4,v102,Tern(v1,v2,Tern(v1,v102,v3)))
proof let v4,v103,v102,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v4,v1,v102))=Tern(v4,v102,Tern(v1,v2,Tern(v1,v102
,v3)))
by A419;
hence thesis by A693;
end;
A1612: for v3,v5,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v4,v3),Tern(v4,Tern(v3,v0,v4),Tern(v4,Tern(v0,v1,
v2)
,v5)))=Tern(v3,v4,Tern(v0,v1,Tern(v0,v4,v2)))
proof let v3,v5,v4,v2,v1,v0;
Tern(v0,v4,v3)=Tern(v3,v0,v4) by A3;
hence thesis by A1609;
end;
A1615: for v4,v5,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v4,v3),Tern(v3,Tern(v4,v0,v3),Tern(v3,Tern(v0,v1,
v2)
,v5)))=Tern(v4,v3,Tern(v0,v1,Tern(v0,v3,v2)))
proof let v4,v5,v3,v2,v1,v0;
Tern(v0,v3,v4)=Tern(v0,v4,v3) by A4;
hence thesis by A1612;
end;
A1618: for v3,v5,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,v4),Tern(v4,Tern(v0,v4,v3),Tern(v4,Tern(v0,v1,
v2)
,v5)))=Tern(v3,v4,Tern(v0,v1,Tern(v0,v4,v2)))
proof let v3,v5,v4,v2,v1,v0;
Tern(v0,v4,v3)=Tern(v3,v0,v4) by A3;
hence thesis by A1615;
end;
A1620: for v3,v5,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,v4),Tern(v4,Tern(v0,v3,v4),Tern(v4,Tern(v0,v1,
v2)
,v5)))=Tern(v3,v4,Tern(v0,v1,Tern(v0,v4,v2)))
proof let v3,v5,v4,v2,v1,v0;
Tern(v0,v4,v3)=Tern(v0,v3,v4) by A4;
hence thesis by A1618;
end;
A1622: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,v4),Tern(v4,Tern(v0,v3,v4),Tern(v4,v5,Tern(v0,
v1
,v2))))=Tern(v3,v4,Tern(v0,v1,Tern(v0,v4,v2)))
proof let v3,v4,v5,v2,v1,v0;
Tern(v4,Tern(v0,v1,v2),v5)=Tern(v4,v5,Tern(v0,v1,v2)) by A4;
hence thesis by A1620;
end;
A1624: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,v4),Tern(v4,Tern(v0,v3,v4),Tern(v4,v5,Tern(v0,
v1
,v2))))=Tern(v3,v4,Tern(v0,v1,Tern(v0,v2,v4)))
proof let v3,v4,v5,v2,v1,v0;
Tern(v0,v4,v2)=Tern(v0,v2,v4) by A4;
hence thesis by A1622;
end;
A1627: for v102,v2,v3,v105,v104,v103 holds
Tern(Tern(v103,v104,v105),Tern(v102,v2,v3),Tern(Tern(v103,v104,v105),v102,Tern
(v103
,v104,Tern(Tern(v103,v104,v105),v103,v105))))=Tern(Tern(v103,v104,v105),v103
,Tern(Tern(v103,v104,v105),Tern(v103,v104,v105),Tern(v102,v2,Tern(v102,Tern(
v103,v104
,v105),v3))))
proof let v102,v2,v3,v105,v104,v103;
Tern(Tern(v103,v104,v105),Tern(v102,v2,v3),Tern(Tern(v103,v104,v105),v102,Tern(
v103,v104
,v105)))=Tern(Tern(v103,v104,v105),Tern(v103,v104,v105),Tern(v102,v2,Tern(v102,
Tern(v103
,v104,v105),v3))) by A419;
hence thesis by A189;
end;
A1630: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,Tern(v2,
Tern(v0,v1,v2)
,v0))))=Tern(Tern(v0,v1,v2),v0,Tern(Tern(v0,v1,v2),Tern(v0,v1,v2),Tern(v3,v4,
Tern(v3,Tern(v0
,v1,v2),v5))))
proof let v3,v4,v5,v2,v1,v0;
Tern(Tern(v0,v1,v2),v0,v2)=Tern(v2,Tern(v0,v1,v2),v0) by A3;
hence thesis by A1627;
end;
A1632: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,Tern(v0,
v2,Tern(v0,v1
,v2)))))=Tern(Tern(v0,v1,v2),v0,Tern(Tern(v0,v1,v2),Tern(v0,v1,v2),Tern(v3,v4,
Tern(v3,Tern(v0
,v1,v2),v5))))
proof let v3,v4,v5,v2,v1,v0;
Tern(v2,Tern(v0,v1,v2),v0)=Tern(v0,v2,Tern(v0,v1,v2)) by A3;
hence thesis by A1630;
end;
A1634: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,Tern(v0,
v1
,v2))))=Tern(Tern(v0,v1,v2),v0,Tern(Tern(v0,v1,v2),Tern(v0,v1,v2),Tern(v3,v4,
Tern(v3,Tern(v0
,v1,v2),v5))))
proof let v3,v4,v5,v2,v1,v0;
Tern(v0,v2,Tern(v0,v1,v2))=Tern(v0,v1,v2) by A63;
hence thesis by A1632;
end;
A1636: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,v2)))=
Tern(Tern(v0,v1
,v2),v0,Tern(Tern(v0,v1,v2),Tern(v0,v1,v2),Tern(v3,v4,Tern(v3,Tern(v0,v1,v2),v5
))))
proof let v3,v4,v5,v2,v1,v0;
Tern(v0,v1,Tern(v0,v1,v2))=Tern(v0,v1,v2) by A74;
hence thesis by A1634;
end;
A1638: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v2)))=
Tern(Tern(v0,v1
,v2),v0,Tern(Tern(v0,v1,v2),Tern(v0,v1,v2),Tern(v3,v4,Tern(v3,Tern(v0,v1,v2),v5
))))
proof let v3,v4,v5,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,v2))
by A3;
hence thesis by A1636;
end;
A1640: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v0,Tern
(Tern(v0,v1,v2)
,Tern(v0,v1,v2),Tern(v3,v4,Tern(v3,Tern(v0,v1,v2),v5))))
proof let v3,v4,v5,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v2))=Tern(v0,v1,v2) by A34;
hence thesis by A1638;
end;
A1642: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v0,Tern
(Tern(v0,v1,v2)
,Tern(v0,v1,v2),Tern(v3,v4,Tern(v3,v5,Tern(v0,v1,v2)))))
proof let v3,v4,v5,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),v5)=Tern(v3,v5,Tern(v0,v1,v2)) by A4;
hence thesis by A1640;
end;
A1644: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v0,Tern
(v0,v1,v2))
proof let v3,v4,v5,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v1,v2),Tern(v3,v4,Tern(v3,v5,Tern(v0,v1,v2))))=Tern
(v0,v1,v2)
by A2;
hence thesis by A1642;
end;
A1646: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(v0,v1,v2))=Tern(v0,Tern(v0,v1,v2),Tern
(v0,v1,v2))
proof let v3,v4,v5,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v0,Tern(v0,v1,v2))
by A3;
hence thesis by A1644;
end;
A1648: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,v5),Tern(v0,v1,v2))=Tern(v0,v1,v2)
proof let v3,v4,v5,v2,v1,v0;
Tern(v0,Tern(v0,v1,v2),Tern(v0,v1,v2))=Tern(v0,v1,v2) by A34;
hence thesis by A1646;
end;
A1651: for v104,v103,v3,v2,v102 holds
Tern(Tern(v102,v2,v3),Tern(Tern(v102,v2,v3),v103,v104),Tern(v102,v2,Tern(v102,
Tern(Tern(v102
,v2,v3),v103,v104),v3)))=Tern(Tern(Tern(v102,v2,v3),v103,v104),Tern(v102,v2,v3)
,Tern(Tern(v102,v2,v3),v104,Tern(Tern(v102,v2,v3),v102,v103)))
proof let v104,v103,v3,v2,v102;
Tern(Tern(Tern(v102,v2,v3),v103,v104),Tern(v102,v2,v3),Tern(Tern(v102,v2,v3),
v102
,Tern(Tern(v102,v2,v3),v103,v104)))=Tern(Tern(v102,v2,v3),Tern(Tern(v102,v2,v3)
,v103
,v104),Tern(v102,v2,Tern(v102,Tern(Tern(v102,v2,v3),v103,v104),v3))) by A419;
hence thesis by A296;
end;
A1654: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v4,Tern(v0,v1,v2),v3),Tern(v0,v1,Tern(v0,Tern(Tern(v0
,v1,v2),v3,v4)
,v2)))=Tern(Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v4,
Tern(Tern(v0,v1
,v2),v0,v3)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),v3,v4)=Tern(v4,Tern(v0,v1,v2),v3) by A3;
hence thesis by A1651;
end;
A1657: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v4,v3,Tern(v0,v1,v2)),Tern(v0,v1,Tern(v0,Tern(Tern(v0
,v1,v2),v4,v3)
,v2)))=Tern(Tern(Tern(v0,v1,v2),v4,v3),Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v3,
Tern(Tern(v0,v1
,v2),v0,v4)))
proof let v4,v3,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),v4)=Tern(v4,v3,Tern(v0,v1,v2)) by A3;
hence thesis by A1654;
end;
A1660: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,Tern(v0,Tern(v4,Tern
(v0,v1,v2),v3)
,v2)))=Tern(Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v4,
Tern(Tern(v0,v1
,v2),v0,v3)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),v3,v4)=Tern(v4,Tern(v0,v1,v2),v3) by A3;
hence thesis by A1657;
end;
A1662: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,Tern(v0,Tern(v3,v4,
Tern(v0,v1,v2))
,v2)))=Tern(Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v4,
Tern(Tern(v0,v1
,v2),v0,v3)))
proof let v3,v4,v2,v1,v0;
Tern(v4,Tern(v0,v1,v2),v3)=Tern(v3,v4,Tern(v0,v1,v2)) by A3;
hence thesis by A1660;
end;
A1664: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,Tern(v0,v2,Tern(v3,
v4,Tern(v0,v1
,v2)))))=Tern(Tern(Tern(v0,v1,v2),v3,v4),Tern(v0,v1,v2),Tern(Tern(v0,v1,v2),v4,
Tern(Tern(v0,v1
,v2),v0,v3)))
proof let v3,v4,v2,v1,v0;
Tern(v0,Tern(v3,v4,Tern(v0,v1,v2)),v2)=Tern(v0,v2,Tern(v3,v4,Tern(v0,v1,v2)))
by A4;
hence thesis by A1662;
end;
A1666: for v3,v4,v2,v1,v0 holds
Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2))))=Tern(Tern(Tern(v0,v1,v2),v3
,v4),Tern(v0,v1
,v2),Tern(Tern(v0,v1,v2),v4,Tern(Tern(v0,v1,v2),v0,v3)))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v2)),Tern(v0,v1,Tern(v0,v2,Tern(v3,v4
,Tern(v0,v1
,v2)))))=Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2)))) by A1604;
hence thesis by A1664;
end;
A1669: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v4,Tern(v0,v2,v1)
,v3),Tern(v0,v2
,v1),Tern(Tern(v0,v2,v1),v4,Tern(Tern(v0,v2,v1),v0,v3)))
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v2,v1),v3,v4)=Tern(v4,Tern(v0,v2,v1),v3) by A3;
hence thesis by A1666;
end;
A1671: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v3,v4,Tern(v0,v2,
v1)),Tern(v0,v2
,v1),Tern(Tern(v0,v2,v1),v4,Tern(Tern(v0,v2,v1),v0,v3)))
proof let v3,v4,v1,v2,v0;
Tern(v4,Tern(v0,v2,v1),v3)=Tern(v3,v4,Tern(v0,v2,v1)) by A3;
hence thesis by A1669;
end;
A1673: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v3,v4,Tern(v0,v2,
v1)),Tern(v0,v2
,v1),Tern(Tern(v0,v2,v1),v4,Tern(v3,Tern(v0,v2,v1),v0)))
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v2,v1),v0,v3)=Tern(v3,Tern(v0,v2,v1),v0) by A3;
hence thesis by A1671;
end;
A1675: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v3,v4,Tern(v0,v2,
v1)),Tern(v0,v2
,v1),Tern(Tern(v0,v2,v1),v4,Tern(v0,v3,Tern(v0,v2,v1))))
proof let v3,v4,v1,v2,v0;
Tern(v3,Tern(v0,v2,v1),v0)=Tern(v0,v3,Tern(v0,v2,v1)) by A3;
hence thesis by A1673;
end;
A1677: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v3,v4,Tern(v0,v2,
v1)),Tern(v0,v2
,v1),Tern(v4,Tern(v0,v3,Tern(v0,v2,v1)),Tern(v0,v2,v1)))
proof let v3,v4,v1,v2,v0;
Tern(v4,Tern(v0,v3,Tern(v0,v2,v1)),Tern(v0,v2,v1))=Tern(Tern(v0,v2,v1),v4,Tern(
v0,v3,Tern(v0
,v2,v1))) by A3;
hence thesis by A1675;
end;
A1679: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v3,v4,Tern(v0,v2,
v1)),Tern(v0,v2
,v1),Tern(v4,Tern(v0,v2,v1),Tern(v0,v3,Tern(v0,v2,v1))))
proof let v3,v4,v1,v2,v0;
Tern(v4,Tern(v0,v3,Tern(v0,v2,v1)),Tern(v0,v2,v1))=Tern(v4,Tern(v0,v2,v1),Tern(
v0,v3,Tern(v0
,v2,v1))) by A4;
hence thesis by A1677;
end;
A1681: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v2,v1),Tern(v4
,Tern(v0,v2,v1)
,Tern(v0,v3,Tern(v0,v2,v1))),Tern(v3,v4,Tern(v0,v2,v1)))
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v2,v1),Tern(v4,Tern(v0,v2,v1),Tern(v0,v3,Tern(v0,v2,v1))),Tern(v3,
v4,Tern(v0,v2
,v1)))=Tern(Tern(v3,v4,Tern(v0,v2,v1)),Tern(v0,v2,v1),Tern(v4,Tern(v0,v2,v1),
Tern(v0,v3
,Tern(v0,v2,v1)))) by A3;
hence thesis by A1679;
end;
A1683: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(Tern(v0,v2,v1),Tern(v3
,v4,Tern(v0,v2
,v1)),Tern(v4,Tern(v0,v2,v1),Tern(v0,v3,Tern(v0,v2,v1))))
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v2,v1),Tern(v4,Tern(v0,v2,v1),Tern(v0,v3,Tern(v0,v2,v1))),Tern(v3,
v4,Tern(v0,v2
,v1)))=Tern(Tern(v0,v2,v1),Tern(v3,v4,Tern(v0,v2,v1)),Tern(v4,Tern(v0,v2,v1),
Tern(v0,v3
,Tern(v0,v2,v1)))) by A4;
hence thesis by A1681;
end;
A1685: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(v3,Tern(v0,v2,v1),Tern
(v4,Tern(v0,v2
,v1),Tern(v0,v3,Tern(v0,v2,v1))))
proof let v3,v4,v1,v2,v0;
Tern(Tern(v0,v2,v1),Tern(v3,v4,Tern(v0,v2,v1)),Tern(v4,Tern(v0,v2,v1),Tern(v0,
v3,Tern(v0,v2
,v1))))=Tern(v3,Tern(v0,v2,v1),Tern(v4,Tern(v0,v2,v1),Tern(v0,v3,Tern(v0,v2,v1)
))) by
A1252;
hence thesis by A1683;
end;
A1689: for v1,v4,v3,v2,v0 holds
Tern(v3,v4,Tern(v0,v1,Tern(v0,Tern(v0,v2,v3),v4)))=Tern(v0,v3,v4)
proof
now let v4,v5,v1,v3,v2,v0;
Tern(Tern(v0,v1,Tern(v0,v2,v3)),Tern(v0,v3,v4),Tern(v4,Tern(v0,v3,v4),Tern(v4,
v5,Tern(v0,v1
,Tern(v0,v2,v3)))))=Tern(v3,v4,Tern(v0,v1,Tern(v0,Tern(v0,v2,v3),v4))) by A1624
;
hence Tern(v3,v4,Tern(v0,v1,Tern(v0,Tern(v0,v2,v3),v4)))=Tern(v0,v3,v4) by
A1466;
end;
hence thesis;
end;
A1692: for v3,v1,v0,v4,v2 holds
Tern(v0,v1,Tern(v2,v3,Tern(v2,v1,Tern(v2,v4,v0))))=Tern(v2,v0,v1)
proof let v3,v1,v0,v4,v2;
Tern(v2,Tern(v2,v4,v0),v1)=Tern(v2,v1,Tern(v2,v4,v0)) by A4;
hence thesis by A1689;
end;
A1695: for v103,v104,v101,v5,v4,v3 holds
Tern(Tern(Tern(v3,v4,v5),v103,Tern(v101,Tern(v3,v4,v5),v104)),v101,Tern(Tern(
v3,v4,v5)
,v103,Tern(v101,Tern(v3,v4,v5),v104)))=Tern(Tern(Tern(v3,v4,v5),v103,Tern(v101,
Tern(v3,v4
,v5),v104)),v101,Tern(v3,v4,v5))
proof let v103,v104,v101,v5,v4,v3;
Tern(Tern(Tern(v3,v4,v5),v103,Tern(v101,Tern(v3,v4,v5),v104)),Tern(v3,v4,v5),
Tern(Tern(v3,v4
,v5),v103,Tern(v101,Tern(v3,v4,v5),v104)))=Tern(Tern(v3,v4,v5),v103,Tern(v101,
Tern(v3,v4
,v5),v104)) by A1648;
hence thesis by A632;
end;
A1698: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(Tern(v0,v1,v2),v3,Tern(v4,v5,Tern(v0,v1,v2))),v4,Tern(Tern(v0,v1,v2)
,v3,Tern(v4
,Tern(v0,v1,v2),v5)))=Tern(Tern(Tern(v0,v1,v2),v3,Tern(v4,Tern(v0,v1,v2),v5)),
v4,Tern(v0,v1
,v2))
proof let v3,v4,v5,v2,v1,v0;
Tern(v4,Tern(v0,v1,v2),v5)=Tern(v4,v5,Tern(v0,v1,v2)) by A4;
hence thesis by A1695;
end;
A1700: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v3,Tern(v4,v5,Tern(v0,v1,v2)),Tern(v0,v1,v2)),v4,Tern(Tern(v0,v1,v2)
,v3,Tern(v4
,Tern(v0,v1,v2),v5)))=Tern(Tern(Tern(v0,v1,v2),v3,Tern(v4,Tern(v0,v1,v2),v5)),
v4,Tern(v0,v1
,v2))
proof let v3,v4,v5,v2,v1,v0;
Tern(v3,Tern(v4,v5,Tern(v0,v1,v2)),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v3,Tern(
v4,v5,Tern(v0
,v1,v2))) by A3;
hence thesis by A1698;
end;
A1703: for v0,v1,v2,v5,v4,v3 holds
Tern(Tern(v0,Tern(v3,v4,v5),Tern(v1,v2,Tern(v3,v4,v5))),v1,Tern(Tern(v3,v4,v5)
,v0,Tern(v1
,Tern(v3,v4,v5),v2)))=Tern(Tern(Tern(v3,v4,v5),v0,Tern(v1,Tern(v3,v4,v5),v2)),
v1,Tern(v3,v4
,v5))
proof let v0,v1,v2,v5,v4,v3;
Tern(v0,Tern(v1,v2,Tern(v3,v4,v5)),Tern(v3,v4,v5))=Tern(v0,Tern(v3,v4,v5),Tern(
v1,v2,Tern(v3
,v4,v5))) by A4;
hence thesis by A1700;
end;
A1706: for v0,v4,v5,v3,v2,v1 holds
Tern(Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),v4,Tern(Tern(v1,v2,v3)
,v0,Tern(v4,v5
,Tern(v1,v2,v3))))=Tern(Tern(Tern(v1,v2,v3),v0,Tern(v4,Tern(v1,v2,v3),v5)),v4,
Tern(v1,v2
,v3))
proof let v0,v4,v5,v3,v2,v1;
Tern(v4,Tern(v1,v2,v3),v5)=Tern(v4,v5,Tern(v1,v2,v3)) by A4;
hence thesis by A1703;
end;
A1708: for v0,v4,v5,v3,v2,v1 holds
Tern(Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),v4,Tern(v0,Tern(v4,v5,
Tern(v1,v2,v3))
,Tern(v1,v2,v3)))=Tern(Tern(Tern(v1,v2,v3),v0,Tern(v4,Tern(v1,v2,v3),v5)),v4,
Tern(v1,v2
,v3))
proof let v0,v4,v5,v3,v2,v1;
Tern(v0,Tern(v4,v5,Tern(v1,v2,v3)),Tern(v1,v2,v3))=Tern(Tern(v1,v2,v3),v0,Tern(
v4,v5,Tern(v1
,v2,v3))) by A3;
hence thesis by A1706;
end;
A1710: for v0,v4,v5,v3,v2,v1 holds
Tern(Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),v4,Tern(v0,Tern(v1,v2,
v3),Tern(v4,v5
,Tern(v1,v2,v3))))=Tern(Tern(Tern(v1,v2,v3),v0,Tern(v4,Tern(v1,v2,v3),v5)),v4,
Tern(v1,v2
,v3))
proof let v0,v4,v5,v3,v2,v1;
Tern(v0,Tern(v4,v5,Tern(v1,v2,v3)),Tern(v1,v2,v3))=Tern(v0,Tern(v1,v2,v3),Tern(
v4,v5,Tern(v1
,v2,v3))) by A4;
hence thesis by A1708;
end;
A1712: for v0,v4,v5,v3,v2,v1 holds
Tern(v4,Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),Tern(v0,Tern(v1,v2,
v3),Tern(v4,v5
,Tern(v1,v2,v3))))=Tern(Tern(Tern(v1,v2,v3),v0,Tern(v4,Tern(v1,v2,v3),v5)),v4,
Tern(v1,v2
,v3))
proof let v0,v4,v5,v3,v2,v1;
Tern(v4,Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),Tern(v0,Tern(v1,v2,
v3),Tern(v4,v5
,Tern(v1,v2,v3))))=Tern(Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),v4,
Tern(v0,Tern(v1
,v2,v3),Tern(v4,v5,Tern(v1,v2,v3)))) by A3;
hence thesis by A1710;
end;
A1715: for v1,v0,v5,v4,v3,v2 holds
Tern(v1,Tern(v2,v3,v4),Tern(v0,v5,Tern(v2,v3,v4)))=Tern(Tern(Tern(v2,v3,v4),v1
,Tern(v0,Tern(v2
,v3,v4),v5)),v0,Tern(v2,v3,v4))
proof let v1,v0,v5,v4,v3,v2;
Tern(v0,Tern(v1,Tern(v2,v3,v4),Tern(v0,v5,Tern(v2,v3,v4))),Tern(v1,Tern(v2,v3,
v4),Tern(v0,v5
,Tern(v2,v3,v4))))=Tern(v1,Tern(v2,v3,v4),Tern(v0,v5,Tern(v2,v3,v4))) by A34;
hence thesis by A1712;
end;
A1718: for v0,v4,v5,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3)))=Tern(Tern(Tern(v1,v2,v3),v0
,Tern(v4,v5
,Tern(v1,v2,v3))),v4,Tern(v1,v2,v3))
proof let v0,v4,v5,v3,v2,v1;
Tern(v4,Tern(v1,v2,v3),v5)=Tern(v4,v5,Tern(v1,v2,v3)) by A4;
hence thesis by A1715;
end;
A1720: for v0,v4,v5,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3)))=Tern(Tern(v0,Tern(v4,v5,
Tern(v1,v2,v3))
,Tern(v1,v2,v3)),v4,Tern(v1,v2,v3))
proof let v0,v4,v5,v3,v2,v1;
Tern(v0,Tern(v4,v5,Tern(v1,v2,v3)),Tern(v1,v2,v3))=Tern(Tern(v1,v2,v3),v0,Tern(
v4,v5,Tern(v1
,v2,v3))) by A3;
hence thesis by A1718;
end;
A1722: for v0,v4,v5,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3)))=Tern(Tern(v0,Tern(v1,v2,v3)
,Tern(v4,v5
,Tern(v1,v2,v3))),v4,Tern(v1,v2,v3))
proof let v0,v4,v5,v3,v2,v1;
Tern(v0,Tern(v4,v5,Tern(v1,v2,v3)),Tern(v1,v2,v3))=Tern(v0,Tern(v1,v2,v3),Tern(
v4,v5,Tern(v1
,v2,v3))) by A4;
hence thesis by A1720;
end;
A1724: for v0,v4,v5,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3)))=Tern(Tern(v1,v2,v3),Tern(v0
,Tern(v1,v2,v3)
,Tern(v4,v5,Tern(v1,v2,v3))),v4)
proof let v0,v4,v5,v3,v2,v1;
Tern(Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),v4,Tern(v1,v2,v3))=Tern
(Tern(v1,v2,v3)
,Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),v4) by A3;
hence thesis by A1722;
end;
A1726: for v0,v4,v5,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3)))=Tern(v4,Tern(v1,v2,v3),Tern
(v0,Tern(v1,v2
,v3),Tern(v4,v5,Tern(v1,v2,v3))))
proof let v0,v4,v5,v3,v2,v1;
Tern(Tern(v1,v2,v3),Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3))),v4)=Tern
(v4,Tern(v1,v2
,v3),Tern(v0,Tern(v1,v2,v3),Tern(v4,v5,Tern(v1,v2,v3)))) by A3;
hence thesis by A1724;
end;
A1731: for v103,v104,v102,v5,v4,v3 holds
Tern(v102,v103,Tern(Tern(v3,v4,v5),v102,v104))=Tern(Tern(v102,v103,Tern(Tern(
v3,v4,v5)
,v102,v104)),Tern(v3,v4,v5),Tern(Tern(v3,v4,v5),v102,Tern(v102,v103,v104)))
proof let v103,v104,v102,v5,v4,v3;
Tern(Tern(v102,v103,Tern(Tern(v3,v4,v5),v102,v104)),Tern(v3,v4,v5),Tern(v102,
v103,Tern(Tern(v3
,v4,v5),v102,v104)))=Tern(v102,v103,Tern(Tern(v3,v4,v5),v102,v104)) by A1648;
hence thesis by A289;
end;
A1734: for v1,v0,v5,v4,v3,v2 holds
Tern(v0,v1,Tern(v5,Tern(v2,v3,v4),v0))=Tern(Tern(v0,v1,Tern(Tern(v2,v3,v4),v0,
v5)),Tern(v2,v3
,v4),Tern(Tern(v2,v3,v4),v0,Tern(v0,v1,v5)))
proof let v1,v0,v5,v4,v3,v2;
Tern(Tern(v2,v3,v4),v0,v5)=Tern(v5,Tern(v2,v3,v4),v0) by A3;
hence thesis by A1731;
end;
A1737: for v1,v0,v2,v5,v4,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5)))=Tern(Tern(v0,v1,Tern(Tern(v3,v4,v5),v0,
v2)),Tern(v3,v4
,v5),Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2)))
proof let v1,v0,v2,v5,v4,v3;
Tern(v2,Tern(v3,v4,v5),v0)=Tern(v0,v2,Tern(v3,v4,v5)) by A3;
hence thesis by A1734;
end;
A1739: for v1,v0,v2,v5,v4,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5)))=Tern(Tern(v0,v1,Tern(v2,Tern(v3,v4,v5),
v0)),Tern(v3,v4
,v5),Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2)))
proof let v1,v0,v2,v5,v4,v3;
Tern(Tern(v3,v4,v5),v0,v2)=Tern(v2,Tern(v3,v4,v5),v0) by A3;
hence thesis by A1737;
end;
A1741: for v1,v0,v2,v5,v4,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5)))=Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,
v5))),Tern(v3,v4
,v5),Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2)))
proof let v1,v0,v2,v5,v4,v3;
Tern(v2,Tern(v3,v4,v5),v0)=Tern(v0,v2,Tern(v3,v4,v5)) by A3;
hence thesis by A1739;
end;
A1743: for v1,v0,v2,v5,v4,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5)))=Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,
v5))),Tern(v3,v4
,v5),Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5)))
proof let v1,v0,v2,v5,v4,v3;
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5))=Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2))
by A3;
hence thesis by A1741;
end;
A1745: for v1,v0,v2,v5,v4,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5)))=Tern(Tern(v3,v4,v5),Tern(v0,Tern(v0,v1,
v2),Tern(v3,v4
,v5)),Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5))))
proof let v1,v0,v2,v5,v4,v3;
Tern(Tern(v3,v4,v5),Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5)),Tern(v0,v1,Tern(v0,
v2,Tern(v3,v4
,v5))))=Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5))),Tern(v3,v4,v5),Tern(v0,Tern
(v0,v1,v2)
,Tern(v3,v4,v5))) by A3;
hence thesis by A1743;
end;
A1747: for v1,v0,v2,v5,v4,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5)))=Tern(Tern(v3,v4,v5),Tern(v0,v1,Tern(v0,
v2,Tern(v3,v4
,v5))),Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5)))
proof let v1,v0,v2,v5,v4,v3;
Tern(Tern(v3,v4,v5),Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5)),Tern(v0,v1,Tern(v0,
v2,Tern(v3,v4
,v5))))=Tern(Tern(v3,v4,v5),Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5))),Tern(v0,Tern
(v0,v1,v2)
,Tern(v3,v4,v5))) by A4;
hence thesis by A1745;
end;
A1752: for v103,v104,v102,v5,v4,v3 holds
Tern(Tern(Tern(v3,v4,v5),v102,Tern(v102,v103,v104)),Tern(v3,v4,v5),Tern(v102,
v103
,Tern(Tern(v3,v4,v5),v102,v104)))=Tern(Tern(v3,v4,v5),v102,Tern(v102,v103,v104)
)
proof let v103,v104,v102,v5,v4,v3;
Tern(Tern(Tern(v3,v4,v5),v102,Tern(v102,v103,v104)),Tern(v3,v4,v5),Tern(Tern(v3
,v4,v5),v102
,Tern(v102,v103,v104)))=Tern(Tern(v3,v4,v5),v102,Tern(v102,v103,v104)) by A1648
;
hence thesis by A289;
end;
A1755: for v0,v1,v2,v5,v4,v3 holds
Tern(Tern(v3,Tern(v3,v4,v5),Tern(v0,v1,v2)),Tern(v0,v1,v2),Tern(v3,v4,Tern(
Tern(v0,v1,v2),v3
,v5)))=Tern(Tern(v0,v1,v2),v3,Tern(v3,v4,v5))
proof let v0,v1,v2,v5,v4,v3;
Tern(v3,Tern(v3,v4,v5),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v3,Tern(v3,v4,v5))
by A3;
hence thesis by A1752;
end;
A1758: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5)),Tern(v3,v4,v5),Tern(v0,v1,Tern(v2,
Tern(v3,v4,v5)
,v0)))=Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2))
proof let v3,v4,v5,v2,v1,v0;
Tern(Tern(v3,v4,v5),v0,v2)=Tern(v2,Tern(v3,v4,v5),v0) by A3;
hence thesis by A1755;
end;
A1760: for v3,v4,v5,v2,v1,v0 holds
Tern(Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5)),Tern(v3,v4,v5),Tern(v0,v1,Tern(v0,
v2,Tern(v3,v4
,v5))))=Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2))
proof let v3,v4,v5,v2,v1,v0;
Tern(v2,Tern(v3,v4,v5),v0)=Tern(v0,v2,Tern(v3,v4,v5)) by A3;
hence thesis by A1758;
end;
A1762: for v1,v0,v2,v5,v4,v3 holds
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5))),Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,
v5)),Tern(v3,v4
,v5))=Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2))
proof let v1,v0,v2,v5,v4,v3;
Tern(Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5)),Tern(v3,v4,v5),Tern(v0,v1,Tern(v0,
v2,Tern(v3,v4
,v5))))=Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5))),Tern(v0,Tern(v0,v1,v2),Tern
(v3,v4,v5))
,Tern(v3,v4,v5)) by A3;
hence thesis by A1760;
end;
A1764: for v1,v0,v2,v5,v4,v3 holds
Tern(Tern(v3,v4,v5),Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5))),Tern(v0,Tern(v0,v1,
v2),Tern(v3,v4
,v5)))=Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2))
proof let v1,v0,v2,v5,v4,v3;
Tern(Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5))),Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,
v5)),Tern(v3,v4
,v5))=Tern(Tern(v3,v4,v5),Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5))),Tern(v0,Tern(
v0,v1,v2)
,Tern(v3,v4,v5))) by A3;
hence thesis by A1762;
end;
A1767: for v4,v3,v5,v2,v1,v0 holds
Tern(v3,v4,Tern(v3,v5,Tern(v0,v1,v2)))=Tern(Tern(v0,v1,v2),v3,Tern(v3,v4,v5))
proof let v4,v3,v5,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v3,v4,Tern(v3,v5,Tern(v0,v1,v2))),Tern(v3,Tern(v3,v4,
v5),Tern(v0,v1
,v2)))=Tern(v3,v4,Tern(v3,v5,Tern(v0,v1,v2))) by A1747;
hence thesis by A1764;
end;
A1770: for v1,v0,v2,v5,v4,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5)))=Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5))
proof let v1,v0,v2,v5,v4,v3;
Tern(v0,Tern(v0,v1,v2),Tern(v3,v4,v5))=Tern(Tern(v3,v4,v5),v0,Tern(v0,v1,v2))
by A3;
hence thesis by A1767;
end;
A1773: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v4,Tern(v1,v2,v3),Tern(v0,Tern(v1,v2,v3),v1)))=
Tern(v1,v3,Tern(v1
,v2,Tern(v0,v4,Tern(v1,v2,v3))))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v1)=Tern(v1,v0,Tern(v1,v2,v3)) by A3;
hence thesis by A1685;
end;
A1775: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v4,Tern(v1,v2,v3),Tern(v0,v1,Tern(v1,v2,v3))))=
Tern(v1,v3,Tern(v1
,v2,Tern(v0,v4,Tern(v1,v2,v3))))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v1)=Tern(v0,v1,Tern(v1,v2,v3)) by A4;
hence thesis by A1773;
end;
A1777: for v0,v4,v3,v2,v1 holds
Tern(v4,Tern(v1,v2,v3),Tern(v0,v1,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v1,v2,Tern(
v0,v4,Tern(v1
,v2,v3))))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v4,Tern(v1,v2,v3),Tern(v0,v1,Tern(v1,v2,v3))))=Tern
(v4,Tern(v1,v2
,v3),Tern(v0,v1,Tern(v1,v2,v3))) by A1726;
hence thesis by A1775;
end;
A1781: for v100,v102,v101,v2 holds
Tern(v100,Tern(v2,v101,v102),Tern(v101,v102,v100))=Tern(v101,v102,v100)
proof
now let v100,v3,v102,v101,v4,v2;
Tern(v101,v102,Tern(v2,v3,Tern(v2,v102,Tern(v2,v4,v101))))=Tern(v2,v101,v102)
by
A1692;
hence Tern(v100,Tern(v2,v101,v102),Tern(v101,v102,v100))=Tern(v101,v102,v100)
by
A729;
end;
hence thesis;
end;
A1784: for v0,v3,v2,v1 holds Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,v3))=Tern(v2,v3,
v0)
proof let v0,v3,v2,v1;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A1781;
end;
A1786: for v0,v3,v2,v1 holds Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,v3))=Tern(v0,v2,
v3)
proof let v0,v3,v2,v1;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A1784;
end;
A1789: for v100,v102,v101,v103 holds
Tern(v100,Tern(v103,v101,v102),Tern(v100,v103,v102))=Tern(v100,v103,v102)
proof
now let v100,v102,v101,v4,v103;
Tern(v101,v102,Tern(v103,v102,Tern(v103,v102,Tern(v103,v4,v101))))=Tern(v103,
v101
,v102) by A1692;
hence Tern(v100,Tern(v103,v101,v102),Tern(v100,v103,v102))=Tern(v100,v103,v102)
by A1094;
end;
hence thesis;
end;
A1793: for v100,v102,v101,v103 holds
Tern(v100,Tern(v103,v101,v102),Tern(v103,v100,v101))=Tern(v103,v100,v101)
proof
now let v100,v102,v101,v4,v103;
Tern(v101,v102,Tern(v103,v101,Tern(v103,v102,Tern(v103,v4,v101))))=Tern(v103,
v101
,v102) by A1692;
hence Tern(v100,Tern(v103,v101,v102),Tern(v103,v100,v101))=Tern(v103,v100,v101)
by A1203;
end;
hence thesis;
end;
A1796: for v0,v3,v2,v1 holds Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,v1))=Tern(v1,v0,
v2)
proof let v0,v3,v2,v1;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A1793;
end;
A1798: for v0,v3,v2,v1 holds Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v2))=Tern(v1,v0,
v2)
proof let v0,v3,v2,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A1796;
end;
A1800: for v0,v3,v2,v1 holds Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v2))=Tern(v0,v2,
v1)
proof let v0,v3,v2,v1;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A1798;
end;
A1802: for v0,v3,v2,v1 holds Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v2))=Tern(v0,v1,
v2)
proof let v0,v3,v2,v1;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A1800;
end;
A1805: for v3,v103,v101,v104,v102 holds
Tern(Tern(v3,v104,v101),v101,Tern(v102,v103,Tern(v102,v104,v101)))=Tern(v102,
Tern(v3
,v104,v101),v101)
proof let v3,v103,v101,v104,v102;
Tern(v102,v101,Tern(v102,v104,Tern(v3,v104,v101)))=Tern(v102,v104,v101) by
A1370;
hence thesis by A1692;
end;
A1808: for v0,v4,v1,v3,v2 holds
Tern(Tern(v0,v1,v2),v2,Tern(v3,v4,Tern(v2,v3,v1)))=Tern(v3,Tern(v0,v1,v2),v2)
proof let v0,v4,v1,v3,v2;
Tern(v3,v1,v2)=Tern(v2,v3,v1) by A3;
hence thesis by A1805;
end;
A1810: for v0,v4,v3,v2,v1 holds
Tern(Tern(v0,v1,v2),v2,Tern(v3,v4,Tern(v1,v2,v3)))=Tern(v3,Tern(v0,v1,v2),v2)
proof let v0,v4,v3,v2,v1;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A1808;
end;
A1812: for v0,v4,v3,v2,v1 holds
Tern(v2,Tern(v3,v4,Tern(v1,v2,v3)),Tern(v0,v1,v2))=Tern(v3,Tern(v0,v1,v2),v2)
proof let v0,v4,v3,v2,v1;
Tern(v2,Tern(v3,v4,Tern(v1,v2,v3)),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v2,Tern(
v3,v4,Tern(v1
,v2,v3))) by A3;
hence thesis by A1810;
end;
A1815: for v4,v2,v1,v0,v3 holds
Tern(v0,Tern(v1,v2,Tern(v3,v0,v1)),Tern(v4,v3,v0))=Tern(v0,v1,Tern(v4,v3,v0))
proof let v4,v2,v1,v0,v3;
Tern(v1,Tern(v4,v3,v0),v0)=Tern(v0,v1,Tern(v4,v3,v0)) by A3;
hence thesis by A1812;
end;
A1818: for v100,v101,v3,v2,v1 holds
Tern(v100,Tern(v101,v2,v3),Tern(v101,Tern(v1,v2,v3),v100))=Tern(v101,Tern(v1,
v2,v3)
,v100)
proof let v100,v101,v3,v2,v1;
Tern(v101,Tern(v1,v2,v3),Tern(v101,v2,v3))=Tern(v101,v2,v3) by A1786;
hence thesis by A729;
end;
A1821: for v0,v1,v2,v4,v3 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,Tern(v3,v4,v2),v0))=Tern(v1,Tern(v4,v2,v3),v0)
proof let v0,v1,v2,v4,v3;
Tern(v4,v2,v3)=Tern(v3,v4,v2) by A3;
hence thesis by A1818;
end;
A1823: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,Tern(v2,v3,v4),v0))=Tern(v1,Tern(v4,v2,v3),v0)
proof let v0,v1,v4,v3,v2;
Tern(v3,v4,v2)=Tern(v2,v3,v4) by A3;
hence thesis by A1821;
end;
A1825: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,v4)))=Tern(v1,Tern(v4,v2,v3),v0)
proof let v0,v1,v4,v3,v2;
Tern(v1,Tern(v2,v3,v4),v0)=Tern(v0,v1,Tern(v2,v3,v4)) by A3;
hence thesis by A1823;
end;
A1827: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,v4)))=Tern(v1,Tern(v3,v4,v2),v0)
proof let v0,v1,v4,v3,v2;
Tern(v4,v2,v3)=Tern(v3,v4,v2) by A3;
hence thesis by A1825;
end;
A1829: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,v4)))=Tern(v1,Tern(v2,v3,v4),v0)
proof let v0,v1,v4,v3,v2;
Tern(v3,v4,v2)=Tern(v2,v3,v4) by A3;
hence thesis by A1827;
end;
A1831: for v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,v4)))=Tern(v0,v1,Tern(v2,v3,v4))
proof let v0,v1,v4,v3,v2;
Tern(v1,Tern(v2,v3,v4),v0)=Tern(v0,v1,Tern(v2,v3,v4)) by A3;
hence thesis by A1829;
end;
A1834: for v1,v102,v101,v104,v103 holds
Tern(Tern(v1,v104,v101),v101,Tern(v102,v103,Tern(v103,v104,v101)))=Tern(v103,
Tern(v1
,v104,v101),v101)
proof let v1,v102,v101,v104,v103;
Tern(v103,Tern(v1,v104,v101),Tern(v103,v104,v101))=Tern(v103,v104,v101) by
A1786;
hence thesis by A1333;
end;
A1837: for v0,v3,v1,v4,v2 holds
Tern(Tern(v0,v1,v2),v2,Tern(v3,v4,Tern(v2,v4,v1)))=Tern(v4,Tern(v0,v1,v2),v2)
proof let v0,v3,v1,v4,v2;
Tern(v4,v1,v2)=Tern(v2,v4,v1) by A3;
hence thesis by A1834;
end;
A1839: for v0,v3,v4,v2,v1 holds
Tern(Tern(v0,v1,v2),v2,Tern(v3,v4,Tern(v1,v2,v4)))=Tern(v4,Tern(v0,v1,v2),v2)
proof let v0,v3,v4,v2,v1;
Tern(v2,v4,v1)=Tern(v1,v2,v4) by A3;
hence thesis by A1837;
end;
A1841: for v0,v3,v4,v2,v1 holds
Tern(v2,Tern(v3,v4,Tern(v1,v2,v4)),Tern(v0,v1,v2))=Tern(v4,Tern(v0,v1,v2),v2)
proof let v0,v3,v4,v2,v1;
Tern(v2,Tern(v3,v4,Tern(v1,v2,v4)),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v2),v2,Tern(
v3,v4,Tern(v1
,v2,v4))) by A3;
hence thesis by A1839;
end;
A1844: for v4,v1,v2,v0,v3 holds
Tern(v0,Tern(v1,v2,Tern(v3,v0,v2)),Tern(v4,v3,v0))=Tern(v0,v2,Tern(v4,v3,v0))
proof let v4,v1,v2,v0,v3;
Tern(v2,Tern(v4,v3,v0),v0)=Tern(v0,v2,Tern(v4,v3,v0)) by A3;
hence thesis by A1841;
end;
A1847: for v100,v102,v103,v2,v101 holds
Tern(v100,v101,Tern(v102,Tern(v101,v2,v103),Tern(v102,v103,v103)))=Tern(v101,
v103
,Tern(v100,v101,Tern(v102,v103,Tern(v102,v2,v103))))
proof let v100,v102,v103,v2,v101;
Tern(v102,Tern(v101,v2,v103),Tern(v102,v103,v103))=Tern(v102,v103,Tern(v101,
v103
,Tern(v102,v2,v103))) by A432;
hence thesis by A236;
end;
A1850: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v2,Tern(v1,v3,v4),v4))=Tern(v1,v4,Tern(v0,v1,Tern(v2,v4,Tern(
v2,v3,v4))))
proof let v0,v2,v4,v3,v1;
Tern(v2,v4,v4)=v4 by A34;
hence thesis by A1847;
end;
A1852: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v2,v4,Tern(v1,v3,v4)))=Tern(v1,v4,Tern(v0,v1,Tern(v2,v4,Tern(
v2,v3,v4))))
proof let v0,v2,v4,v3,v1;
Tern(v2,Tern(v1,v3,v4),v4)=Tern(v2,v4,Tern(v1,v3,v4)) by A4;
hence thesis by A1850;
end;
A1855: for v0,v2,v3,v4,v1 holds
Tern(v0,v1,Tern(v2,v3,Tern(v1,v4,v3)))=Tern(v1,v3,Tern(v0,v1,Tern(v2,v4,v3)))
proof let v0,v2,v3,v4,v1;
Tern(v2,v3,Tern(v2,v4,v3))=Tern(v2,v4,v3) by A63;
hence thesis by A1852;
end;
A1858: for v102,v103,v3,v2,v1 holds
Tern(v102,Tern(v1,v2,v3),Tern(v102,v103,Tern(v103,Tern(v1,v2,v3),Tern(v102,v1
,v2))))=Tern(v103,Tern(v1,v2,v3),Tern(v102,v103,Tern(v102,v1,v2)))
proof let v102,v103,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v102,v103,Tern(v102,v1,v2)))=Tern(v102,v103,Tern(
v102,v1
,v2)) by A677;
hence thesis by A389;
end;
A1861: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v4,Tern(v1,v2,v3)))=Tern(v4,Tern(v1,v2,v3),Tern
(v0,v4,Tern(v0
,v1,v2)))
proof let v0,v4,v3,v2,v1;
Tern(v0,v4,Tern(v4,Tern(v1,v2,v3),Tern(v0,v1,v2)))=Tern(v0,v4,Tern(v1,v2,v3))
by A1040;
hence thesis by A1858;
end;
A1863: for v0,v4,v3,v2,v1 holds
Tern(v0,v4,Tern(v1,v2,v3))=Tern(v4,Tern(v1,v2,v3),Tern(v0,v4,Tern(v0,v1,v2)))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v4,Tern(v1,v2,v3)))=Tern(v0,v4,Tern(v1,v2,v3))
by A63;
hence thesis by A1861;
end;
A1869: for v101,v100,v103,v3,v2,v1 holds
Tern(v100,v101,Tern(v100,v103,Tern(v1,v2,v3)))=Tern(v100,v103,Tern(v100,v101,
Tern(v100
,Tern(v1,v2,v103),Tern(v1,v2,v3))))
proof let v101,v100,v103,v3,v2,v1;
Tern(v100,Tern(v1,v2,v3),Tern(v100,v103,Tern(v1,v2,v103)))=Tern(v100,v103,Tern(
v1,v2
,v3)) by A872;
hence thesis by A139;
end;
A1872: for v1,v0,v2,v5,v4,v3 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,v5)))=Tern(v0,v2,Tern(v0,v1,Tern(v0,Tern(v2,
v3,v4),Tern(v3
,v4,v5))))
proof let v1,v0,v2,v5,v4,v3;
Tern(v3,v4,v2)=Tern(v2,v3,v4) by A3;
hence thesis by A1869;
end;
A1876: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v1,v4)))=Tern(v0,v4,Tern(v1,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,Tern(v1,v2,v4))=Tern(v2,v4,Tern(v0,v1,v4)) by A898;
hence thesis by A872;
end;
A1879: for v104,v100,v1,v3,v2,v101 holds
Tern(v100,Tern(v1,v101,Tern(v101,v2,v3)),Tern(v100,Tern(v101,v2,v3),v104))=
Tern(v100
,v104,Tern(Tern(v1,v101,v2),Tern(v101,v2,v3),Tern(v100,v101,Tern(v101,v2,v3))))
proof let v104,v100,v1,v3,v2,v101;
Tern(v101,Tern(v1,v101,v2),Tern(v101,v2,v3))=Tern(v1,v101,Tern(v101,v2,v3)) by
A517;
hence thesis by A922;
end;
A1882: for v5,v0,v1,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,v5,Tern(v2,v3,v4)))=Tern(v0,v5,Tern
(Tern(v1,v2,v3)
,Tern(v2,v3,v4),Tern(v0,v2,Tern(v2,v3,v4))))
proof let v5,v0,v1,v4,v3,v2;
Tern(v0,Tern(v2,v3,v4),v5)=Tern(v0,v5,Tern(v2,v3,v4)) by A4;
hence thesis by A1879;
end;
A1887: for v103,v101,v100,v3,v2,v1 holds
Tern(v100,Tern(v100,Tern(v1,v2,v3),Tern(v101,v100,v1)),Tern(v101,v103,v100))=
Tern(v100
,Tern(v1,v2,Tern(v100,v1,v3)),Tern(v101,v103,v100))
proof let v103,v101,v100,v3,v2,v1;
Tern(v100,Tern(v1,v2,v3),Tern(v101,v100,v1))=Tern(v101,v100,Tern(v1,v2,Tern(
v100,v1
,v3))) by A948;
hence thesis by A1460;
end;
A1890: for v5,v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,v0)),Tern(v4,v5,v0))=Tern(v0,Tern(v1
,v2,Tern(v0,v1
,v3)),Tern(v4,v5,v0))
proof let v5,v4,v0,v3,v2,v1;
Tern(v4,v0,v1)=Tern(v1,v4,v0) by A3;
hence thesis by A1887;
end;
A1892: for v5,v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v4)),Tern(v4,v5,v0))=Tern(v0,Tern(v1
,v2,Tern(v0,v1
,v3)),Tern(v4,v5,v0))
proof let v5,v4,v0,v3,v2,v1;
Tern(v1,v4,v0)=Tern(v0,v1,v4) by A3;
hence thesis by A1890;
end;
A1894: for v5,v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v4)),Tern(v0,v4,v5))=Tern(v0,Tern(v1
,v2,Tern(v0,v1
,v3)),Tern(v4,v5,v0))
proof let v5,v4,v0,v3,v2,v1;
Tern(v4,v5,v0)=Tern(v0,v4,v5) by A3;
hence thesis by A1892;
end;
A1896: for v4,v5,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v1,v4),Tern(v0,v4,v5)))=Tern(v0,Tern(v1
,v2,Tern(v0,v1
,v3)),Tern(v4,v5,v0))
proof let v4,v5,v0,v3,v2,v1;
Tern(v0,Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v4)),Tern(v0,v4,v5))=Tern(v0,Tern(v1,
v2,v3),Tern(v0
,Tern(v0,v1,v4),Tern(v0,v4,v5))) by A1770;
hence thesis by A1894;
end;
A1898: for v4,v5,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v0,v4,Tern(v0,v4,v5))))=Tern(v0,Tern(v1
,v2,Tern(v0,v1
,v3)),Tern(v4,v5,v0))
proof let v4,v5,v0,v3,v2,v1;
Tern(v0,Tern(v0,v1,v4),Tern(v0,v4,v5))=Tern(v0,v1,Tern(v0,v4,Tern(v0,v4,v5)))
by A1770;
hence thesis by A1896;
end;
A1900: for v4,v5,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v0,v4,v5)))=Tern(v0,Tern(v1,v2,Tern(v0,
v1,v3)),Tern(v4
,v5,v0))
proof let v4,v5,v0,v3,v2,v1;
Tern(v0,v4,Tern(v0,v4,v5))=Tern(v0,v4,v5) by A74;
hence thesis by A1898;
end;
A1902: for v4,v5,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v0,v4,v5)))=Tern(v0,Tern(v1,v2,Tern(v0,
v1,v3)),Tern(v0
,v4,v5))
proof let v4,v5,v0,v3,v2,v1;
Tern(v4,v5,v0)=Tern(v0,v4,v5) by A3;
hence thesis by A1900;
end;
A1904: for v4,v5,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v0,v4,v5)))=Tern(v0,v1,Tern(v0,v4,Tern(
v0,v5,Tern(v1
,v2,v3))))
proof let v4,v5,v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,Tern(v0,v1,v3)),Tern(v0,v4,v5))=Tern(v0,v1,Tern(v0,v4,Tern(
v0,v5,Tern(v1,v2
,v3)))) by A1076;
hence thesis by A1902;
end;
A1906: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v3,v4)))=Tern(v0,v4,Tern(v1,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,Tern(v2,v3,v4))=Tern(v2,v4,Tern(v0,v3,v4)) by A719;
hence thesis by A983;
end;
A1909: for v104,v102,v4,v101,v100 holds
Tern(v100,v101,Tern(v100,v101,Tern(v100,Tern(v102,Tern(v100,v101,v4),v104),
Tern(v101
,v102,v4))))=Tern(v100,v101,Tern(v102,Tern(v100,v101,v4),v104))
proof let v104,v102,v4,v101,v100;
Tern(v100,Tern(v102,Tern(v100,v101,v4),v104),Tern(v101,v102,Tern(v100,v101
,v4)))=Tern(v100,v101,Tern(v100,Tern(v102,Tern(v100,v101,v4),v104),Tern(v101,
v102
,v4))) by A103;
hence thesis by A1017;
end;
A1912: for v2,v4,v3,v1,v0 holds
Tern(v0,v1,Tern(v0,v1,Tern(v0,Tern(v2,v4,Tern(v0,v1,v3)),Tern(v1,v2,v3))))=
Tern(v0,v1,Tern(v2
,Tern(v0,v1,v3),v4))
proof let v2,v4,v3,v1,v0;
Tern(v2,Tern(v0,v1,v3),v4)=Tern(v2,v4,Tern(v0,v1,v3)) by A4;
hence thesis by A1909;
end;
A1915: for v2,v3,v4,v1,v0 holds
Tern(v0,v1,Tern(v0,v1,Tern(v0,Tern(v1,v2,v4),Tern(v2,v3,Tern(v0,v1,v4)))))=
Tern(v0,v1,Tern(v2
,Tern(v0,v1,v4),v3))
proof let v2,v3,v4,v1,v0;
Tern(v0,Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v4))=Tern(v0,Tern(v1,v2,v4),Tern(
v2,v3,Tern(v0
,v1,v4))) by A4;
hence thesis by A1912;
end;
A1918: for v2,v4,v3,v1,v0 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v1,v3))))=Tern(v0,v1,Tern
(v2,Tern(v0,v1
,v3),v4))
proof let v2,v4,v3,v1,v0;
Tern(v0,v1,Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v1,v3)))))=Tern
(v0,v1,Tern(v0
,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v1,v3)))) by A74;
hence thesis by A1915;
end;
A1920: for v2,v4,v3,v1,v0 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v1,v3))))=Tern(v0,v1,Tern
(v2,v4,Tern(v0
,v1,v3)))
proof let v2,v4,v3,v1,v0;
Tern(v2,Tern(v0,v1,v3),v4)=Tern(v2,v4,Tern(v0,v1,v3)) by A4;
hence thesis by A1918;
end;
A1923: for v103,v100,v105,v104,v101 holds
Tern(v100,v101,Tern(v100,Tern(v101,v104,v105),Tern(v103,v104,Tern(v100,v103
,v105))))=Tern(v100,v103,Tern(v100,v101,Tern(v103,v104,v105)))
proof let v103,v100,v105,v104,v101;
Tern(v100,v101,Tern(v100,Tern(v101,v104,v105),Tern(v103,v104,v105)))=Tern(v100,
v101
,Tern(v103,v104,v105)) by A1178;
hence thesis by A189;
end;
A1926: for v4,v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v4,v2,Tern(v0,v3,v4))))=Tern(v0,v4,Tern
(v0,v1,Tern(v4
,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v3)=Tern(v0,v3,v4) by A4;
hence thesis by A1923;
end;
A1928: for v4,v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v2,Tern(v0,v3,v4),v4)))=Tern(v0,v4,Tern
(v0,v1,Tern(v4
,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v2,Tern(v0,v3,v4),v4)=Tern(v4,v2,Tern(v0,v3,v4)) by A3;
hence thesis by A1926;
end;
A1930: for v4,v0,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v3,v4))))=Tern(v0,v4,Tern
(v0,v1,Tern(v4
,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v2,Tern(v0,v3,v4),v4)=Tern(v2,v4,Tern(v0,v3,v4)) by A4;
hence thesis by A1928;
end;
A1932: for v0,v4,v3,v2,v1 holds
Tern(v0,v1,Tern(v0,v4,Tern(v1,v2,v3)))=Tern(v0,v4,Tern(v0,v1,Tern(v4,v2,v3)))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v3,v4)))=Tern(v0,v4,Tern(v1,v2,v3))
by A1906;
hence thesis by A1930;
end;
A1935: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v3,v4)))=Tern(v0,v2,Tern(v0,v1,Tern(v4,v2,v3)))
proof let v0,v2,v4,v3,v1;
Tern(v2,v3,v4)=Tern(v4,v2,v3) by A3;
hence thesis by A1932;
end;
A1937: for v0,v2,v4,v3,v1 holds
Tern(v0,v1,Tern(v0,v2,Tern(v1,v3,v4)))=Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,v2)))
proof let v0,v2,v4,v3,v1;
Tern(v4,v2,v3)=Tern(v3,v4,v2) by A3;
hence thesis by A1935;
end;
A1942: for v101,v103,v102,v4,v3,v2,v100 holds
Tern(v100,Tern(v101,v102,v103),Tern(v100,v103,Tern(v100,v102,Tern(v4,v2,Tern(
v100,v2
,v3)))))=Tern(v100,Tern(v2,v3,Tern(v100,v4,v2)),Tern(v100,v102,v103))
proof let v101,v103,v102,v4,v3,v2,v100;
Tern(v100,v102,Tern(v2,v3,Tern(v100,v4,v2)))=Tern(v100,v102,Tern(v4,v2,Tern(
v100,v2
,v3))) by A1335;
hence thesis by A971;
end;
A1945: for v2,v3,v4,v6,v5,v0 holds
Tern(v0,Tern(v4,v5,Tern(v0,v5,v6)),Tern(v0,v2,v3))=Tern(v0,Tern(v5,v6,Tern(v0,
v4,v5)),Tern(v0
,v2,v3))
proof
now let v1,v3,v2,v4,v6,v5,v0;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v3,Tern(v0,v2,Tern(v4,v5,Tern(v0,v5,v6)))))=Tern
(v0,Tern(v4,v5
,Tern(v0,v5,v6)),Tern(v0,v2,v3)) by A971;
hence
Tern(v0,Tern(v4,v5,Tern(v0,v5,v6)),Tern(v0,v2,v3))=Tern(v0,Tern(v5,v6,Tern(v0,
v4,v5)),Tern(v0
,v2,v3)) by A1942;
end;
hence thesis;
end;
A1948: for v4,v0,v5,v3,v2,v1 holds
Tern(v0,v2,Tern(v0,v4,Tern(v0,v5,Tern(v1,v2,v3))))=Tern(v0,Tern(v2,v3,Tern(v0,
v1,v2)),Tern(v0
,v4,v5))
proof let v4,v0,v5,v3,v2,v1;
Tern(v0,Tern(v1,v2,Tern(v0,v2,v3)),Tern(v0,v4,v5))=Tern(v0,v2,Tern(v0,v4,Tern(
v0,v5,Tern(v1,v2
,v3)))) by A1097;
hence thesis by A1945;
end;
A1954: for v102,v103,v101,v100,v1 holds
Tern(v100,Tern(v101,v102,v103),Tern(v100,Tern(v1,v100,v101),Tern(v102,v103,
Tern(v1,v100
,v101))))=Tern(v1,v100,Tern(v101,v102,Tern(v100,v101,v103)))
proof let v102,v103,v101,v100,v1;
Tern(v100,Tern(v1,v100,v101),Tern(v101,v102,v103))=Tern(v1,v100,Tern(v101,v102,
Tern(v100
,v101,v103))) by A1565;
hence thesis by A983;
end;
A1957: for v2,v3,v1,v0,v4 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v1,v4,v0),Tern(v2,v3,Tern(v4,v0,v1))))=
Tern(v4,v0,Tern(v1
,v2,Tern(v0,v1,v3)))
proof let v2,v3,v1,v0,v4;
Tern(v4,v0,v1)=Tern(v1,v4,v0) by A3;
hence thesis by A1954;
end;
A1959: for v2,v3,v1,v0,v4 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v1,v4),Tern(v2,v3,Tern(v4,v0,v1))))=
Tern(v4,v0,Tern(v1
,v2,Tern(v0,v1,v3)))
proof let v2,v3,v1,v0,v4;
Tern(v1,v4,v0)=Tern(v0,v1,v4) by A3;
hence thesis by A1957;
end;
A1961: for v2,v3,v0,v4,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v1,v4),Tern(v2,v3,Tern(v1,v4,v0))))=
Tern(v4,v0,Tern(v1
,v2,Tern(v0,v1,v3)))
proof let v2,v3,v0,v4,v1;
Tern(v4,v0,v1)=Tern(v1,v4,v0) by A3;
hence thesis by A1959;
end;
A1963: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v0,v1,v4),Tern(v2,v3,Tern(v0,v1,v4))))=
Tern(v4,v0,Tern(v1
,v2,Tern(v0,v1,v3)))
proof let v2,v3,v4,v1,v0;
Tern(v1,v4,v0)=Tern(v0,v1,v4) by A3;
hence thesis by A1961;
end;
A1965: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v0,v4,Tern(v2,v3,Tern(v0,v1,v4)))))=
Tern(v4,v0,Tern(v1
,v2,Tern(v0,v1,v3)))
proof let v2,v3,v4,v1,v0;
Tern(v0,Tern(v0,v1,v4),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,v1,Tern(v0,v4,Tern(
v2,v3,Tern(v0,v1
,v4)))) by A1770;
hence thesis by A1963;
end;
A1967: for v2,v3,v4,v1,v0 holds
Tern(v0,v1,Tern(v0,v4,Tern(v0,Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v3))))=
Tern(v4,v0,Tern(v1
,v2,Tern(v0,v1,v3)))
proof let v2,v3,v4,v1,v0;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,Tern(v0,v4,Tern(v2,v3,Tern(v0,v1,v4)))))=Tern
(v0,v1,Tern(v0
,v4,Tern(v0,Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v3)))) by A1904;
hence thesis by A1965;
end;
A1970: for v3,v4,v2,v1,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v0,Tern(v1,v3,v4),Tern(v3,v4,Tern(v0,v1,v2)))))=
Tern(v2,v0,Tern(v1
,v3,Tern(v0,v1,v4)))
proof let v3,v4,v2,v1,v0;
Tern(v0,Tern(v3,v4,Tern(v0,v1,v2)),Tern(v1,v3,v4))=Tern(v0,Tern(v1,v3,v4),Tern(
v3,v4,Tern(v0
,v1,v2))) by A4;
hence thesis by A1967;
end;
A1972: for v3,v4,v2,v1,v0 holds
Tern(v0,v2,Tern(v0,v1,Tern(v3,v4,Tern(v0,v1,v2))))=Tern(v2,v0,Tern(v1,v3,Tern(
v0,v1,v4)))
proof let v3,v4,v2,v1,v0;
Tern(v0,v1,Tern(v0,v2,Tern(v0,Tern(v1,v3,v4),Tern(v3,v4,Tern(v0,v1,v2)))))=Tern
(v0,v2,Tern(v0
,v1,Tern(v3,v4,Tern(v0,v1,v2)))) by A1872;
hence thesis by A1970;
end;
A1975: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(v0,Tern(v2,v3,Tern(v0,
v2,v4)),v1)
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v2,v3,Tern(v0,v2,v4)),v1)=Tern(v1,v0,Tern(v2,v3,Tern(v0,v2,v4)))
by A3;
hence thesis by A1972;
end;
A1977: for v3,v4,v1,v2,v0 holds
Tern(v0,v1,Tern(v0,v2,Tern(v3,v4,Tern(v0,v2,v1))))=Tern(v0,v1,Tern(v2,v3,Tern(
v0,v2,v4)))
proof let v3,v4,v1,v2,v0;
Tern(v0,Tern(v2,v3,Tern(v0,v2,v4)),v1)=Tern(v0,v1,Tern(v2,v3,Tern(v0,v2,v4)))
by A4;
hence thesis by A1975;
end;
A1979: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,Tern(v1,v2,v3),v4))=Tern(v1,v3,Tern(v1,v2,Tern(
v4,v0,Tern(v1
,v2,v3))))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v4)=Tern(v4,v1,Tern(v1,v2,v3)) by A3;
hence thesis by A1777;
end;
A1981: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v1,v2,Tern(
v4,v0,Tern(v1
,v2,v3))))
proof let v4,v0,v3,v2,v1;
Tern(v1,Tern(v1,v2,v3),v4)=Tern(v1,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A1979;
end;
A1983: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v1,v2,Tern(
v0,Tern(v1,v2
,v3),v4)))
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v4)=Tern(v4,v0,Tern(v1,v2,v3)) by A3;
hence thesis by A1981;
end;
A1985: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v1,v2,Tern(
v0,v4,Tern(v1
,v2,v3))))
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v4)=Tern(v0,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A1983;
end;
A1987: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v2,v0,Tern(
v1,v2,v4)))
proof let v4,v0,v3,v2,v1;
Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3))))=Tern(v1,v3,Tern(v2,v0,Tern(
v1,v2,v4)))
by A1977;
hence thesis by A1985;
end;
A1989: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v0,Tern(v1,
v2,v4),v2))
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v4),v2)=Tern(v2,v0,Tern(v1,v2,v4)) by A3;
hence thesis by A1987;
end;
A1991: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v0,v2,Tern(
v1,v2,v4)))
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v4),v2)=Tern(v0,v2,Tern(v1,v2,v4)) by A4;
hence thesis by A1989;
end;
A1993: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v2,v0,Tern(v1,v2,v4))))=Tern(v1,v3,Tern
(v1,v2,Tern(v0
,v4,Tern(v1,v2,v3))))
proof let v3,v0,v4,v2,v1;
Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3))))=Tern(v1,v3,Tern(v2,v0,Tern(
v1,v2,v4)))
by A1977;
hence thesis by A1553;
end;
A1995: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,Tern(v1,v2,v4),v2)))=Tern(v1,v3,Tern
(v1,v2,Tern(v0
,v4,Tern(v1,v2,v3))))
proof let v3,v0,v4,v2,v1;
Tern(v0,Tern(v1,v2,v4),v2)=Tern(v2,v0,Tern(v1,v2,v4)) by A3;
hence thesis by A1993;
end;
A1997: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,v2,Tern(v1,v2,v4))))=Tern(v1,v3,Tern
(v1,v2,Tern(v0
,v4,Tern(v1,v2,v3))))
proof let v3,v0,v4,v2,v1;
Tern(v0,Tern(v1,v2,v4),v2)=Tern(v0,v2,Tern(v1,v2,v4)) by A4;
hence thesis by A1995;
end;
A1999: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,v2,Tern(v1,v2,v4))))=Tern(v1,v3,Tern
(v2,v0,Tern(v1
,v2,v4)))
proof let v3,v0,v4,v2,v1;
Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3))))=Tern(v1,v3,Tern(v2,v0,Tern(
v1,v2,v4)))
by A1977;
hence thesis by A1997;
end;
A2001: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,v2,Tern(v1,v2,v4))))=Tern(v1,v3,Tern
(v0,Tern(v1,v2
,v4),v2))
proof let v3,v0,v4,v2,v1;
Tern(v0,Tern(v1,v2,v4),v2)=Tern(v2,v0,Tern(v1,v2,v4)) by A3;
hence thesis by A1999;
end;
A2003: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,v2,Tern(v1,v2,v4))))=Tern(v1,v3,Tern
(v0,v2,Tern(v1
,v2,v4)))
proof let v3,v0,v4,v2,v1;
Tern(v0,Tern(v1,v2,v4),v2)=Tern(v0,v2,Tern(v1,v2,v4)) by A4;
hence thesis by A2001;
end;
A2005: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v1,v2,Tern(v0,Tern(v1,v2,v3),v4))))=
Tern(v4,Tern(v1,v2
,v3),Tern(v1,v0,Tern(v1,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v4)=Tern(v4,v0,Tern(v1,v2,v3)) by A3;
hence thesis by A1510;
end;
A2007: for v0,v4,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3)))))=
Tern(v4,Tern(v1,v2
,v3),Tern(v1,v0,Tern(v1,v2,v3)))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),v4)=Tern(v0,v4,Tern(v1,v2,v3)) by A4;
hence thesis by A2005;
end;
A2009: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v2,v0,Tern(v1,v2,v4))))=Tern(v4,Tern(v1
,v2,v3),Tern(v1
,v0,Tern(v1,v2,v3)))
proof let v3,v0,v4,v2,v1;
Tern(v1,v3,Tern(v1,v2,Tern(v0,v4,Tern(v1,v2,v3))))=Tern(v1,v3,Tern(v2,v0,Tern(
v1,v2,v4)))
by A1977;
hence thesis by A2007;
end;
A2011: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,Tern(v1,v2,v4),v2)))=Tern(v4,Tern(v1
,v2,v3),Tern(v1
,v0,Tern(v1,v2,v3)))
proof let v3,v0,v4,v2,v1;
Tern(v0,Tern(v1,v2,v4),v2)=Tern(v2,v0,Tern(v1,v2,v4)) by A3;
hence thesis by A2009;
end;
A2013: for v3,v0,v4,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,v2,Tern(v1,v2,v4))))=Tern(v4,Tern(v1
,v2,v3),Tern(v1
,v0,Tern(v1,v2,v3)))
proof let v3,v0,v4,v2,v1;
Tern(v0,Tern(v1,v2,v4),v2)=Tern(v0,v2,Tern(v1,v2,v4)) by A4;
hence thesis by A2011;
end;
A2015: for v3,v0,v4,v2,v1 holds
Tern(v1,v3,Tern(v0,v2,Tern(v1,v2,v4)))=Tern(v4,Tern(v1,v2,v3),Tern(v1,v0,Tern(
v1,v2,v3)))
proof let v3,v0,v4,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v3,Tern(v0,v2,Tern(v1,v2,v4))))=Tern(v1,v3,Tern(
v0,v2,Tern(v1
,v2,v4))) by A2003;
hence thesis by A2013;
end;
A2018: for v1,v2,v4,v3,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v3,v4)))=Tern(v4,Tern(v0,v3,v1),Tern(v2,Tern(v0,
v3,v1),v0))
proof let v1,v2,v4,v3,v0;
Tern(v2,Tern(v0,v3,v1),v0)=Tern(v0,v2,Tern(v0,v3,v1)) by A3;
hence thesis by A2015;
end;
A2020: for v1,v2,v4,v3,v0 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v3,v4)))=Tern(v4,Tern(v0,v3,v1),Tern(v2,v0,Tern(
v0,v3,v1)))
proof let v1,v2,v4,v3,v0;
Tern(v2,Tern(v0,v3,v1),v0)=Tern(v2,v0,Tern(v0,v3,v1)) by A4;
hence thesis by A2018;
end;
A2024: for v3,v0,v4,v2,v1 holds
Tern(v1,v3,Tern(v0,v2,Tern(v1,v2,v4)))=Tern(v4,Tern(v1,v2,v3),Tern(v1,v3,Tern(
v0,v1,v2)))
proof let v3,v0,v4,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v1,v4,Tern(v1,v2,v3)))=Tern(v1,v3,Tern(v0,v2,Tern(
v1,v2,v4)))
by A1991;
hence thesis by A763;
end;
A2029: for v1,v5,v0,v4,v3,v2 holds
Tern(v0,v1,Tern(v3,v5,Tern(v0,v4,Tern(v3,v4,Tern(v2,v3,v4)))))=Tern(v0,Tern(v2
,v3,Tern(v3,v4
,v5)),Tern(v0,v1,Tern(v3,v4,v5)))
proof let v1,v5,v0,v4,v3,v2;
Tern(Tern(v2,v3,v4),Tern(v3,v4,v5),Tern(v0,v3,Tern(v3,v4,v5)))=Tern(v3,v5,Tern(
v0,v4,Tern(v3
,v4,Tern(v2,v3,v4)))) by A2020;
hence thesis by A1882;
end;
A2032: for v1,v3,v0,v4,v2,v5 holds
Tern(v0,v1,Tern(v2,v3,Tern(v0,v4,Tern(v5,v2,v4))))=Tern(v0,Tern(v5,v2,Tern(v2,
v4,v3)),Tern(v0
,v1,Tern(v2,v4,v3)))
proof let v1,v3,v0,v4,v2,v5;
Tern(v2,v4,Tern(v5,v2,v4))=Tern(v5,v2,v4) by A366;
hence thesis by A2029;
end;
A2036: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v3,Tern(v1,v2,v3))))=Tern(v0,Tern(v1
,v2,v3),Tern(v2
,v3,v4))
proof let v4,v0,v3,v2,v1;
Tern(v0,Tern(v1,v2,Tern(v2,v3,v4)),Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,v4)))=Tern
(v0,Tern(v1,v2
,v3),Tern(v2,v4,Tern(v0,v3,Tern(v1,v2,v3)))) by A2032;
hence thesis by A974;
end;
A2039: for v101,v102,v2,v1,v100,v103 holds
Tern(v100,Tern(v101,v102,v103),Tern(v100,Tern(v1,v2,Tern(v103,v100,v1)),Tern(
v102,v103
,v100)))=Tern(v100,v1,Tern(v102,v103,v100))
proof let v101,v102,v2,v1,v100,v103;
Tern(v100,Tern(v1,v2,Tern(v103,v100,v1)),Tern(v102,v103,v100))=Tern(v100,v1,
Tern(v102
,v103,v100)) by A1815;
hence thesis by A1397;
end;
A2042: for v1,v2,v5,v3,v4,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v4,v5,Tern(v0,v4,v3)),Tern(v2,v3,v0)))=
Tern(v0,v4,Tern(v2
,v3,v0))
proof let v1,v2,v5,v3,v4,v0;
Tern(v0,v4,v3)=Tern(v3,v0,v4) by A3;
hence thesis by A2039;
end;
A2044: for v1,v2,v5,v4,v3,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v4,v5,Tern(v0,v3,v4)),Tern(v2,v3,v0)))=
Tern(v0,v4,Tern(v2
,v3,v0))
proof let v1,v2,v5,v4,v3,v0;
Tern(v0,v4,v3)=Tern(v0,v3,v4) by A4;
hence thesis by A2042;
end;
A2046: for v1,v2,v5,v4,v3,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v4,v5,Tern(v0,v3,v4)),Tern(v0,v2,v3)))=
Tern(v0,v4,Tern(v2
,v3,v0))
proof let v1,v2,v5,v4,v3,v0;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A2044;
end;
A2048: for v1,v2,v0,v5,v4,v3 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v4,Tern(v0,v2,Tern(v0,v3,Tern(v3,v4,v5)))))=
Tern(v0,v4,Tern(v2
,v3,v0))
proof let v1,v2,v0,v5,v4,v3;
Tern(v0,Tern(v4,v5,Tern(v0,v3,v4)),Tern(v0,v2,v3))=Tern(v0,v4,Tern(v0,v2,Tern(
v0,v3,Tern(v3,v4
,v5)))) by A1948;
hence thesis by A2046;
end;
A2050: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v0,v3,v4)))=Tern(v0,v4,Tern(v2,v3,v0))
proof
now let v1,v2,v0,v5,v4,v3;
Tern(v0,v4,Tern(v0,v2,Tern(v0,v3,Tern(v3,v4,v5))))=Tern(v0,v2,Tern(v0,v3,v4))
by A619;
hence Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v0,v3,v4)))=Tern(v0,v4,Tern(v2,v3,
v0)) by
A2048;
end;
hence thesis;
end;
A2052: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v0,v3,v4)))=Tern(v0,v4,Tern(v0,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A2050;
end;
A2055: for v4,v1,v2,v102,v3 holds
Tern(Tern(v1,v2,Tern(v3,v102,v2)),Tern(v4,v3,v102),v102)=Tern(v102,v2,Tern(v4,
v3,v102))
proof let v4,v1,v2,v102,v3;
Tern(v102,Tern(v1,v2,Tern(v3,v102,v2)),Tern(v4,v3,v102))=Tern(v102,v2,Tern(v4,
v3,v102))
by A1844;
hence thesis by A3;
end;
A2058: for v4,v0,v3,v2,v1 holds
Tern(Tern(v0,v1,Tern(v1,v2,v3)),Tern(v4,v2,v3),v3)=Tern(v3,v1,Tern(v4,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A2055;
end;
A2060: for v4,v0,v3,v2,v1 holds
Tern(Tern(v0,v1,Tern(v1,v2,v3)),Tern(v3,v4,v2),v3)=Tern(v3,v1,Tern(v4,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v4,v2,v3)=Tern(v3,v4,v2) by A3;
hence thesis by A2058;
end;
A2062: for v4,v0,v3,v2,v1 holds
Tern(Tern(v0,v1,Tern(v1,v2,v3)),Tern(v2,v3,v4),v3)=Tern(v3,v1,Tern(v4,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(v3,v4,v2)=Tern(v2,v3,v4) by A3;
hence thesis by A2060;
end;
A2064: for v4,v0,v3,v2,v1 holds
Tern(v3,Tern(v0,v1,Tern(v1,v2,v3)),Tern(v2,v3,v4))=Tern(v3,v1,Tern(v4,v2,v3))
proof let v4,v0,v3,v2,v1;
Tern(Tern(v0,v1,Tern(v1,v2,v3)),Tern(v2,v3,v4),v3)=Tern(v3,Tern(v0,v1,Tern(v1,
v2,v3)),Tern(v2
,v3,v4)) by A3;
hence thesis by A2062;
end;
A2067: for v4,v1,v0,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v0)),Tern(v3,v0,v4))=Tern(v0,v2,Tern(v0,v4,v3))
proof let v4,v1,v0,v3,v2;
Tern(v4,v3,v0)=Tern(v0,v4,v3) by A3;
hence thesis by A2064;
end;
A2069: for v4,v1,v0,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v0)),Tern(v3,v0,v4))=Tern(v0,v2,Tern(v3,v0,v4))
proof let v4,v1,v0,v3,v2;
Tern(v0,v4,v3)=Tern(v3,v0,v4) by A3;
hence thesis by A2067;
end;
A2071: for v4,v1,v0,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v0)),Tern(v3,v0,v4))=Tern(v2,Tern(v3,v0,v4),v0)
proof let v4,v1,v0,v3,v2;
Tern(v2,Tern(v3,v0,v4),v0)=Tern(v0,v2,Tern(v3,v0,v4)) by A3;
hence thesis by A2069;
end;
A2073: for v4,v1,v0,v3,v2 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,v0)),Tern(v3,v0,v4))=Tern(v2,v0,Tern(v3,v0,v4))
proof let v4,v1,v0,v3,v2;
Tern(v2,Tern(v3,v0,v4),v0)=Tern(v2,v0,Tern(v3,v0,v4)) by A4;
hence thesis by A2071;
end;
A2076: for v104,v102,v4,v3,v2 holds
Tern(v102,Tern(v104,v2,v3),Tern(v102,Tern(v2,v3,v4),Tern(Tern(v104,v2,v3),v104
,Tern(v2,v3
,v4))))=Tern(Tern(v104,v2,v3),Tern(v2,v3,v4),Tern(v102,v104,Tern(v2,v3,v4)))
proof let v104,v102,v4,v3,v2;
Tern(v102,Tern(v104,v2,v3),Tern(v102,v104,Tern(v2,v3,v4)))=Tern(v102,v104,Tern(
v2,v3
,v4)) by A1831;
hence thesis by A1855;
end;
A2079: for v1,v0,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v2,v3,v4),Tern(v1,Tern(v2,v3,v4),Tern(v1,
v2
,v3))))=Tern(Tern(v1,v2,v3),Tern(v2,v3,v4),Tern(v0,v1,Tern(v2,v3,v4)))
proof let v1,v0,v4,v3,v2;
Tern(v1,Tern(v2,v3,v4),Tern(v1,v2,v3))=Tern(Tern(v1,v2,v3),v1,Tern(v2,v3,v4))
by A3;
hence thesis by A2076;
end;
A2081: for v1,v0,v4,v3,v2 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v2,v3,v4),Tern(v1,v2,v3)))=Tern(Tern(v1,v2
,v3),Tern(v2,v3
,v4),Tern(v0,v1,Tern(v2,v3,v4)))
proof let v1,v0,v4,v3,v2;
Tern(v1,Tern(v2,v3,v4),Tern(v1,v2,v3))=Tern(v1,v2,v3) by A1802;
hence thesis by A2079;
end;
A2083: for v1,v0,v4,v3,v2 holds
Tern(v0,Tern(v2,v3,v4),Tern(v1,v2,v3))=Tern(Tern(v1,v2,v3),Tern(v2,v3,v4),Tern
(v0,v1,Tern(v2
,v3,v4)))
proof let v1,v0,v4,v3,v2;
Tern(v0,Tern(v1,v2,v3),Tern(v0,Tern(v2,v3,v4),Tern(v1,v2,v3)))=Tern(v0,Tern(v2,
v3,v4),Tern(v1
,v2,v3)) by A63;
hence thesis by A2081;
end;
A2089: for v104,v103,v102,v101,v1 holds
Tern(Tern(v1,v101,v102),Tern(v101,v102,v103),Tern(v104,v101,v102))=Tern(v104,
Tern(v1
,v101,v102),Tern(v101,v102,v103))
proof let v104,v103,v102,v101,v1;
Tern(v104,Tern(v1,v101,v102),Tern(v104,v101,v102))=Tern(v104,v101,v102) by
A1786;
hence thesis by A1863;
end;
A2092: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v2,v4,v1))=Tern(v4,Tern(v0,v1,v2),Tern
(v1,v2,v3))
proof let v4,v3,v2,v1,v0;
Tern(v4,v1,v2)=Tern(v2,v4,v1) by A3;
hence thesis by A2089;
end;
A2094: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v1,v2,v4))=Tern(v4,Tern(v0,v1,v2),Tern
(v1,v2,v3))
proof let v4,v3,v2,v1,v0;
Tern(v2,v4,v1)=Tern(v1,v2,v4) by A3;
hence thesis by A2092;
end;
A2097: for v104,v103,v102,v2,v101 holds
Tern(Tern(v101,v2,v102),Tern(v101,v102,v103),Tern(v104,v101,v102))=Tern(v104,
Tern(v101
,v2,v102),Tern(v101,v102,v103))
proof let v104,v103,v102,v2,v101;
Tern(v104,Tern(v101,v2,v102),Tern(v104,v101,v102))=Tern(v104,v101,v102) by
A1789;
hence thesis by A1863;
end;
A2100: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v2,v4,v0))=Tern(v4,Tern(v0,v1,v2),Tern
(v0,v2,v3))
proof let v4,v3,v2,v1,v0;
Tern(v4,v0,v2)=Tern(v2,v4,v0) by A3;
hence thesis by A2097;
end;
A2102: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v0,v2,v4))=Tern(v4,Tern(v0,v1,v2),Tern
(v0,v2,v3))
proof let v4,v3,v2,v1,v0;
Tern(v2,v4,v0)=Tern(v0,v2,v4) by A3;
hence thesis by A2100;
end;
A2105: for v104,v103,v3,v102,v101 holds
Tern(Tern(v101,v102,v3),Tern(v101,v102,v103),Tern(v104,v101,v102))=Tern(v104,
Tern(v101
,v102,v3),Tern(v101,v102,v103))
proof let v104,v103,v3,v102,v101;
Tern(v104,Tern(v101,v102,v3),Tern(v104,v101,v102))=Tern(v104,v101,v102) by
A1802;
hence thesis by A1863;
end;
A2108: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v1,v4,v0))=Tern(v4,Tern(v0,v1,v2),Tern
(v0,v1,v3))
proof let v4,v3,v2,v1,v0;
Tern(v4,v0,v1)=Tern(v1,v4,v0) by A3;
hence thesis by A2105;
end;
A2110: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v0,v1,v4))=Tern(v4,Tern(v0,v1,v2),Tern
(v0,v1,v3))
proof let v4,v3,v2,v1,v0;
Tern(v1,v4,v0)=Tern(v0,v1,v4) by A3;
hence thesis by A2108;
end;
A2113: for v101,v104,v3,v102 holds
Tern(Tern(v101,v102,v3),Tern(v101,v102,Tern(v102,v3,v104)),Tern(v104,Tern(v101
,v102,v3)
,Tern(v104,v101,v102)))=Tern(v102,v104,Tern(v101,v102,v3))
proof let v101,v104,v3,v102;
Tern(v104,Tern(v101,v102,v3),Tern(v101,v102,Tern(v102,v3,v104)))=Tern(v102,v104
,Tern(v101,v102,v3)) by A1073;
hence thesis by A1863;
end;
A2116: for v0,v3,v2,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,Tern(v1,v2,v3)),Tern(v3,Tern(v0,v1,v2),Tern(v1,
v3
,v0)))=Tern(v1,v3,Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v3,v0,v1)=Tern(v1,v3,v0) by A3;
hence thesis by A2113;
end;
A2118: for v0,v3,v2,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,Tern(v1,v2,v3)),Tern(v3,Tern(v0,v1,v2),Tern(v0,
v1
,v3)))=Tern(v1,v3,Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v1,v3,v0)=Tern(v0,v1,v3) by A3;
hence thesis by A2116;
end;
A2120: for v0,v3,v2,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,Tern(v1,v2,v3)),Tern(v0,v1,v3))=Tern(v1,v3,Tern
(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v3))=Tern(v0,v1,v3) by A729;
hence thesis by A2118;
end;
A2122: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v0,v1,Tern(v1,v2,v3)))=Tern(v1,v3,Tern
(v0,v1,v2))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v1,Tern(v1,v2,v3)),Tern(v0,v1,v3))=Tern(Tern(v0,v1,
v2),Tern(v0,v1
,v3),Tern(v0,v1,Tern(v1,v2,v3))) by A4;
hence thesis by A2120;
end;
A2124: for v0,v3,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v0,v1,v2),Tern(v0,v1,v3))=Tern(v1,v3,Tern(v0,v1,v2))
proof let v0,v3,v2,v1;
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v0,v1,Tern(v1,v2,v3)))=Tern(Tern(v1,v2,
v3),Tern(v0,v1
,v2),Tern(v0,v1,v3)) by A2110;
hence thesis by A2122;
end;
A2128: for v2,v1,v0,v3 holds
Tern(Tern(v3,v0,v1),Tern(v3,v0,v2),Tern(v0,v1,v2))=Tern(v0,v2,Tern(v3,v0,v1))
proof let v2,v1,v0,v3;
Tern(Tern(v0,v1,v2),Tern(v3,v0,v1),Tern(v3,v0,v2))=Tern(v0,v2,Tern(v3,v0,v1))
by A2124;
hence thesis by A3;
end;
A2131: for v3,v0,v2,v1 holds
Tern(Tern(v1,v2,v0),Tern(v3,v0,v1),Tern(v3,v0,v2))=Tern(v0,v2,Tern(v3,v0,v1))
proof let v3,v0,v2,v1;
Tern(v1,v2,v0)=Tern(v0,v1,v2) by A3;
hence thesis by A2124;
end;
A2134: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,v2),Tern(v3,v2,v1))=Tern(v2,v1,Tern(v3,v2,v0))
proof let v3,v2,v1,v0;
Tern(v3,v2,v0)=Tern(v0,v3,v2) by A3;
hence thesis by A2131;
end;
A2136: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v3,v2,v1))=Tern(v2,v1,Tern(v3,v2,v0))
proof let v3,v2,v1,v0;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A2134;
end;
A2138: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v1,v3,v2))=Tern(v2,v1,Tern(v3,v2,v0))
proof let v3,v2,v1,v0;
Tern(v3,v2,v1)=Tern(v1,v3,v2) by A3;
hence thesis by A2136;
end;
A2140: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v1,v2,v3))=Tern(v2,v1,Tern(v3,v2,v0))
proof let v3,v2,v1,v0;
Tern(v1,v3,v2)=Tern(v1,v2,v3) by A4;
hence thesis by A2138;
end;
A2142: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v1,v2,v3))=Tern(v2,v1,Tern(v0,v3,v2))
proof let v3,v2,v1,v0;
Tern(v3,v2,v0)=Tern(v0,v3,v2) by A3;
hence thesis by A2140;
end;
A2144: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v1,v2,v3))=Tern(v2,v1,Tern(v0,v2,v3))
proof let v3,v2,v1,v0;
Tern(v0,v3,v2)=Tern(v0,v2,v3) by A4;
hence thesis by A2142;
end;
A2146: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v1,v2,v3))=Tern(v1,Tern(v0,v2,v3),v2)
proof let v3,v2,v1,v0;
Tern(v1,Tern(v0,v2,v3),v2)=Tern(v2,v1,Tern(v0,v2,v3)) by A3;
hence thesis by A2144;
end;
A2148: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v1,v2,v3))=Tern(v1,v2,Tern(v0,v2,v3))
proof let v3,v2,v1,v0;
Tern(v1,Tern(v0,v2,v3),v2)=Tern(v1,v2,Tern(v0,v2,v3)) by A4;
hence thesis by A2146;
end;
A2151: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,v2,v3)))=Tern(Tern(v0,v1
,v2),Tern(v0,v2
,v3),Tern(v1,v2,v3))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v1,v2,v3))=Tern(v1,v2,Tern(v0,v2,v3))
by A2148;
hence thesis by A63;
end;
A2153: for v1,v3,v2,v0 holds
Tern(Tern(v0,v2,v3),Tern(v0,v1,v2),Tern(v1,v2,v3))=Tern(Tern(v0,v1,v2),Tern(v0
,v2,v3),Tern(v1
,v2,v3))
proof let v1,v3,v2,v0;
Tern(Tern(v0,v1,v2),Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,v2,v3)))=Tern(Tern(v0,v2,
v3),Tern(v0,v1
,v2),Tern(v1,v2,v3)) by A2094;
hence thesis by A2151;
end;
A2156: for v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,v1),Tern(v3,v1,v2))=Tern(v3,v1,Tern(v0,v1,v2))
proof let v3,v2,v1,v0;
Tern(Tern(v0,v3,v1),Tern(v0,v1,v2),Tern(v3,v1,v2))=Tern(v3,v1,Tern(v0,v1,v2))
by A2148;
hence thesis by A2153;
end;
A2159: for v0,v104,v105,v103,v100 holds
Tern(v100,Tern(v103,v104,Tern(v0,v104,Tern(v100,v103,v105))),Tern(Tern(v0,v104
,Tern(v100
,v103,v105)),Tern(v0,v103,v104),Tern(v100,v103,Tern(v100,Tern(v0,v104,Tern(v100
,v103
,v105)),Tern(v103,v104,v105)))))=Tern(v100,Tern(v0,v104,Tern(v100,v103,v105))
,Tern(Tern(v0,v104,Tern(v100,v103,v105)),Tern(v0,v103,v104),Tern(v103,v104,Tern
(v100
,v103,v105))))
proof let v0,v104,v105,v103,v100;
Tern(Tern(v0,v104,Tern(v100,v103,v105)),Tern(v0,v103,v104),Tern(v103,v104,Tern(
v100,v103
,v105)))=Tern(v103,v104,Tern(v0,v104,Tern(v100,v103,v105))) by A2156;
hence thesis by A355;
end;
A2162: for v3,v2,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,Tern(v0,v1,v4),v3)),Tern(Tern(v3,v2,Tern(v0,v1,v4))
,Tern(v3,v1,v2)
,Tern(v0,v1,Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),Tern(v1,v2,v4)))))=Tern(v0,Tern(
v3,v2,Tern(v0
,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,
v4))))
proof let v3,v2,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v3,v2,Tern(v0,v1,v4)) by A3;
hence thesis by A2159;
end;
A2165: for v2,v4,v3,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v4,Tern(v0,v1,v3))),Tern(Tern(v4,v2,Tern(v0,v1,v3))
,Tern(v4,v1,v2)
,Tern(v0,v1,Tern(v0,Tern(v4,v2,Tern(v0,v1,v3)),Tern(v1,v2,v3)))))=Tern(v0,Tern(
v4,v2,Tern(v0
,v1,v3)),Tern(Tern(v4,v2,Tern(v0,v1,v3)),Tern(v4,v1,v2),Tern(v1,v2,Tern(v0,v1,
v3))))
proof let v2,v4,v3,v1,v0;
Tern(v2,Tern(v0,v1,v3),v4)=Tern(v2,v4,Tern(v0,v1,v3)) by A4;
hence thesis by A2162;
end;
A2168: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v2,Tern(v0,v1,v4),v3)
,Tern(v3,v1,v2)
,Tern(v0,v1,Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),Tern(v1,v2,v4)))))=Tern(v0,Tern(
v3,v2,Tern(v0
,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,
v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v3,v2,Tern(v0,v1,v4)) by A3;
hence thesis by A2165;
end;
A2170: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v2,v3,Tern(v0,v1,v4))
,Tern(v3,v1,v2)
,Tern(v0,v1,Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),Tern(v1,v2,v4)))))=Tern(v0,Tern(
v3,v2,Tern(v0
,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,
v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v2,v3,Tern(v0,v1,v4)) by A4;
hence thesis by A2168;
end;
A2172: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v2,v3,Tern(v0,v1,v4))
,Tern(v2,v3,v1)
,Tern(v0,v1,Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),Tern(v1,v2,v4)))))=Tern(v0,Tern(
v3,v2,Tern(v0
,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,
v4))))
proof let v2,v3,v4,v1,v0;
Tern(v3,v1,v2)=Tern(v2,v3,v1) by A3;
hence thesis by A2170;
end;
A2174: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v2,v3,Tern(v0,v1,v4))
,Tern(v1,v2,v3)
,Tern(v0,v1,Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),Tern(v1,v2,v4)))))=Tern(v0,Tern(
v3,v2,Tern(v0
,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,
v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A2172;
end;
A2176: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v2,v3,Tern(v0,v1,v4))
,Tern(v1,v2,v3)
,Tern(v0,v1,Tern(v0,Tern(v2,Tern(v0,v1,v4),v3),Tern(v1,v2,v4)))))=Tern(v0,Tern(
v3,v2,Tern(v0
,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,
v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v3,v2,Tern(v0,v1,v4)) by A3;
hence thesis by A2174;
end;
A2178: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v2,v3,Tern(v0,v1,v4))
,Tern(v1,v2,v3)
,Tern(v0,v1,Tern(v0,Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v4)))))=Tern(v0,Tern(
v3,v2,Tern(v0
,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,
v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v2,v3,Tern(v0,v1,v4)) by A4;
hence thesis by A2176;
end;
A2180: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v2,v3,Tern(v0,v1,v4))
,Tern(v1,v2,v3)
,Tern(v0,v1,Tern(v0,Tern(v1,v2,v4),Tern(v2,v3,Tern(v0,v1,v4))))))=Tern(v0,Tern(
v3,v2,Tern(v0
,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,
v4))))
proof let v2,v3,v4,v1,v0;
Tern(v0,Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v4))=Tern(v0,Tern(v1,v2,v4),Tern(
v2,v3,Tern(v0
,v1,v4))) by A4;
hence thesis by A2178;
end;
A2182: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v2,v3,Tern(v0,v1,v4))
,Tern(v1,v2,v3)
,Tern(v0,v1,Tern(v2,v3,Tern(v0,v1,v4)))))=Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),
Tern(Tern(v3,v2
,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v0,v1,Tern(v0,Tern(v1,v2,v4),Tern(v2,v3,Tern(v0,v1,v4))))=Tern(v0,v1,Tern(
v2,v3,Tern(v0
,v1,v4))) by A1920;
hence thesis by A2180;
end;
A2184: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v1,v2,v3),Tern(v0,v1,
Tern(v2,v3,Tern(v0
,v1,v4))),Tern(v2,v3,Tern(v0,v1,v4))))=Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),Tern(
Tern(v3,v2
,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,Tern(v0,v1,v4))),Tern(v2,v3,Tern(v0,
v1
,v4)))=Tern(Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,
Tern(v0,v1
,v4)))) by A3;
hence thesis by A2182;
end;
A2186: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(Tern(v1,v2,v3),Tern(v2,v3,
Tern(v0,v1,v4))
,Tern(v0,v1,Tern(v2,v3,Tern(v0,v1,v4)))))=Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),
Tern(Tern(v3,v2
,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(Tern(v1,v2,v3),Tern(v0,v1,Tern(v2,v3,Tern(v0,v1,v4))),Tern(v2,v3,Tern(v0,
v1
,v4)))=Tern(Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)),Tern(v0,v1,Tern(v2,v3,
Tern(v0,v1
,v4)))) by A4;
hence thesis by A2184;
end;
A2188: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(v0,Tern(v2,v3,Tern(v0,v1,
v4)),Tern(v1,v2
,v3)))=Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(
v3,v1,v2)
,Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)),Tern(v0,v1,Tern(v2,v3,Tern(v0,v1
,v4))))=Tern(v0
,Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v3)) by A2083;
hence thesis by A2186;
end;
A2190: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(v0,Tern(v1,v2,v3),Tern(v2,
v3,Tern(v0,v1
,v4))))=Tern(v0,Tern(v3,v2,Tern(v0,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern
(v3,v1,v2)
,Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v0,Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v3))=Tern(v0,Tern(v1,v2,v3),Tern(
v2,v3,Tern(v0
,v1,v4))) by A4;
hence thesis by A2188;
end;
A2192: for v3,v2,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,Tern(v0,v1,v4),Tern(v0,v3,Tern(v1,v2,v3))))=
Tern(v0,Tern(v3,v2
,Tern(v0,v1,v4)),Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern
(v0,v1
,v4))))
proof let v3,v2,v4,v1,v0;
Tern(v0,Tern(v1,v2,Tern(v2,v3,Tern(v0,v1,v4))),Tern(v0,Tern(v1,v2,v3),Tern(v2,
v3,Tern(v0,v1
,v4))))=Tern(v0,Tern(v1,v2,v3),Tern(v2,Tern(v0,v1,v4),Tern(v0,v3,Tern(v1,v2,v3)
))) by
A2032;
hence thesis by A2190;
end;
A2194: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v3,v2,Tern(v0,
v1,v4))
,Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v0,Tern(v1,v2,v3),Tern(v2,Tern(v0,v1,v4),Tern(v0,v3,Tern(v1,v2,v3))))=Tern
(v0,Tern(v1,v2
,v3),Tern(v2,v3,Tern(v0,v1,v4))) by A2036;
hence thesis by A2192;
end;
A2196: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v2,Tern(v0,v1,
v4),v3)
,Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v3,v2,Tern(v0,v1,v4)) by A3;
hence thesis by A2194;
end;
A2198: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v2,v3,Tern(v0,
v1,v4))
,Tern(Tern(v3,v2,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v2,v3,Tern(v0,v1,v4)) by A4;
hence thesis by A2196;
end;
A2200: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v2,v3,Tern(v0,
v1,v4))
,Tern(Tern(v2,Tern(v0,v1,v4),v3),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v3,v2,Tern(v0,v1,v4)) by A3;
hence thesis by A2198;
end;
A2202: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v2,v3,Tern(v0,
v1,v4))
,Tern(Tern(v2,v3,Tern(v0,v1,v4)),Tern(v3,v1,v2),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,Tern(v0,v1,v4),v3)=Tern(v2,v3,Tern(v0,v1,v4)) by A4;
hence thesis by A2200;
end;
A2204: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v2,v3,Tern(v0,
v1,v4))
,Tern(Tern(v2,v3,Tern(v0,v1,v4)),Tern(v2,v3,v1),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v3,v1,v2)=Tern(v2,v3,v1) by A3;
hence thesis by A2202;
end;
A2206: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v2,v3,Tern(v0,
v1,v4))
,Tern(Tern(v2,v3,Tern(v0,v1,v4)),Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(v2,v3,v1)=Tern(v1,v2,v3) by A3;
hence thesis by A2204;
end;
A2208: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v2,v3,Tern(v0,
v1,v4))
,Tern(Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,v1,v4)),Tern(v2,v3,Tern(v0,v1,v4))))
proof let v2,v3,v4,v1,v0;
Tern(Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,v1,v4)),Tern(v2,v3,Tern(v0,v1,v4)))=Tern
(Tern(v2,v3
,Tern(v0,v1,v4)),Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,v1,v4))) by A3;
hence thesis by A2206;
end;
A2210: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v0,Tern(v2,v3,Tern(v0,
v1,v4)),Tern(v2
,Tern(v0,v1,v4),Tern(v1,v2,v3)))
proof let v2,v3,v4,v1,v0;
Tern(Tern(v1,v2,v3),Tern(v1,v2,Tern(v0,v1,v4)),Tern(v2,v3,Tern(v0,v1,v4)))=Tern
(v2,Tern(v0,v1
,v4),Tern(v1,v2,v3)) by A2128;
hence thesis by A2208;
end;
A2212: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v2,Tern(v0,v1,v4),Tern
(v1,v3,Tern(v2
,v3,v0)))
proof let v2,v3,v4,v1,v0;
Tern(v0,Tern(v2,v3,Tern(v0,v1,v4)),Tern(v2,Tern(v0,v1,v4),Tern(v1,v2,v3)))=Tern
(v2,Tern(v0,v1
,v4),Tern(v1,v3,Tern(v2,v3,v0))) by A2024;
hence thesis by A2210;
end;
A2214: for v2,v3,v4,v1,v0 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v3,Tern(v0,v1,v4)))=Tern(v2,Tern(v0,v1,v4),Tern
(v1,v3,Tern(v0
,v2,v3)))
proof let v2,v3,v4,v1,v0;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A2212;
end;
A2218: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v4,v1)))=Tern(v1,Tern(v2,v0,v4),Tern
(v0,v4,Tern(v1
,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v1)=Tern(v1,v0,v4) by A3;
hence thesis by A2214;
end;
A2220: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v1,v4)))=Tern(v1,Tern(v2,v0,v4),Tern
(v0,v4,Tern(v1
,v2,v3)))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v1)=Tern(v0,v1,v4) by A4;
hence thesis by A2218;
end;
A2222: for v0,v4,v3,v2,v1 holds
Tern(v0,v4,Tern(v1,v2,v3))=Tern(v1,Tern(v2,v0,v4),Tern(v0,v4,Tern(v1,v2,v3)))
proof let v0,v4,v3,v2,v1;
Tern(v0,Tern(v1,v2,v3),Tern(v2,v4,Tern(v0,v1,v4)))=Tern(v0,v4,Tern(v1,v2,v3))
by A1876;
hence thesis by A2220;
end;
A2225: for v0,v1,v4,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v4))=Tern(v2,Tern(v0,v1,v3),Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v1,v4,v3,v2;
Tern(v0,v1,v3)=Tern(v3,v0,v1) by A3;
hence thesis by A2222;
end;
A2227: for v0,v1,v4,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v4))=Tern(v2,Tern(v0,v3,v1),Tern(v0,v1,Tern(v2,v3,v4)))
proof let v0,v1,v4,v3,v2;
Tern(v0,v1,v3)=Tern(v0,v3,v1) by A4;
hence thesis by A2225;
end;
A2232: for v101,v100,v103,v4,v3,v102 holds
Tern(v100,Tern(v101,v102,v103),Tern(v100,v102,Tern(v100,v103,Tern(v102,v3
,v4))))=Tern(v100,Tern(v3,v4,v103),Tern(v100,v102,v103))
proof let v101,v100,v103,v4,v3,v102;
Tern(v100,v103,Tern(v100,v102,Tern(v3,v4,v103)))=Tern(v100,v102,Tern(v100,v103,
Tern(v102
,v3,v4))) by A1937;
hence thesis by A971;
end;
A2235: for v3,v0,v5,v4,v2 holds
Tern(v0,Tern(v2,v4,v5),Tern(v0,v2,v3))=Tern(v0,Tern(v4,v5,v3),Tern(v0,v2,v3))
proof
now let v1,v0,v3,v5,v4,v2;
Tern(v0,Tern(v1,v2,v3),Tern(v0,v2,Tern(v0,v3,Tern(v2,v4,v5))))=Tern(v0,Tern(v2,
v4,v5),Tern(v0
,v2,v3)) by A2052;
hence Tern(v0,Tern(v2,v4,v5),Tern(v0,v2,v3))=Tern(v0,Tern(v4,v5,v3),Tern(v0,v2,
v3)) by
A2232;
end;
hence thesis;
end;
A2238: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v0,v1,v4))=Tern(v0,Tern(v4,v2,v3),Tern(v0,v1,v4))
proof let v4,v0,v3,v2,v1;
Tern(v2,v3,v4)=Tern(v4,v2,v3) by A3;
hence thesis by A2235;
end;
A2243: for v102,v4,v3,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v102,v4,v1),v102)=Tern(v102,Tern(v4,v2,v3),Tern(v102,
v4,v1))
proof let v102,v4,v3,v2,v1;
Tern(v102,Tern(v1,v2,v3),Tern(v102,v4,v1))=Tern(v102,Tern(v4,v2,v3),Tern(v102,
v4,v1))
by A2238;
hence thesis by A3;
end;
A2246: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v3,v4),v3)=Tern(v3,Tern(v4,v1,v2),Tern(v3,v4,v0))
proof let v3,v4,v2,v1,v0;
Tern(v3,v4,v0)=Tern(v0,v3,v4) by A3;
hence thesis by A2243;
end;
A2248: for v4,v3,v2,v1,v0 holds
Tern(v3,Tern(v0,v1,v2),Tern(v0,v3,v4))=Tern(v3,Tern(v4,v1,v2),Tern(v3,v4,v0))
proof let v4,v3,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v3,v4),v3)=Tern(v3,Tern(v0,v1,v2),Tern(v0,v3,v4))
by A3;
hence thesis by A2246;
end;
A2251: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v0,v4))=Tern(v0,Tern(v3,v4,v2),Tern(v0,v4,v1))
proof let v4,v0,v3,v2,v1;
Tern(v4,v2,v3)=Tern(v3,v4,v2) by A3;
hence thesis by A2248;
end;
A2253: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v0,v4))=Tern(v0,Tern(v2,v3,v4),Tern(v0,v4,v1))
proof let v4,v0,v3,v2,v1;
Tern(v3,v4,v2)=Tern(v2,v3,v4) by A3;
hence thesis by A2251;
end;
A2255: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v0,v4))=Tern(v0,Tern(v2,v3,v4),Tern(v1,v0,v4))
proof let v4,v0,v3,v2,v1;
Tern(v0,v4,v1)=Tern(v1,v0,v4) by A3;
hence thesis by A2253;
end;
A2260: for v3,v101,v102,v104,v2,v1 holds
Tern(Tern(v1,v2,v3),Tern(v101,v102,Tern(v1,v2,v104)),Tern(v1,v2,v104))=Tern(
Tern(v1,v2,v3)
,Tern(v104,v101,v102),Tern(v104,Tern(v1,v2,v3),Tern(v1,v2,v104)))
proof let v3,v101,v102,v104,v2,v1;
Tern(v104,Tern(v1,v2,v3),Tern(v1,v2,v104))=Tern(v1,v2,v104) by A729;
hence thesis by A2255;
end;
A2263: for v2,v3,v4,v5,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v5),Tern(v3,v4,Tern(v0,v1,v5)))=Tern(Tern(v0,v1
,v2),Tern(v5,v3
,v4),Tern(v5,Tern(v0,v1,v2),Tern(v0,v1,v5)))
proof let v2,v3,v4,v5,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v3,v4,Tern(v0,v1,v5)),Tern(v0,v1,v5))=Tern(Tern(v0,v1,
v2),Tern(v0,v1
,v5),Tern(v3,v4,Tern(v0,v1,v5))) by A4;
hence thesis by A2260;
end;
A2266: for v2,v4,v5,v3,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v4,v5,Tern(v0,v1,v3)))=Tern(Tern(v0,v1
,v2),Tern(v5,v3
,v4),Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v3)))
proof let v2,v4,v5,v3,v1,v0;
Tern(v3,v4,v5)=Tern(v5,v3,v4) by A3;
hence thesis by A2263;
end;
A2268: for v2,v4,v5,v3,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v4,v5,Tern(v0,v1,v3)))=Tern(Tern(v0,v1
,v2),Tern(v4,v5
,v3),Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v3)))
proof let v2,v4,v5,v3,v1,v0;
Tern(v5,v3,v4)=Tern(v4,v5,v3) by A3;
hence thesis by A2266;
end;
A2270: for v2,v4,v5,v3,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v4,v5,Tern(v0,v1,v3)))=Tern(Tern(v0,v1
,v2),Tern(v4,v5
,v3),Tern(v0,v1,v3))
proof let v2,v4,v5,v3,v1,v0;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v3))=Tern(v0,v1,v3) by A729;
hence thesis by A2268;
end;
A2273: for v104,v103,v4,v2,v1 holds
Tern(Tern(v1,v2,v4),Tern(Tern(v1,v2,v103),v103,Tern(v1,v2,v4)),Tern(v103,Tern(
v1,v2,v4)
,v104))=Tern(Tern(v1,v2,v103),Tern(v1,v2,v4),Tern(v103,Tern(v1,v2,v4),v104))
proof let v104,v103,v4,v2,v1;
Tern(Tern(v1,v2,v103),Tern(v1,v2,v103),Tern(Tern(v1,v2,v103),v103,Tern(v1,v2
,v4)))=Tern(Tern(v1,v2,v103),v103,Tern(v1,v2,v4)) by A889;
hence thesis by A2073;
end;
A2276: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v3)),Tern(v3,Tern(v0,v1,
v2)
,v4))=Tern(Tern(v0,v1,v3),Tern(v0,v1,v2),Tern(v3,Tern(v0,v1,v2),v4))
proof let v4,v3,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v3))=Tern(Tern(v0,v1,v3),v3,Tern(v0,v1,v2))
by A3;
hence thesis by A2273;
end;
A2278: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v3,Tern(v0,v1,v2),v4))=Tern(Tern(v0,v1
,v3),Tern(v0,v1
,v2),Tern(v3,Tern(v0,v1,v2),v4))
proof let v4,v3,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v1,v3))=Tern(v0,v1,v3) by A729;
hence thesis by A2276;
end;
A2280: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v3,v4,Tern(v0,v1,v2)))=Tern(Tern(v0,v1
,v3),Tern(v0,v1
,v2),Tern(v3,Tern(v0,v1,v2),v4))
proof let v3,v4,v2,v1,v0;
Tern(v3,Tern(v0,v1,v2),v4)=Tern(v3,v4,Tern(v0,v1,v2)) by A4;
hence thesis by A2278;
end;
A2282: for v2,v4,v3,v1,v0 holds
Tern(v4,Tern(v0,v1,v3),Tern(v0,v1,v2))=Tern(Tern(v0,v1,v3),Tern(v0,v1,v2),Tern
(v3,Tern(v0,v1
,v2),v4))
proof let v2,v4,v3,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v0,v1,v3),Tern(v3,v4,Tern(v0,v1,v2)))=Tern(v4,Tern(v0,
v1,v3),Tern(v0
,v1,v2)) by A881;
hence thesis by A2280;
end;
A2285: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v4))=Tern(Tern(v1,v2,v3),Tern(v1,v2,v4),Tern
(v3,v0,Tern(v1
,v2,v4)))
proof let v4,v0,v3,v2,v1;
Tern(v3,Tern(v1,v2,v4),v0)=Tern(v3,v0,Tern(v1,v2,v4)) by A4;
hence thesis by A2282;
end;
A2287: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v4))=Tern(Tern(v1,v2,v3),Tern(v3,v0,v4),Tern
(v1,v2,v4))
proof let v4,v0,v3,v2,v1;
Tern(Tern(v1,v2,v3),Tern(v1,v2,v4),Tern(v3,v0,Tern(v1,v2,v4)))=Tern(Tern(v1,v2,
v3),Tern(v3,v0
,v4),Tern(v1,v2,v4)) by A2270;
hence thesis by A2285;
end;
A2289: for v4,v0,v3,v2,v1 holds
Tern(v0,Tern(v1,v2,v3),Tern(v1,v2,v4))=Tern(Tern(v1,v2,v3),Tern(v4,v3,v0),Tern
(v1,v2,v4))
proof let v4,v0,v3,v2,v1;
Tern(v3,v0,v4)=Tern(v4,v3,v0) by A3;
hence thesis by A2287;
end;
A2294: for v101,v102,v4,v2,v104 holds
Tern(Tern(v101,v2,v102),Tern(v101,v102,Tern(v104,v2,v4)),Tern(v104,Tern(v101,
v2,v102)
,Tern(v104,v101,v102)))=Tern(v101,v102,Tern(v104,v2,v4))
proof let v101,v102,v4,v2,v104;
Tern(v104,Tern(v101,v2,v102),Tern(v101,v102,Tern(v104,v2,v4)))=Tern(v101,v102,
Tern(v104
,v2,v4)) by A2227;
hence thesis by A1863;
end;
A2297: for v0,v2,v3,v4,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,Tern(v1,v4,v3)),Tern(v3,Tern(v0,v1,v2),Tern(v3,
v0
,v2)))=Tern(v0,v2,Tern(v3,v1,v4))
proof let v0,v2,v3,v4,v1;
Tern(v1,v4,v3)=Tern(v3,v1,v4) by A3;
hence thesis by A2294;
end;
A2300: for v0,v2,v3,v4,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,Tern(v1,v4,v3)),Tern(v4,Tern(v0,v1,v2),Tern(v4,
v0
,v2)))=Tern(v0,v2,Tern(v4,v1,v3))
proof let v0,v2,v3,v4,v1;
Tern(v1,v3,v4)=Tern(v1,v4,v3) by A4;
hence thesis by A2297;
end;
A2303: for v0,v2,v4,v3,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,Tern(v1,v3,v4)),Tern(v3,Tern(v0,v1,v2),Tern(v2,
v3
,v0)))=Tern(v0,v2,Tern(v3,v1,v4))
proof let v0,v2,v4,v3,v1;
Tern(v3,v0,v2)=Tern(v2,v3,v0) by A3;
hence thesis by A2300;
end;
A2305: for v0,v2,v4,v3,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,Tern(v1,v3,v4)),Tern(v3,Tern(v0,v1,v2),Tern(v0,
v2
,v3)))=Tern(v0,v2,Tern(v3,v1,v4))
proof let v0,v2,v4,v3,v1;
Tern(v2,v3,v0)=Tern(v0,v2,v3) by A3;
hence thesis by A2303;
end;
A2307: for v0,v2,v4,v3,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,Tern(v1,v3,v4)),Tern(v0,v2,v3))=Tern(v0,v2,Tern
(v3,v1,v4))
proof let v0,v2,v4,v3,v1;
Tern(v3,Tern(v0,v1,v2),Tern(v0,v2,v3))=Tern(v0,v2,v3) by A1389;
hence thesis by A2305;
end;
A2309: for v0,v2,v4,v3,v1 holds
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v0,v2,Tern(v1,v3,v4)))=Tern(v0,v2,Tern
(v3,v1,v4))
proof let v0,v2,v4,v3,v1;
Tern(Tern(v0,v1,v2),Tern(v0,v2,Tern(v1,v3,v4)),Tern(v0,v2,v3))=Tern(Tern(v0,v1,
v2),Tern(v0,v2
,v3),Tern(v0,v2,Tern(v1,v3,v4))) by A4;
hence thesis by A2307;
end;
A2311: for v0,v2,v4,v3,v1 holds
Tern(Tern(v1,v3,v4),Tern(v0,v1,v2),Tern(v0,v2,v3))=Tern(v0,v2,Tern(v3,v1,v4))
proof let v0,v2,v4,v3,v1;
Tern(Tern(v0,v1,v2),Tern(v0,v2,v3),Tern(v0,v2,Tern(v1,v3,v4)))=Tern(Tern(v1,v3,
v4),Tern(v0,v1
,v2),Tern(v0,v2,v3)) by A2102;
hence thesis by A2309;
end;
A2314: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v0,v4),Tern(v3,v4,v1))=Tern(v3,v4,Tern(v0,v2,v1))
proof let v3,v4,v2,v1,v0;
Tern(v0,v2,v1)=Tern(v1,v0,v2) by A3;
hence thesis by A2311;
end;
A2316: for v3,v4,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),Tern(v3,v0,v4),Tern(v3,v4,v1))=Tern(v3,v4,Tern(v0,v1,v2))
proof let v3,v4,v2,v1,v0;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A2314;
end;
A2319: for v3,v4,v2,v1,v0 holds
Tern(v3,v4,Tern(v0,v1,v2))=Tern(Tern(v3,v4,v1),Tern(v0,v1,v2),Tern(v3,v0,v4))
proof let v3,v4,v2,v1,v0;
Tern(Tern(v0,v1,v2),Tern(v3,v0,v4),Tern(v3,v4,v1))=Tern(v3,v4,Tern(v0,v1,v2))
by A2316;
hence thesis by A3;
end;
A2322: for v0,v1,v4,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v4))=Tern(Tern(v0,v1,v3),Tern(v2,v3,v4),Tern(v0,v1,v2))
proof let v0,v1,v4,v3,v2;
Tern(v0,v2,v1)=Tern(v0,v1,v2) by A4;
hence thesis by A2319;
end;
A2324: for v0,v1,v4,v3,v2 holds
Tern(v0,v1,Tern(v2,v3,v4))=Tern(v4,Tern(v0,v1,v3),Tern(v0,v1,v2))
proof let v0,v1,v4,v3,v2;
Tern(Tern(v0,v1,v3),Tern(v2,v3,v4),Tern(v0,v1,v2)) =
Tern(v4,Tern(v0,v1,v3),Tern(v0,v1,v2)) by A2289;
hence thesis by A2322;
end;
not Tern(c1,c2,Tern(c5,c3,c4))=Tern(c1,c2,Tern(c3,c4,c5)) by A32,A2324;
hence thesis by A3;
end;
theorem TBA2:
(for v2,v1,v0 holds Tern(v0,v1,v2)=(((v0"\/"v1)"/\"(v1"\/"v2))"/\"(v0"\/"v2)))
&
(for v0,v2,v1 holds v0"\/"(v1"/\"v2) = (v0"\/"v1)"/\"(v0"\/"v2)) &
(for v0,v2,v1 holds v0"/\"(v1"\/"v2) = (v0"/\"v1)"\/"(v0"/\"v2)) &
(for v2,v1,v0 holds (v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2)) &
(for v2,v1,v0 holds (v0"/\"v1)"/\"v2 = v0"/\"(v1"/\"v2)) implies
for v1,v2,v3,v4 holds
Tern(Tern(v1,v2,v3),v2,v4)=Tern(v1,v2,Tern(v3,v2,v4))
proof
assume A1: for v2,v1,v0 holds
Tern(v0,v1,v2)=(((v0"\/"v1)"/\"(v1"\/"v2))"/\"(v0"\/"v2));
assume A4: for v0,v2,v1 holds (v0"\/"(v1"/\"v2))=((v0"\/"v1)"/\"(v0"\/"v2));
assume A6: for v0,v2,v1 holds (v0"/\"(v1"\/"v2))=((v0"/\"v1)"\/"(v0"/\"v2));
assume A8: for v2,v1,v0 holds ((v0"\/"v1)"\/"v2)=(v0"\/"(v1"\/"v2));
assume A14: for v2,v1,v0 holds ((v0"/\"v1)"/\"v2)=(v0"/\"(v1"/\"v2));
assume not thesis; then
consider c1,c2,c3,c4 being Element of BA2TBAA B such that
A20: not Tern(Tern(c1,c2,c3),c2,c4)=Tern(c1,c2,Tern(c3,c2,c4));
not
Tern((((c1"\/"c2)"/\"(c2"\/"c3))"/\"(c1"\/"c3)),c2,c4)=Tern(c1,c2,Tern(c3,c2,
c4)) by
A1,A20; then
not
Tern(((c1"\/"c2)"/\"((c2"\/"c3)"/\"(c1"\/"c3))),c2,c4)=Tern(c1,c2,Tern(c3,c2,
c4)) by A14; then
AA:
not
(((((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3)))"\/"c2)"/\"(c2"\/"c4))"/\"(((c1
"\/"c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3)))"\/"c4))=Tern(c1,c2,Tern(c3,c2,c4)) by A1;
A38: not
((c2"\/"(c4"/\"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3)))))"/\"(c4"\/"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3)))))=Tern(c1,c2,Tern(c3,c2,c4)) by A4,AA;
A42: not
((c4"\/"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3))))))=Tern(c1,c2,(((c3"\/"c2)"/\"(c2"\/"c4))"/\"(c3"\/"
c4))) by
A1,A38;
A48: not
((c4"\/"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3))))))=Tern(c1,c2,((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))) by
A4,A42;
A52: not
((c4"\/"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3))))))=((c1"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))"/\"((
c1"\/"c2)"/\"
(c2"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A1,A48;
A56: not
((c4"\/"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3))))))=((c1"\/"c2)"/\"((c1"\/"((c3"\/"c4)"/\"(c2"\/"(c3
"/\"c4))))"/\"
(c2"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A52,A14;
A63: for v2,v1,v0 holds Tern(v0,v1,v2)=((v0"\/"v2)"/\"(v1"\/"(v0"/\"v2)))
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A1;
end;
A69: for v2,v101,v1,v0 holds
(((v0"/\"v1)"\/"v101)"/\"(v0"/\"(v1"\/"v2)))=((v0"/\"v1)"\/"(v101"/\"(v0"/\"v2
)))
proof let v2,v101,v1,v0;
((v0"/\"v1)"\/"(v0"/\"v2))=(v0"/\"(v1"\/"v2)) by A6;
hence thesis by A4;
end;
A75: for v3,v0,v2,v1 holds
(v1"/\"((v2"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=((v1"/\"v2)"\/"(v0"/\"(v1"/\"v3)))
proof let v3,v0,v2,v1;
(v1"/\"((v2"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=((v0"\/"(v1"/\"v2))"/\"(v1"/\"(v2
"\/"v3))) by A14;
hence thesis by A69;
end;
A78: for v2,v3,v1,v0 holds
(v0"/\"((v1"\/"v2)"/\"(v3"\/"(v0"/\"v1))))=((v0"/\"v1)"\/"(v0"/\"(v2"/\"v3)))
proof let v2,v3,v1,v0;
(v0"/\"(v2"/\"v3))=(v3"/\"(v0"/\"v2)) by A14;
hence thesis by A75;
end;
A82: for v2,v3,v1,v0 holds
(v0"/\"((v1"\/"v2)"/\"(v3"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v3"/\"v2)))
proof let v2,v3,v1,v0;
((v0"/\"v1)"\/"(v0"/\"(v3"/\"v2)))=(v0"/\"(v1"\/"(v3"/\"v2))) by A6;
hence thesis by A78;
end;
A85: for v102,v1,v101 holds
(((v101"/\"v1)"\/"v101)"/\"((v101"/\"v1)"\/"v102))=(v101"/\"(v1"\/"v102))
proof let v102,v1,v101;
((v101"/\"v1)"\/"(v101"/\"v102))=(v101"/\"(v1"\/"v102)) by A6;
hence thesis by A4;
end;
A93: for v2,v101,v1,v0 holds
((v0"\/"v1)"/\"v101)"\/"(v0"\/"(v1"/\"v2)) =
(v0"\/"v1)"/\"(v101"\/"(v0"\/"v2))
proof let v2,v101,v1,v0;
(v0"\/"v1)"/\"(v0"\/"v2) = v0"\/"(v1"/\"v2) by A4;
hence thesis by A6;
end;
A99: for v3,v0,v2,v1 holds
(v1"\/"((v2"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=((v1"\/"v2)"/\"(v0"\/"(v1"\/"v3)))
proof let v3,v0,v2,v1;
(v1"\/"((v2"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=
((v0"/\"(v1"\/"v2))"\/"(v1"\/"(v2"/\"v3))) by A8;
hence thesis by A93;
end;
A102: for v2,v3,v1,v0 holds
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v1))))=((v0"\/"v1)"/\"(v0"\/"(v2"\/"v3)))
proof let v2,v3,v1,v0;
(v0"\/"(v2"\/"v3))=(v3"\/"(v0"\/"v2)) by A8;
hence thesis by A99;
end;
A106: for v2,v3,v1,v0 holds
v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v1))) = v0"\/"(v1"/\"(v3"\/"v2))
proof let v2,v3,v1,v0;
(v0"\/"v1)"/\"(v0"\/"(v3"\/"v2)) = v0"\/"(v1"/\"(v3"\/"v2)) by A4;
hence thesis by A102;
end;
A109: for v102,v2,v1,v100 holds
(v2"\/"(v100"\/"v1))"/\"(v100"\/"v102) = v100"\/"((v1"\/"v2)"/\"v102)
proof let v102,v2,v1,v100;
v100"\/"(v1"\/"v2) = v2"\/"(v100"\/"v1) by A8;
hence thesis by A4;
end;
A117: for v102,v0,v100,v1 holds
(v0"\/"(v1"\/"v100))"/\"(v100"\/"v102) = v100"\/"((v0"\/"v1)"/\"v102)
proof let v102,v0,v100,v1;
v0"\/"(v1"\/"v100) = v100"\/"(v0"\/"v1) by A8;
hence thesis by A4;
end;
A123: for v102,v2,v1,v100 holds
(v2"/\"(v100"/\"v1))"\/"(v100"/\"v102) = v100"/\"((v1"/\"v2)"\/"v102)
proof let v102,v2,v1,v100;
v100"/\"(v1"/\"v2) = v2"/\"(v100"/\"v1) by A14;
hence thesis by A6;
end;
A131: for v102,v0,v100,v1 holds
((v0"/\"(v1"/\"v100))"\/"(v100"/\"v102))=(v100"/\"((v0"/\"v1)"\/"v102))
proof let v102,v0,v100,v1;
(v0"/\"(v1"/\"v100))=(v100"/\"(v0"/\"v1)) by A14;
hence thesis by A6;
end;
A137: for v2,v101,v1,v0 holds
(((v0"\/"v1)"/\"v101)"\/"(v1"\/"(v0"/\"v2)))=((v0"\/"v1)"/\"(v101"\/"(v1"\/"v2
)))
proof let v2,v101,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A6;
end;
A143: for v3,v0,v2,v1 holds
(v2"\/"((v1"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=((v1"\/"v2)"/\"(v0"\/"(v2"\/"v3)))
proof let v3,v0,v2,v1;
(v2"\/"((v1"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=
((v0"/\"(v1"\/"v2))"\/"(v2"\/"(v1"/\"v3))) by A8;
hence thesis by A137;
end;
A146: for v2,v3,v0,v1 holds
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v1"\/"v0))))=((v1"\/"v0)"/\"(v0"\/"(v2"\/"v3)))
proof let v2,v3,v0,v1;
(v0"\/"(v2"\/"v3))=(v3"\/"(v0"\/"v2)) by A8;
hence thesis by A143;
end;
A150: for v2,v3,v0,v1 holds
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v1"\/"v0))))=(v0"\/"(v1"/\"(v3"\/"v2)))
proof let v2,v3,v0,v1;
((v1"\/"v0)"/\"(v0"\/"(v3"\/"v2)))=(v0"\/"(v1"/\"(v3"\/"v2))) by A4;
hence thesis by A146;
end;
A153: for v2,v100,v1,v0 holds
((v100"\/"(v0"/\"v1))"/\"(v0"/\"(v1"\/"v2)))=
((v0"/\"v1)"\/"(v100"/\"(v0"/\"v2)))
proof let v2,v100,v1,v0;
((v0"/\"v1)"\/"(v0"/\"v2))=(v0"/\"(v1"\/"v2)) by A6;
hence thesis by A4;
end;
A156: for v3,v0,v2,v1 holds
(v1"/\"((v2"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=((v1"/\"v2)"\/"(v0"/\"(v1"/\"v3)))
proof let v3,v0,v2,v1;
(v1"/\"((v2"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=
((v0"\/"(v1"/\"v2))"/\"(v1"/\"(v2"\/"v3))) by A14;
hence thesis by A153;
end;
A159: for v0,v1,v2,v3 holds
(v0"/\"(v1"\/"(v3"/\"v2)))=((v0"/\"v1)"\/"(v3"/\"(v0"/\"v2)))
proof let v0,v1,v2,v3;
(v0"/\"((v1"\/"v2)"/\"(v3"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v3"/\"v2))) by A82;
hence thesis by A156;
end;
A164: for v102,v2,v1,v100 holds
((v2"\/"(v100"\/"v1))"/\"((v1"\/"v2)"\/"v102))=((v1"\/"v2)"\/"(v100"/\"v102))
proof let v102,v2,v1,v100;
(v100"\/"(v1"\/"v2))=(v2"\/"(v100"\/"v1)) by A8;
hence thesis by A4;
end;
A171: for v3,v0,v2,v1 holds
((v0"\/"(v1"\/"v2))"/\"(v2"\/"(v3"\/"v0)))=((v2"\/"v0)"\/"(v1"/\"v3))
proof let v3,v0,v2,v1;
(v3"\/"(v0"\/"v2))=(v2"\/"(v3"\/"v0)) by A8;
hence thesis by A164;
end;
A175: for v3,v0,v2,v1 holds
((v0"\/"(v1"\/"v2))"/\"(v0"\/"(v3"\/"v2)))=((v2"\/"v0)"\/"(v1"/\"v3))
proof let v3,v0,v2,v1;
(v0"\/"(v3"\/"v2))=(v2"\/"(v0"\/"v3)) by A8;
hence thesis by A171;
end;
A179: for v0,v3,v2,v1 holds
(v0"\/"((v1"\/"v2)"/\"(v2"\/"v3)))=((v2"\/"v0)"\/"(v1"/\"v3))
proof let v0,v3,v2,v1;
((v0"\/"(v1"\/"v2))"/\"(v0"\/"(v2"\/"v3)))=
(v0"\/"((v1"\/"v2)"/\"(v2"\/"v3))) by A4;
hence thesis by A175;
end;
A181: for v0,v2,v3,v1 holds (v0"\/"(v2"\/"(v1"/\"v3)))=((v2"\/"v0)"\/"(v1"/\"v3
))
proof let v0,v2,v3,v1;
((v1"\/"v2)"/\"(v2"\/"v3))=(v2"\/"(v1"/\"v3)) by A4;
hence thesis by A179;
end;
A188: for v0,v102,v2,v1 holds
((v0"\/"v1)"/\"((v1"\/"v2)"/\"v102))=(v102"/\"(v1"\/"(v0"/\"v2)))
proof let v0,v102,v2,v1;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A14;
end;
A194: for v2,v0,v3,v1 holds
(v2"/\"((v1"\/"v3)"/\"(v0"\/"v1)))=(v2"/\"(v1"\/"(v0"/\"v3)))
proof let v2,v0,v3,v1;
(v2"/\"((v1"\/"v3)"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v2"/\"(v1"\/"v3))) by A14;
hence thesis by A188;
end;
A198: for v2,v101,v1,v0 holds
(((v0"\/"v1)"\/"v101)"/\"(v101"\/"(v1"\/"v2)))=(v101"\/"(v1"\/"(v0"/\"v2)))
proof let v2,v101,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A4;
end;
A204: for v3,v2,v1,v0 holds
((v2"\/"(v0"\/"v1))"/\"(v0"\/"(v2"\/"v3)))=(v0"\/"(v2"\/"(v1"/\"v3)))
proof let v3,v2,v1,v0;
(v0"\/"(v1"\/"v2))=(v2"\/"(v0"\/"v1)) by A8;
hence thesis by A198;
end;
A210: for v3,v1,v0,v2 holds
((v1"\/"(v2"\/"v0))"/\"(v2"\/"(v0"\/"v3)))=(v2"\/"(v0"\/"(v1"/\"v3)))
proof let v3,v1,v0,v2;
v1"\/"(v2"\/"v0) = v0"\/"(v1"\/"v2) by A8;
hence thesis by A204;
end;
A216: for v3,v0,v2,v1 holds
((v0"\/"(v1"\/"v2))"/\"(v1"\/"(v3"\/"v2)))=(v2"\/"(v1"\/"(v0"/\"v3)))
proof let v3,v0,v2,v1;
v1"\/"(v3"\/"v2) = v2"\/"(v1"\/"v3) by A8;
hence thesis by A210;
end;
A220: for v1,v0,v3,v2 holds
(v1"\/"((v2"\/"v3)"/\"(v0"\/"v2)))=(v2"\/"(v1"\/"(v0"/\"v3)))
proof let v1,v0,v3,v2;
((v0"\/"(v1"\/"v2))"/\"(v1"\/"(v2"\/"v3)))=
(v1"\/"((v2"\/"v3)"/\"(v0"\/"v2))) by A109;
hence thesis by A216;
end;
A223: for v0,v3,v2,v1 holds
(v0"\/"((v1"\/"v2)"/\"(v3"\/"v1)))=(v0"\/"((v3"/\"v2)"\/"v1))
proof let v0,v3,v2,v1;
(v0"\/"((v3"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v3"/\"v2))) by A8;
hence thesis by A220;
end;
A228: for v2,v101,v1,v0 holds
(((v0"/\"v1)"\/"v101)"/\"(v1"/\"(v0"\/"v2)))=((v0"/\"v1)"\/"(v101"/\"(v1"/\"v2
)))
proof let v2,v101,v1,v0;
((v0"/\"v1)"\/"(v1"/\"v2))=(v1"/\"(v0"\/"v2)) by A6;
hence thesis by A4;
end;
A234: for v3,v0,v2,v1 holds
(v2"/\"((v1"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=((v1"/\"v2)"\/"(v0"/\"(v2"/\"v3)))
proof let v3,v0,v2,v1;
(v2"/\"((v1"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=
((v0"\/"(v1"/\"v2))"/\"(v2"/\"(v1"\/"v3))) by A14;
hence thesis by A228;
end;
A237: for v2,v3,v0,v1 holds
(v0"/\"((v1"\/"v2)"/\"(v3"\/"(v1"/\"v0))))=((v1"/\"v0)"\/"(v0"/\"(v2"/\"v3)))
proof let v2,v3,v0,v1;
(v0"/\"(v2"/\"v3))=(v3"/\"(v0"/\"v2)) by A14;
hence thesis by A234;
end;
A241: for v2,v3,v0,v1 holds
(v0"/\"((v1"\/"v2)"/\"(v3"\/"(v1"/\"v0))))=(v0"/\"(v1"\/"(v3"/\"v2)))
proof let v2,v3,v0,v1;
((v1"/\"v0)"\/"(v0"/\"(v3"/\"v2)))=(v0"/\"(v1"\/"(v3"/\"v2))) by A6;
hence thesis by A237;
end;
A244: for v102,v0,v2,v1 holds
((v0"\/"(v1"/\"v2))"\/"((v0"\/"v2)"/\"v102))=
((v0"\/"v2)"/\"((v0"\/"v1)"\/"v102))
proof let v102,v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A6;
end;
A249: for v1,v3,v2,v0 holds
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2))))=((v0"\/"v2)"/\"((v0"\/"v1)"\/"v3))
proof let v1,v3,v2,v0;
((v0"\/"(v1"/\"v2))"\/"(v3"/\"(v0"\/"v2)))=
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2)))) by A181;
hence thesis by A244;
end;
A253: for v1,v3,v2,v0 holds
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2))))=((v0"\/"v2)"/\"(v1"\/"(v3"\/"v0)))
proof let v1,v3,v2,v0;
(v3"\/"(v0"\/"v1))=(v1"\/"(v3"\/"v0)) by A8;
hence thesis by A249;
end;
A257: for v1,v3,v2,v0 holds
v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2))) = (v0"\/"v2)"/\"(v0"\/"(v3"\/"v1))
proof let v1,v3,v2,v0;
v0"\/"(v3"\/"v1) = v1"\/"(v0"\/"v3) by A8;
hence thesis by A253;
end;
A261: for v1,v3,v2,v0 holds
v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2))) = v0"\/"(v2"/\"(v1"\/"v3))
proof let v1,v3,v2,v0;
(v0"\/"v2)"/\"(v0"\/"(v1"\/"v3)) = v0"\/"(v2"/\"(v1"\/"v3)) by A4;
hence thesis by A257;
end;
A264: for v2,v100,v1,v0 holds
(v100"/\"(v0"\/"v1))"\/"(v0"\/"(v1"/\"v2)) =
(v0"\/"v1)"/\"(v100"\/"(v0"\/"v2))
proof let v2,v100,v1,v0;
(v0"\/"v1)"/\"(v0"\/"v2) = v0"\/"(v1"/\"v2) by A4;
hence thesis by A6;
end;
A267: for v3,v0,v2,v1 holds
v1"\/"((v2"/\"v3)"\/"(v0"/\"(v1"\/"v2))) = (v1"\/"v2)"/\"(v0"\/"(v1"\/"v3))
proof let v3,v0,v2,v1;
v1"\/"((v2"/\"v3)"\/"(v0"/\"(v1"\/"v2))) =
(v0"/\"(v1"\/"v2))"\/"(v1"\/"(v2"/\"v3)) by A8;
hence thesis by A264;
end;
A270: for v0,v1,v2,v3 holds
v0"\/"(v1"/\"(v3"\/"v2)) = (v0"\/"v1)"/\"(v3"\/"(v0"\/"v2))
proof let v0,v1,v2,v3;
v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v1))) = v0"\/"(v1"/\"(v3"\/"v2)) by A106;
hence thesis by A267;
end;
A275: for v102,v2,v1,v100 holds
(v2"/\"(v100"/\"v1))"\/"((v1"/\"v2)"/\"v102) = (v1"/\"v2)"/\"(v100"\/"v102)
proof let v102,v2,v1,v100;
v100"/\"(v1"/\"v2) = v2"/\"(v100"/\"v1) by A14;
hence thesis by A6;
end;
A282: for v3,v0,v2,v1 holds
((v0"/\"(v1"/\"v2))"\/"(v2"/\"(v3"/\"v0)))=((v2"/\"v0)"/\"(v1"\/"v3))
proof let v3,v0,v2,v1;
(v3"/\"(v0"/\"v2))=(v2"/\"(v3"/\"v0)) by A14;
hence thesis by A275;
end;
A286: for v3,v0,v2,v1 holds
(v0"/\"(v1"/\"v2))"\/"(v0"/\"(v3"/\"v2)) = (v2"/\"v0)"/\"(v1"\/"v3)
proof let v3,v0,v2,v1;
v0"/\"(v3"/\"v2) = v2"/\"(v0"/\"v3) by A14;
hence thesis by A282;
end;
A290: for v0,v3,v2,v1 holds
(v0"/\"((v1"/\"v2)"\/"(v2"/\"v3)))=((v2"/\"v0)"/\"(v1"\/"v3))
proof let v0,v3,v2,v1;
((v0"/\"(v1"/\"v2))"\/"(v0"/\"(v2"/\"v3)))=(v0"/\"((v1"/\"v2)"\/"(v2"/\"v3)))
by A6;
hence thesis by A286;
end;
A292: for v0,v2,v3,v1 holds (v0"/\"(v2"/\"(v1"\/"v3)))=((v2"/\"v0)"/\"(v1"\/"v3
))
proof let v0,v2,v3,v1;
(v1"/\"v2)"\/"(v2"/\"v3) = v2"/\"(v1"\/"v3) by A6;
hence thesis by A290;
end;
A299: for v2,v100,v1,v0 holds
((v100"/\"(v0"\/"v1))"\/"(v1"\/"(v0"/\"v2)))=((v0"\/"v1)"/\"(v100"\/"(v1"\/"v2
)))
proof let v2,v100,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A6;
end;
A302: for v3,v0,v2,v1 holds
(v2"\/"((v1"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=((v1"\/"v2)"/\"(v0"\/"(v2"\/"v3)))
proof let v3,v0,v2,v1;
(v2"\/"((v1"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=((v0"/\"(v1"\/"v2))"\/"(v2"\/"(v1
"/\"v3))) by
A8;
hence thesis by A299;
end;
A305: for v0,v1,v2,v3 holds
(v0"\/"(v1"/\"(v3"\/"v2)))=((v1"\/"v0)"/\"(v3"\/"(v0"\/"v2)))
proof let v0,v1,v2,v3;
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v1"\/"v0))))=(v0"\/"(v1"/\"(v3"\/"v2))) by A150;
hence thesis by A302;
end;
A311: for v2,v101,v1,v0 holds
((v0"/\"v1)"/\"v101)"\/"(v101"/\"(v1"/\"v2)) = v101"/\"(v1"/\"(v0"\/"v2))
proof let v2,v101,v1,v0;
(v0"/\"v1)"\/"(v1"/\"v2) = v1"/\"(v0"\/"v2) by A6;
hence thesis by A6;
end;
A317: for v3,v2,v1,v0 holds
((v2"/\"(v0"/\"v1))"\/"(v0"/\"(v2"/\"v3)))=(v0"/\"(v2"/\"(v1"\/"v3)))
proof let v3,v2,v1,v0;
(v0"/\"(v1"/\"v2))=(v2"/\"(v0"/\"v1)) by A14;
hence thesis by A311;
end;
A323: for v3,v1,v0,v2 holds
(v1"/\"(v2"/\"v0))"\/"(v2"/\"(v0"/\"v3)) = v2"/\"(v0"/\"(v1"\/"v3))
proof let v3,v1,v0,v2;
v1"/\"(v2"/\"v0) = v0"/\"(v1"/\"v2) by A14;
hence thesis by A317;
end;
A329: for v3,v0,v2,v1 holds
(v0"/\"(v1"/\"v2))"\/"(v1"/\"(v3"/\"v2)) = v2"/\"(v1"/\"(v0"\/"v3))
proof let v3,v0,v2,v1;
v1"/\"(v3"/\"v2) = v2"/\"(v1"/\"v3) by A14;
hence thesis by A323;
end;
A333: for v1,v0,v3,v2 holds
(v1"/\"((v2"/\"v3)"\/"(v0"/\"v2)))=(v2"/\"(v1"/\"(v0"\/"v3)))
proof let v1,v0,v3,v2;
((v0"/\"(v1"/\"v2))"\/"(v1"/\"(v2"/\"v3)))=
(v1"/\"((v2"/\"v3)"\/"(v0"/\"v2))) by A123;
hence thesis by A329;
end;
A336: for v0,v3,v2,v1 holds
v0"/\"((v1"/\"v2)"\/"(v3"/\"v1)) = v0"/\"((v3"\/"v2)"/\"v1)
proof let v0,v3,v2,v1;
v0"/\"((v3"\/"v2)"/\"v1) = v1"/\"(v0"/\"(v3"\/"v2)) by A14;
hence thesis by A333;
end;
A341: for v102,v103,v0,v2,v1 holds
((v0"/\"(v1"\/"v2))"\/"(v102"/\"v103))=
((v0"/\"v1)"\/"((v0"/\"v2)"\/"(v102"/\"v103)))
proof let v102,v103,v0,v2,v1;
((v0"/\"v1)"\/"(v0"/\"v2))=(v0"/\"(v1"\/"v2)) by A6;
hence thesis by A181;
end;
A346: for v102,v0,v1,v3,v2 holds
((v0"\/"(v1"\/"(v2"/\"v3)))"/\"((v2"/\"v3)"\/"v102))=
((v2"/\"v3)"\/"((v0"\/"v1)"/\"v102))
proof let v102,v0,v1,v3,v2;
((v0"\/"v1)"\/"(v2"/\"v3))=(v0"\/"(v1"\/"(v2"/\"v3))) by A181;
hence thesis by A4;
end;
A354: for v102,v103,v0,v2,v1 holds
((v0"\/"(v1"/\"v2))"/\"(v102"\/"v103))=
((v0"\/"v1)"/\"((v0"\/"v2)"/\"(v102"\/"v103)))
proof let v102,v103,v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A292;
end;
A360: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"c2)"/\"((
c1"\/"c3)"/\"
(c2"\/"c3))))))=((c1"\/"c2)"/\"((c1"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))"/\"(
c2"\/"(
(c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A354,A56;
A362: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"
((c1"\/"(c2"/\"c3))"/\"(c2"\/"c3)))))=
((c1"\/"c2)"/\"((c1"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))"/\"(c2"\/"
((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A354,A360;
A368: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"
(c2"\/"(c4"/\"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))))=
((c2"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))"/\"
(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A362,A354;
A371: for v102,v103,v100 holds
(v100"/\"(v103"\/"(v102"/\"(v100"/\"v103))))=(v100"/\"(v103"\/"(v103"/\"v102))
)
proof let v102,v103,v100;
((v103"\/"v102)"/\"(v103"\/"(v100"/\"v103)))=(v103"\/"(v102"/\"(v100"/\"v103)))
by
A4;
hence thesis by A82;
end;
A374: for v1,v0,v2 holds
v0"/\"(v1"\/"(v1"/\"(v2"/\"v0))) = v0"/\"(v1"\/"(v1"/\"v2))
proof let v1,v0,v2;
v2"/\"(v0"/\"v1) = v1"/\"(v2"/\"v0) by A14;
hence thesis by A371;
end;
A378: for v0,v1,v2 holds
v0"/\"(v1"\/"(v0"/\"(v2"/\"v1))) = v0"/\"(v1"\/"(v1"/\"v2))
proof let v0,v1,v2;
v0"/\"(v2"/\"v1) = v1"/\"(v0"/\"v2) by A14;
hence thesis by A374;
end;
A383: for v102,v100,v101,v1 holds
(v100"/\"((v101"\/"v102)"/\"(v100"/\"(v1"\/"v101))))=(v100"/\"(v101"\/"(
(v100"/\"v1)"/\"v102)))
proof let v102,v100,v101,v1;
((v100"/\"v1)"\/"(v100"/\"v101))=(v100"/\"(v1"\/"v101)) by A6;
hence thesis by A82;
end;
A388: for v0,v2,v3,v1 holds
(v0"/\"(v0"/\"((v1"\/"v3)"/\"(v1"\/"v2))))=(v0"/\"(v1"\/"((v0"/\"v3)"/\"v2)))
proof let v0,v2,v3,v1;
(v0"/\"((v1"\/"v3)"/\"(v1"\/"v2)))=((v1"\/"v2)"/\"(v0"/\"(v1"\/"v3))) by A14;
hence thesis by A383;
end;
A391: for v0,v1,v3,v2 holds
(v0"/\"(v0"/\"(v1"\/"(v2"/\"v3))))=(v0"/\"(v1"\/"((v0"/\"v2)"/\"v3)))
proof let v0,v1,v3,v2;
((v1"\/"v2)"/\"(v1"\/"v3))=(v1"\/"(v2"/\"v3)) by A4;
hence thesis by A388;
end;
A398: for v0,v1,v3,v2 holds
(v0"/\"(v0"/\"(v1"\/"(v2"/\"v3))))=(v0"/\"(v1"\/"(v0"/\"(v3"/\"v2))))
proof let v0,v1,v3,v2;
(v0"/\"(v3"/\"v2))=(v2"/\"(v0"/\"v3)) by A14;
hence thesis by A391;
end;
A408: for v100,v1 holds
(v100"/\"(v1"\/"v100))=(v100"\/"((v100"/\"v1)"/\"(v100"/\"v1)))
proof let v100,v1;
((v100"\/"(v100"/\"v1))"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v1"\/"v100)) by
A85;
hence thesis;
end;
A413: for v1,v0 holds (v0"/\"(v0"\/"v1))=(v0"\/"(v1"/\"((v0"/\"v1)"/\"v0)))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"/\"v1))=(v1"/\"((v0"/\"v1)"/\"v0)) by A14;
hence thesis by A408;
end;
A417: for v1,v0 holds (v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"((v0"/\"v1)"/\"v1)))
proof let v1,v0;
(v0"/\"((v0"/\"v1)"/\"v1))=(v1"/\"(v0"/\"(v0"/\"v1))) by A14;
hence thesis by A413;
end;
A421: for v1,v0 holds (v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"(v0"/\"(v1"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A417;
end;
A425: for v102,v0,v2,v1 holds
((v0"/\"(v1"\/"v2))"\/"((v0"\/"(v0"/\"v1))"/\"v102))=
((v0"\/"(v0"/\"v1))"/\"((v2"\/"(v0"/\"v1))"\/"v102))
proof let v102,v0,v2,v1;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v2)) by A85;
hence thesis by A6;
end;
A432: for v3,v0,v2,v1 holds
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=
((v0"\/"(v0"/\"v1))"/\"(v2"\/"((v0"/\"v1)"\/"v3)))
proof let v3,v0,v2,v1;
(v2"\/"((v0"/\"v1)"\/"v3))=(v3"\/"(v2"\/"(v0"/\"v1))) by A8;
hence thesis by A425;
end;
A438: for v2,v101,v1,v0 holds
(((v0"\/"(v0"/\"v1))"/\"v101)"\/"(v0"/\"(v1"\/"v2)))=
((v0"\/"(v0"/\"v1))"/\"(v101"\/"(v2"\/"(v0"/\"v1))))
proof let v2,v101,v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v2)) by A85;
hence thesis by A6;
end;
A444: for v3,v0,v2,v1 holds
((v0"/\"(v1"\/"(v1"/\"v2)))"\/"(v1"/\"(v2"\/"v3)))=
((v1"/\"(v2"\/"v0))"\/"(v3"/\"(v1"\/"(v1"/\"v2))))
proof let v3,v0,v2,v1;
((v1"\/"(v1"/\"v2))"/\"(v0"\/"(v3"\/"(v1"/\"v2))))=
((v1"/\"(v2"\/"v0))"\/"(v3"/\"(v1"\/"(v1"/\"v2)))) by A432;
hence thesis by A438;
end;
A447: for v100,v101,v2,v1 holds
((v100"\/"(v100"/\"v101))"/\"((v1"\/"v2)"\/"(v100"/\"v101)))=
(v100"/\"(v2"\/"(v101"\/"v1)))
proof let v100,v101,v2,v1;
(v101"\/"(v1"\/"v2))=(v2"\/"(v101"\/"v1)) by A8;
hence thesis by A85;
end;
A450: for v2,v3,v1,v0 holds
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v3"\/"(v0"/\"v1))))=(v0"/\"(v3"\/"(v1"\/"v2)))
proof let v2,v3,v1,v0;
((v2"\/"v3)"\/"(v0"/\"v1))=(v2"\/"(v3"\/"(v0"/\"v1))) by A181;
hence thesis by A447;
end;
A452: for v3,v0,v2,v1 holds
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v3"\/"(v1"\/"v2)))
proof let v3,v0,v2,v1;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v3"\/"(v0"/\"v1))))=
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1)))) by A432;
hence thesis by A450;
end;
A454: for v3,v0,v2,v1 holds
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v2"\/"(v3"\/"v1)))
proof let v3,v0,v2,v1;
(v3"\/"(v1"\/"v2))=(v2"\/"(v3"\/"v1)) by A8;
hence thesis by A452;
end;
A458: for v3,v0,v2,v1 holds
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v3"\/"v2)))
proof let v3,v0,v2,v1;
(v1"\/"(v3"\/"v2))=(v2"\/"(v1"\/"v3)) by A8;
hence thesis by A454;
end;
A504: for v102,v2,v1,v0 holds
((v0"/\"(v1"\/"v2))"\/"((v2"\/"(v0"/\"v1))"/\"v102))=((v2"\/"(v0"/\"v1))"/\"((
v0"\/"
(v0"/\"v1))"\/"v102))
proof let v102,v2,v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v2)) by A85;
hence thesis by A6;
end;
A511: for v3,v2,v1,v0 holds
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v2"\/"(v0"/\"v1))))=((v2"\/"(v0"/\"v1))"/\"(v0
"\/"(
(v0"/\"v1)"\/"v3)))
proof let v3,v2,v1,v0;
(v0"\/"((v0"/\"v1)"\/"v3))=(v3"\/"(v0"\/"(v0"/\"v1))) by A8;
hence thesis by A504;
end;
A516: for v102,v101,v1,v0 holds
((v0"\/"(v1"\/"((v0"\/"v1)"/\"v101)))"/\"(v102"\/"((v0"\/"v1)"/\"v101)))=((v0
"\/"v1)"/\"
(v101"\/"v102))
proof let v102,v101,v1,v0;
((v0"\/"v1)"\/"((v0"\/"v1)"/\"v101))=(v0"\/"(v1"\/"((v0"\/"v1)"/\"v101))) by
A181;
hence thesis by A85;
end;
A523: for v3,v2,v1,v0 holds
((v2"/\"(v0"\/"v1))"\/"(v3"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v2"\/"v3))
proof let v3,v2,v1,v0;
((v0"\/"(v1"\/"(v2"/\"(v0"\/"v1))))"/\"(v3"\/"(v2"/\"(v0"\/"v1))))=((v2"/\"(v0
"\/"v1))"\/"
(v3"/\"(v0"\/"v1))) by A346;
hence thesis by A516;
end;
A527: for v103,v100 holds
(v100"/\"(v100"/\"(v100"\/"v103)))=(v100"/\"(v100"\/"(v103"/\"(v100"/\"v100)))
)
proof let v103,v100;
((v100"\/"(v100"/\"v100))"/\"(v103"\/"(v100"/\"v100)))=(v100"/\"(v100"\/"v103))
;
hence thesis by A82;
end;
A530: for v1,v0 holds (v0"/\"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"(v0"/\"(v1"/\"v0
))))
proof let v1,v0;
(v1"/\"(v0"/\"v0))=(v0"/\"(v1"/\"v0)) by A14;
hence thesis by A527;
end;
A534: for v1,v0 holds (v0"/\"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"(v0"/\"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"/\"(v0"/\"v1))))=(v0"/\"(v0"\/"(v0"/\"v1))) by A378;
hence thesis by A530;
end;
A539: for v102,v1,v100 holds
((v100"/\"(v100"\/"v1))"/\"(v100"\/"v102))=(v100"\/"((v100"/\"(v100"/\"
(v1"/\"v1)))"/\"v102))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v100"/\"(v1"/\"v1))))=(v100"/\"(v100"\/"v1)) by A421;
hence thesis by A4;
end;
A542: for v2,v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2)))=(v0"\/"((v0"/\"(v0"/\"(v1"/\"v1)))"/\"v2))
proof let v2,v1,v0;
((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2))) by A292;
hence thesis by A539;
end;
A544: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v1"/\"v2)))=(v0"\/"((v0"/\"(v0"/\"(v1"/\"v1)))"/\"v2))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A542;
end;
A548: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v1"/\"v2)))=(v0"\/"(v0"/\"((v0"/\"(v1"/\"v1))"/\"v2)))
proof let v0,v2,v1;
(v0"/\"((v0"/\"(v1"/\"v1))"/\"v2))=(v2"/\"(v0"/\"(v0"/\"(v1"/\"v1)))) by A14;
hence thesis by A544;
end;
A552: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v1"/\"v2)))=(v0"\/"(v0"/\"(v0"/\"((v1"/\"v1)"/\"v2))))
proof let v0,v2,v1;
(v0"/\"((v1"/\"v1)"/\"v2))=(v2"/\"(v0"/\"(v1"/\"v1))) by A14;
hence thesis by A548;
end;
A556: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v1"/\"v2)))=(v0"\/"(v0"/\"(v0"/\"(v1"/\"(v2"/\"v1)))))
proof let v0,v2,v1;
(v2"/\"(v1"/\"v1))=(v1"/\"(v2"/\"v1)) by A14;
hence thesis by A552;
end;
A576: for v1,v101,v100 holds
((v100"\/"v101)"/\"(v101"/\"(v101"\/"v1)))=(v101"\/"(v100"/\"(v101"/\"(v101
"/\"
(v1"/\"v1)))))
proof let v1,v101,v100;
(v101"\/"(v101"/\"(v101"/\"(v1"/\"v1))))=(v101"/\"(v101"\/"v1)) by A421;
hence thesis by A4;
end;
A579: for v0,v2,v1 holds
(v1"/\"((v1"\/"v2)"/\"(v0"\/"v1)))=(v1"\/"(v0"/\"(v1"/\"(v1"/\"(v2"/\"v2)))))
proof let v0,v2,v1;
(v1"/\"((v1"\/"v2)"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v1"/\"(v1"\/"v2))) by A14;
hence thesis by A576;
end;
A582: for v0,v1,v2 holds
(v0"/\"(v0"\/"(v2"/\"v1)))=(v0"\/"(v2"/\"(v0"/\"(v0"/\"(v1"/\"v1)))))
proof let v0,v1,v2;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"v0)))=(v0"/\"(v0"\/"(v2"/\"v1))) by A194;
hence thesis by A579;
end;
A590: for v1,v0 holds
(v0"\/"(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"(v0"\/"(v1"\/"v1)))
proof let v1,v0;
(v0"/\"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1)))) by A398;
hence thesis by A421;
end;
A592: for v1,v0 holds (v0"\/"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"
v1)))
proof let v1,v0;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v1"\/"(v1"/\"v1))) by A378;
hence thesis by A590;
end;
A693: for v102,v1,v100 holds
(v100"/\"(((v100"/\"(v1"/\"v1))"\/"v102)"/\"(v100"/\"(v100"\/"v1))))=(v100"/\"
(
(v100"/\"(v1"/\"v1))"\/"(v100"/\"v102)))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v100"/\"(v1"/\"v1))))=(v100"/\"(v100"\/"v1)) by A421;
hence thesis by A82;
end;
A699: for v1,v2,v0 holds
(v0"/\"((v0"\/"v2)"/\"((v1"\/"(v0"/\"(v2"/\"v2)))"/\"v0)))=(v0"/\"((v0"/\"(v2
"/\"v2))"\/"
(v0"/\"v1)))
proof let v1,v2,v0;
((v1"\/"(v0"/\"(v2"/\"v2)))"/\"(v0"/\"(v0"\/"v2)))=((v0"\/"v2)"/\"((v1"\/"(v0
"/\"
(v2"/\"v2)))"/\"v0)) by A14;
hence thesis by A693;
end;
A704: for v2,v1,v0 holds
(v0"/\"(v0"/\"((v2"\/"(v0"/\"(v1"/\"v1)))"/\"(v0"\/"v1))))=(v0"/\"((v0"/\"(v1
"/\"v1))"\/"
(v0"/\"v2)))
proof let v2,v1,v0;
(v0"/\"((v2"\/"(v0"/\"(v1"/\"v1)))"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v0"/\"(v2
"\/"(v0"/\"
(v1"/\"v1))))) by A14;
hence thesis by A699;
end;
A710: for v2,v1,v0 holds
(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1))))))=(v0"/\"(v0"/\"(
(v1"/\"v1)"\/"v2)))
proof let v2,v1,v0;
((v0"/\"(v1"/\"v1))"\/"(v0"/\"v2))=(v0"/\"((v1"/\"v1)"\/"v2)) by A6;
hence thesis by A704;
end;
A714: for v2,v1,v0 holds
(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1))))))=(v0"/\"(v2"\/"(v0
"/\"
(v1"/\"v1))))
proof let v2,v1,v0;
(v0"/\"(v0"/\"(v2"\/"(v1"/\"v1))))=(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1)))) by A398;
hence thesis by A710;
end;
A717: for v100,v1,v103 holds
(v100"/\"((v103"\/"(v103"/\"(v1"/\"v1)))"/\"(v103"\/"(v100"/\"v103))))=(v100
"/\"
(v103"/\"(v103"\/"v1)))
proof let v100,v1,v103;
(v103"\/"(v103"/\"(v103"/\"(v1"/\"v1))))=(v103"/\"(v103"\/"v1)) by A421;
hence thesis by A82;
end;
A720: for v0,v2,v1 holds
(v0"/\"(v1"\/"((v1"/\"(v2"/\"v2))"/\"(v0"/\"v1))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v2,v1;
((v1"\/"(v1"/\"(v2"/\"v2)))"/\"(v1"\/"(v0"/\"v1)))=(v1"\/"((v1"/\"(v2"/\"v2))
"/\"
(v0"/\"v1))) by A4;
hence thesis by A717;
end;
A722: for v0,v2,v1 holds
(v0"/\"(v1"\/"(v1"/\"((v1"/\"(v2"/\"v2))"/\"v0))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v2,v1;
((v1"/\"(v2"/\"v2))"/\"(v0"/\"v1))=(v1"/\"((v1"/\"(v2"/\"v2))"/\"v0)) by A14;
hence thesis by A720;
end;
A726: for v0,v2,v1 holds
(v0"/\"(v1"\/"(v0"/\"((v1"/\"(v2"/\"v2))"/\"v1))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v2,v1;
(v0"/\"((v1"/\"(v2"/\"v2))"/\"v1))=(v1"/\"(v0"/\"(v1"/\"(v2"/\"v2)))) by A14;
hence thesis by A722;
end;
A730: for v1,v2,v0 holds
(v0"/\"(v1"/\"(v1"\/"(v0"/\"v2))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v1"\/"(v0"/\"(v1"/\"(v1"/\"(v2"/\"v2)))))=(v1"/\"(v1"\/"(v0"/\"v2))) by A582;
hence thesis by A726;
end;
A733: for v1,v100 holds
(v100"\/"(v100"/\"(v100"/\"(v1"\/"(v1"/\"(v100"/\"v1))))))=(v100"/\"(v100"\/"(
v1"\/"
(v100"/\"v1))))
proof let v1,v100;
(v100"/\"((v1"\/"(v100"/\"v1))"/\"(v1"\/"(v100"/\"v1))))=(v100"/\"(v1"\/"(v1
"/\"
(v100"/\"v1)))) by A82;
hence thesis by A421;
end;
A736: for v1,v0 holds
(v0"\/"(v0"/\"(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1))))))=(v0"/\"(v0"\/"(v1"\/"(v0
"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A733;
end;
A738: for v1,v0 holds
(v0"\/"(v0"/\"(v0"/\"(v1"\/"(v1"/\"v1)))))=(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v1"\/"(v1"/\"v1))) by A378;
hence thesis by A736;
end;
A740: for v1,v0 holds
(v0"\/"(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1)))) by A398;
hence thesis by A738;
end;
A742: for v1,v0 holds
(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v1"\/"(v1"/\"v1))) by A378;
hence thesis by A740;
end;
A744: for v1,v0 holds (v0"/\"(v0"\/"(v1"\/"v1)))=(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1
))))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"v1))) by A592;
hence thesis by A742;
end;
A754: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"/\"((v0"/\"
v1)"/\"
(v0"/\"v1)))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"(v0
"\/"
(v0"/\"v1)))) by A85;
hence thesis by A421;
end;
A756: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"/\"(v1"/\"(
(v0"/\"v1)"/\"v0)))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"/\"v1))=(v1"/\"((v0"/\"v1)"/\"v0)) by A14;
hence thesis by A754;
end;
A760: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(
(v0"/\"v1)"/\"v1)))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v0"/\"v1)"/\"v1))=(v1"/\"(v0"/\"(v0"/\"v1))) by A14;
hence thesis by A756;
end;
A764: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(
v0"/\"
(v1"/\"v1))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A760;
end;
A766: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"((v0"/\"(v1"/\"v1))"/\"(
v0"\/"
(v0"/\"v1))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v0"/\"(v1"/\"v1))"/\"(v0"\/"(v0"/\"v1))))=((v0"\/"(v0"/\"v1))"/\"(v0
"/\"(v0"/\"
(v1"/\"v1)))) by A14;
hence thesis by A764;
end;
A768: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(v0"/\"((v1"/\"v1)"/\"(v0
"\/"
(v0"/\"v1)))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v0"/\"(v1"/\"v1))"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"((v1"/\"v1)"/\"(v0"\/"(v0"/\"
v1)))) by
A292;
hence thesis by A766;
end;
A770: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(v0"/\"(v1"/\"(v1"/\"(v0
"\/"
(v0"/\"v1))))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v1"/\"v1)"/\"(v0"\/"(v0"/\"v1)))=(v1"/\"(v1"/\"(v0"\/"(v0"/\"v1)))) by A292;
hence thesis by A768;
end;
A772: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v1
"/\"
(v0"/\"v1))))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v1"/\"(v1"/\"(v0"\/"(v0"/\"v1))))=(v1"/\"(v0"\/"(v1"/\"(v0"/\"v1)))) by A398;
hence thesis by A770;
end;
A774: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v0
"/\"
(v1"/\"v1))))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A772;
end;
A776: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"((v0"/\"(v1"/\"(v0"\/"(v0"/\"(v1"/\"v1)))))"/\"(
v0"\/"
(v0"/\"v1)))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v0"/\"(v1"/\"(v0"\/"(v0"/\"(v1"/\"v1)))))"/\"(v0"\/"(v0"/\"v1))))=((v0
"\/"
(v0"/\"v1))"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v0"/\"(v1"/\"v1))))))) by A14;
hence thesis by A774;
end;
A780: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"((v1"/\"(v0"\/"(v0"/\"(v1"/\"v1))))"/\"(
v0"\/"
(v0"/\"v1))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v1"/\"(v0"\/"(v0"/\"(v1"/\"v1))))"/\"(v0"\/"(v0"/\"v1))))=((v0"\/"(v0
"/\"v1))"/\"
(v0"/\"(v1"/\"(v0"\/"(v0"/\"(v1"/\"v1)))))) by A14;
hence thesis by A776;
end;
A784: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"((v0"\/"(v0"/\"(v1"/\"v1)))"/\"(v0
"\/"
(v0"/\"v1)))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v1"/\"((v0"\/"(v0"/\"(v1"/\"v1)))"/\"(v0"\/"(v0"/\"v1))))=((v0"\/"(v0"/\"v1))
"/\"(v1"/\"
(v0"\/"(v0"/\"(v1"/\"v1))))) by A14;
hence thesis by A780;
end;
A788: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"((v0"/\"v1)"/\"(v0"/\"(v1
"/\"v1))))))))=
(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v0"\/"(v0"/\"(v1"/\"v1))))=(v0"\/"((v0"/\"v1)"/\"(v0
"/\"
(v1"/\"v1))));
hence thesis by A784;
end;
A790: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v0"/\"((v1"/\"v1)"/\"(v0
"/\"v1))))))))=
(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v1"/\"v1)"/\"(v0"/\"v1)))=((v0"/\"v1)"/\"(v0"/\"(v1"/\"v1))) by A14;
hence thesis by A788;
end;
A796: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v0"/\"(v0"/\"((v1"/\"v1)
"/\"v1))))))))=
(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v1"/\"v1)"/\"v1))=(v1"/\"(v0"/\"(v1"/\"v1))) by A14;
hence thesis by A790;
end;
A800: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"/\"(v0"\/"(v1"/\"v1)))))))=(v0
"/\"(v1"\/"
(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"\/"(v0"/\"(v0"/\"(v1"/\"(v1"/\"v1)))))=(v0"/\"(v0"\/"(v1"/\"v1))) by A556;
hence thesis by A796;
end;
A802: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"/\"(v0"\/"v1))))))=(v0"/\"(v1
"\/"(v0"\/"
(v0"/\"v1))))
proof let v1,v0;
(v1"/\"(v0"/\"(v0"\/"(v1"/\"v1))))=(v1"/\"(v0"/\"(v0"\/"v1)));
hence thesis by A800;
end;
A804: for v1,v0 holds
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v0"/\"((v0"\/"v1)"/\"v1)))))=(v0"/\"(v1
"\/"(v0"\/"
(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v0"\/"v1)"/\"v1))=(v1"/\"(v0"/\"(v0"\/"v1))) by A14;
hence thesis by A802;
end;
A808: for v1,v0 holds
(v0"\/"((v0"/\"v1)"\/"(v0"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1)))))))=(v0"/\"(v1
"\/"(v0"\/"
(v0"/\"v1))))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1))))))=(v0"\/"((v0
"/\"v1)"\/"
(v0"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1))))))) by A181;
hence thesis by A804;
end;
A810: for v1,v0 holds
(v0"\/"(v0"/\"(v1"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1)))))))=(v0"/\"(v1"\/"(v0
"\/"
(v0"/\"v1))))
proof let v1,v0;
((v0"/\"v1)"\/"(v0"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1))))))=(v0"/\"(v1"\/"(v0
"/\"(v0"/\"(v1"/\"
(v0"\/"v1)))))) by A6;
hence thesis by A808;
end;
A812: for v1,v0 holds
(v0"\/"(v0"/\"(v1"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1)))))))=(v0"/\"(v0"\/"(
(v0"/\"v1)"\/"v1)))
proof let v1,v0;
(v0"\/"((v0"/\"v1)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v1))) by A8;
hence thesis by A810;
end;
A816: for v1,v0 holds
(v0"\/"(v0"/\"(v1"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1)))))))=(v0"/\"(v0"\/"(v1
"\/"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"v1))) by A744;
hence thesis by A812;
end;
A821: for v102,v1,v100 holds
(v100"/\"((v100"/\"(v100"\/"v1))"/\"v102))=(v102"/\"(v100"/\"(v100"\/"(v100
"/\"v1))))
proof let v102,v1,v100;
(v100"/\"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"(v100"/\"v1))) by A534;
hence thesis by A14;
end;
A827: for v1,v2,v0 holds
(v0"/\"(v0"/\"((v0"\/"v2)"/\"v1)))=(v1"/\"(v0"/\"(v0"\/"(v0"/\"v2))))
proof let v1,v2,v0;
(v0"/\"((v0"\/"v2)"/\"v1))=(v1"/\"(v0"/\"(v0"\/"v2))) by A14;
hence thesis by A821;
end;
A833: for v1,v2,v0 holds
(v0"/\"(v0"/\"(v1"/\"(v0"\/"v2))))=(v0"/\"((v0"\/"(v0"/\"v2))"/\"v1))
proof let v1,v2,v0;
(v0"/\"((v0"\/"(v0"/\"v2))"/\"v1))=(v1"/\"(v0"/\"(v0"\/"(v0"/\"v2)))) by A14;
hence thesis by A827;
end;
A839: for v2,v1,v0 holds
((v0"\/"v1)"/\"((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1"\/"v2))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A534;
end;
A841: for v2,v1,v0 holds
((v0"\/"v1)"/\"((v0"\/"v1)"/\"(v2"\/"((v0"\/"v1)"\/"v1))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v2,v1,v0;
((v0"\/"v1)"\/"(v1"\/"v2))=(v2"\/"((v0"\/"v1)"\/"v1)) by A8;
hence thesis by A839;
end;
A845: for v2,v1,v0 holds
((v0"\/"v1)"/\"((v0"\/"v1)"/\"(v2"\/"(v0"\/"(v1"\/"v1)))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v2,v1,v0;
(v0"\/"(v1"\/"v1))=(v1"\/"(v0"\/"v1)) by A8;
hence thesis by A841;
end;
A847: for v0,v2,v1 holds
((v0"\/"v1)"/\"((v0"\/"v1)"/\"(v0"\/"((v1"\/"v1)"\/"v2))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v0,v2,v1;
(v0"\/"((v1"\/"v1)"\/"v2))=(v2"\/"(v0"\/"(v1"\/"v1))) by A8;
hence thesis by A845;
end;
A851: for v0,v1,v2 holds
((v0"\/"v1)"/\"((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v2"\/"v1)))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v0,v1,v2;
(v2"\/"(v1"\/"v1))=(v1"\/"(v2"\/"v1)) by A8;
hence thesis by A847;
end;
A855: for v0,v2,v1 holds
((v0"\/"v1)"/\"(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2)))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"(v1"\/"
(v0"/\"v2))))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v1"\/"v2))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2))))
by A4;
hence thesis by A851;
end;
A857: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"/\"(v1"\/"(v1"\/"v2)))))=((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1
"\/"
(v0"/\"v2))))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2)))))=(v0"\/"(v1"/\"(v1"/\"(v1"\/"
(v1"\/"v2))))) by A4;
hence thesis by A855;
end;
A859: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1
"\/"
(v0"/\"v2))))
proof let v0,v2,v1;
(v1"/\"(v1"/\"(v1"\/"(v1"\/"v2))))=(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))) by A534;
hence thesis by A857;
end;
A861: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"(v1"\/"((v0"/\"v2)
"\/"
(v0"\/"v1))))
proof let v0,v2,v1;
(v1"\/"((v0"/\"v2)"\/"(v0"\/"v1)))=((v0"\/"v1)"\/"(v1"\/"(v0"/\"v2))) by A8;
hence thesis by A859;
end;
A863: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"(v1"\/"(v1"\/"(
(v0"/\"v2)"\/"v0))))
proof let v0,v2,v1;
((v0"/\"v2)"\/"(v0"\/"v1))=(v1"\/"((v0"/\"v2)"\/"v0)) by A8;
hence thesis by A861;
end;
A867: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"(v1"\/"(v0"\/"(
(v0"/\"v2)"\/"v1))))
proof let v0,v2,v1;
(v0"\/"((v0"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v2))) by A8;
hence thesis by A863;
end;
A871: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"(v0"\/"((v1"\/"
(v0"/\"v2))"\/"v1)))
proof let v0,v2,v1;
(v0"\/"((v1"\/"(v0"/\"v2))"\/"v1))=(v1"\/"(v0"\/"(v1"\/"(v0"/\"v2)))) by A8;
hence thesis by A867;
end;
A875: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"
v2)))))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"
(v0"/\"v2))))) by A4;
hence thesis by A871;
end;
A879: for v102,v1,v100 holds
((v100"/\"(v100"\/"(v100"/\"v1)))"\/"((v100"/\"(v100"\/"v1))"/\"v102))=((v100
"/\"
(v100"\/"v1))"/\"(v100"\/"v102))
proof let v102,v1,v100;
(v100"/\"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"(v100"/\"v1))) by A534;
hence thesis by A6;
end;
A884: for v2,v1,v0 holds
((v0"/\"(v0"\/"(v0"/\"v1)))"\/"(v0"/\"((v0"\/"v1)"/\"v2)))=((v0"/\"(v0"\/"v1))
"/\"
(v0"\/"v2))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"v2))=(v2"/\"(v0"/\"(v0"\/"v1))) by A14;
hence thesis by A879;
end;
A888: for v2,v1,v0 holds
(v0"/\"((v0"\/"(v0"/\"v1))"\/"(v2"/\"(v0"\/"v1))))=((v0"/\"(v0"\/"v1))"/\"(v0
"\/"v2))
proof let v2,v1,v0;
((v0"/\"(v0"\/"(v0"/\"v1)))"\/"(v0"/\"(v2"/\"(v0"\/"v1))))=(v0"/\"((v0"\/"(v0
"/\"v1))"\/"
(v2"/\"(v0"\/"v1)))) by A6;
hence thesis by A884;
end;
A890: for v2,v1,v0 holds
(v0"/\"(v0"\/"((v0"/\"v1)"\/"(v2"/\"(v0"\/"v1)))))=((v0"/\"(v0"\/"v1))"/\"(v0
"\/"v2))
proof let v2,v1,v0;
((v0"\/"(v0"/\"v1))"\/"(v2"/\"(v0"\/"v1)))=(v0"\/"((v0"/\"v1)"\/"(v2"/\"(v0"\/"
v1)))) by
A181;
hence thesis by A888;
end;
A892: for v1,v2,v0 holds
(v0"/\"(v0"\/"(v1"/\"(v0"\/"v2))))=((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))
proof let v1,v2,v0;
(v0"\/"((v0"/\"v1)"\/"(v2"/\"(v0"\/"v1))))=(v0"\/"(v1"/\"(v0"\/"v2))) by A261;
hence thesis by A890;
end;
A894: for v1,v2,v0 holds
(v0"/\"(v0"\/"(v1"/\"(v0"\/"v2))))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2)))
proof let v1,v2,v0;
((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2))) by A292;
hence thesis by A892;
end;
A896: for v1,v2,v0 holds
(v0"/\"(v0"\/"(v1"/\"(v0"\/"v2))))=(v0"/\"(v0"\/"(v1"/\"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A894;
end;
A907: for v102,v103,v1,v100 holds
((v100"/\"(v100"\/"(v100"/\"v1)))"/\"(v102"\/"v103))=(v100"/\"((v100"/\"
(v100"\/"v1))"/\"(v102"\/"v103)))
proof let v102,v103,v1,v100;
(v100"/\"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"(v100"/\"v1))) by A534;
hence thesis by A292;
end;
A910: for v2,v3,v1,v0 holds
(v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2"\/"v3)))=(v0"/\"((v0"/\"(v0"\/"v1))"/\"(v2
"\/"v3)))
proof let v2,v3,v1,v0;
((v0"/\"(v0"\/"(v0"/\"v1)))"/\"(v2"\/"v3))=(v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2
"\/"v3))) by
A292;
hence thesis by A907;
end;
A912: for v2,v3,v1,v0 holds
(v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2"\/"v3)))=(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2
"\/"v3))))
proof let v2,v3,v1,v0;
((v0"/\"(v0"\/"v1))"/\"(v2"\/"v3))=(v0"/\"((v0"\/"v1)"/\"(v2"\/"v3))) by A292;
hence thesis by A910;
end;
A932: for v1,v2,v0 holds
(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v1"/\"v2))))
proof let v1,v2,v0;
(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2))))=(v1"/\"(v1"\/"(v1"/\"v2))) by A896;
hence thesis by A875;
end;
A941: for v102,v100,v101,v1 holds
(v100"\/"((v101"/\"v102)"\/"(v100"\/"(v1"/\"v101))))=(v100"\/"(v101"/\"(
(v100"\/"v1)"\/"v102)))
proof let v102,v100,v101,v1;
((v100"\/"v1)"/\"(v100"\/"v101))=(v100"\/"(v1"/\"v101)) by A4;
hence thesis by A106;
end;
A946: for v0,v2,v3,v1 holds
(v0"\/"(v0"\/"((v1"/\"v3)"\/"(v1"/\"v2))))=(v0"\/"(v1"/\"((v0"\/"v3)"\/"v2)))
proof let v0,v2,v3,v1;
(v0"\/"((v1"/\"v3)"\/"(v1"/\"v2)))=((v1"/\"v2)"\/"(v0"\/"(v1"/\"v3))) by A8;
hence thesis by A941;
end;
A949: for v0,v1,v3,v2 holds
(v0"\/"(v0"\/"(v1"/\"(v2"\/"v3))))=(v0"\/"(v1"/\"((v0"\/"v2)"\/"v3)))
proof let v0,v1,v3,v2;
((v1"/\"v2)"\/"(v1"/\"v3))=(v1"/\"(v2"\/"v3)) by A6;
hence thesis by A946;
end;
A956: for v0,v1,v3,v2 holds
(v0"\/"(v0"\/"(v1"/\"(v2"\/"v3))))=(v0"\/"(v1"/\"(v0"\/"(v3"\/"v2))))
proof let v0,v1,v3,v2;
(v0"\/"(v3"\/"v2))=(v2"\/"(v0"\/"v3)) by A8;
hence thesis by A949;
end;
A982: for v103,v100,v1,v101 holds
((v100"/\"(v101"/\"(v101"\/"(v101"/\"v1))))"\/"((v101"/\"(v101"\/"v1))"/\"v103
))=(
(v101"/\"(v101"\/"v1))"/\"(v103"\/"(v100"/\"v101)))
proof let v103,v100,v1,v101;
(v101"/\"(v101"/\"(v101"\/"v1)))=(v101"/\"(v101"\/"(v101"/\"v1))) by A534;
hence thesis by A131;
end;
A987: for v3,v0,v2,v1 holds
((v0"/\"(v1"/\"(v1"\/"(v1"/\"v2))))"\/"(v1"/\"((v1"\/"v2)"/\"v3)))=((v1"/\"(v1
"\/"v2))"/\"
(v3"\/"(v0"/\"v1)))
proof let v3,v0,v2,v1;
(v1"/\"((v1"\/"v2)"/\"v3))=(v3"/\"(v1"/\"(v1"\/"v2))) by A14;
hence thesis by A982;
end;
A991: for v0,v3,v2,v1 holds
(v1"/\"((v3"/\"(v1"\/"v2))"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=((v1"/\"(v1"\/"v2))
"/\"(v3"\/"
(v0"/\"v1)))
proof let v0,v3,v2,v1;
((v0"/\"(v1"/\"(v1"\/"(v1"/\"v2))))"\/"(v1"/\"(v3"/\"(v1"\/"v2))))=(v1"/\"((v3
"/\"
(v1"\/"v2))"\/"(v0"/\"(v1"\/"(v1"/\"v2))))) by A123;
hence thesis by A987;
end;
A994: for v3,v1,v2,v0 holds
(v0"/\"((v1"/\"(v0"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v2)))))=(v0"/\"((v0"\/"v2)
"/\"(v1"\/"
(v3"/\"v0))))
proof let v3,v1,v2,v0;
((v0"/\"(v0"\/"v2))"/\"(v1"\/"(v3"/\"v0)))=(v0"/\"((v0"\/"v2)"/\"(v1"\/"(v3"/\"
v0)))) by
A292;
hence thesis by A991;
end;
A1005: for v100,v3,v101 holds
(v100"/\"(v101"\/"(v101"/\"v3)))=(v101"/\"(v100"\/"(v100"/\"v3)))
proof let v100,v3,v101;
((v100"/\"v101)"\/"(v101"/\"(v100"/\"v3)))=(v100"/\"(v101"\/"(v101"/\"v3))) by
A159;
hence thesis by A6;
end;
A1020: for v2,v101,v100 holds
(v100"/\"((v100"\/"v101)"\/"((v100"\/"v101)"/\"v2)))=(v100"\/"(v101"/\"(v100
"/\"v2)))
proof let v2,v101,v100;
((v100"\/"v101)"/\"(v100"\/"(v100"/\"v2)))=(v100"/\"((v100"\/"v101)"\/"(
(v100"\/"v101)"/\"v2))) by A1005;
hence thesis by A4;
end;
A1025: for v2,v1,v0 holds
(v0"/\"(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))))=(v0"\/"(v1"/\"(v0"/\"v2)))
proof let v2,v1,v0;
((v0"\/"v1)"\/"(v2"/\"(v0"\/"v1)))=(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))) by A181;
hence thesis by A1020;
end;
A1027: for v2,v1,v0 holds
(v0"/\"(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))))=(v0"\/"(v0"/\"(v2"/\"v1)))
proof let v2,v1,v0;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1025;
end;
A1032: for v100,v102,v101 holds
(v100"/\"(v100"/\"((v101"\/"v102)"\/"((v101"\/"v102)"/\"v101))))=(v100"/\"(
v101"\/"
(v100"/\"v102)))
proof let v100,v102,v101;
((v101"\/"v102)"/\"(v100"\/"(v100"/\"v101)))=(v100"/\"((v101"\/"v102)"\/"(
(v101"\/"v102)"/\"v101))) by A1005;
hence thesis by A82;
end;
A1037: for v0,v2,v1 holds
(v0"/\"(v0"/\"(v1"\/"(v2"\/"(v1"/\"(v1"\/"v2))))))=(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v0,v2,v1;
((v1"\/"v2)"\/"(v1"/\"(v1"\/"v2)))=(v1"\/"(v2"\/"(v1"/\"(v1"\/"v2)))) by A181;
hence thesis by A1032;
end;
A1040: for v101,v100 holds
(v100"/\"((v100"\/"(v100"/\"v101))"\/"((v100"\/"(v100"/\"v101))"/\"v101)))=(
v100"/\"
(v101"\/"v100))
proof let v101,v100;
((v100"\/"(v100"/\"v101))"/\"(v100"\/"(v100"/\"v101)))=(v100"/\"((v100"\/"
(v100"/\"v101))"\/"((v100"\/"(v100"/\"v101))"/\"v101))) by A1005;
hence thesis by A85;
end;
A1045: for v1,v0 holds
(v0"/\"(v0"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"(v0"/\"v1))))))=(v0"/\"(v1"\/"v0))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"\/"(v1"/\"(v0"\/"(v0"/\"v1))))=(v0"\/"((v0"/\"v1)"\/"(v1
"/\"(v0"\/"
(v0"/\"v1))))) by A181;
hence thesis by A1040;
end;
A1047: for v1,v0 holds
(v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"\/"(v0"/\"v1))))))=(v0"/\"(v1"\/"v0))
proof let v1,v0;
((v0"/\"v1)"\/"(v1"/\"(v0"\/"(v0"/\"v1))))=(v1"/\"(v0"\/"(v0"\/"(v0"/\"v1))))
by A6;
hence thesis by A1045;
end;
A1049: for v1,v0 holds
(v0"/\"(v0"\/"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1))))))=(v0"/\"(v1"\/"v0))
proof let v1,v0;
(v0"\/"(v1"/\"(v0"\/"(v0"\/"(v0"/\"v1)))))=(v0"\/"(v0"\/"(v1"/\"(v0"\/"(v0"/\"
v1))))) by
A956;
hence thesis by A1047;
end;
A1054: for v100,v2,v1 holds
(v100"/\"(v100"/\"(v100"\/"(v1"\/"(v1"/\"v2)))))=(v100"/\"(v100"\/"(v1"/\"(
v100"\/"
(v100"/\"v2)))))
proof let v100,v2,v1;
(v100"/\"(v1"\/"(v1"/\"v2)))=(v1"/\"(v100"\/"(v100"/\"v2))) by A1005;
hence thesis by A534;
end;
A1057: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"/\"
v2)))))
proof let v0,v2,v1;
(v0"/\"(v0"/\"(v0"\/"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"
v2))))) by
A534;
hence thesis by A1054;
end;
A1059: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v1"/\"(v0"/\"v2))))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v2)))))=(v0"/\"(v0"\/"(v1"/\"(v0"/\"v2))))
by A896;
hence thesis by A1057;
end;
A1061: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v0"/\"(v2"/\"v1))))
proof let v0,v2,v1;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1059;
end;
A1066: for v103,v102,v2,v100 holds
(v100"\/"(((v100"/\"v2)"/\"v102)"\/"(v100"/\"(v103"\/"(v103"/\"v2)))))=(v100
"\/"(
(v100"/\"v2)"/\"(v103"\/"v102)))
proof let v103,v102,v2,v100;
(v103"/\"(v100"\/"(v100"/\"v2)))=(v100"/\"(v103"\/"(v103"/\"v2))) by A1005;
hence thesis by A106;
end;
A1072: for v3,v2,v0,v1 holds
(v0"\/"((v2"/\"(v1"/\"v0))"\/"(v0"/\"(v3"\/"(v3"/\"v2)))))=(v0"\/"((v0"/\"v2)
"/\"
(v3"\/"v1)))
proof let v3,v2,v0,v1;
(v1"/\"(v0"/\"v2))=(v2"/\"(v1"/\"v0)) by A14;
hence thesis by A1066;
end;
A1077: for v3,v0,v1,v2 holds
(v0"\/"((v0"/\"(v2"/\"v1))"\/"(v0"/\"(v3"\/"(v3"/\"v1)))))=(v0"\/"((v0"/\"v1)
"/\"
(v3"\/"v2)))
proof let v3,v0,v1,v2;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1072;
end;
A1085: for v0,v3,v2,v1 holds
(v0"\/"(v0"/\"((v1"/\"v2)"\/"(v3"\/"(v1"/\"v3)))))=(v0"\/"((v0"/\"v1)"/\"(v3
"\/"v2)))
proof let v0,v3,v2,v1;
((v0"/\"(v1"/\"v2))"\/"(v0"/\"(v3"\/"(v1"/\"v3))))=(v0"/\"((v1"/\"v2)"\/"(v3
"\/"
(v1"/\"v3)))) by A6;
hence thesis by A1077;
end;
A1087: for v0,v2,v3,v1 holds
(v0"\/"(v0"/\"(v3"\/"((v1"/\"v3)"\/"(v1"/\"v2)))))=(v0"\/"((v0"/\"v1)"/\"(v3
"\/"v2)))
proof let v0,v2,v3,v1;
(v3"\/"((v1"/\"v3)"\/"(v1"/\"v2)))=((v1"/\"v2)"\/"(v3"\/"(v1"/\"v3))) by A8;
hence thesis by A1085;
end;
A1090: for v0,v2,v3,v1 holds
(v0"\/"(v0"/\"(v1"\/"(v2"/\"(v1"\/"v3)))))=(v0"\/"((v0"/\"v2)"/\"(v1"\/"v3)))
proof let v0,v2,v3,v1;
((v2"/\"v1)"\/"(v2"/\"v3))=(v2"/\"(v1"\/"v3)) by A6;
hence thesis by A1087;
end;
A1096: for v0,v2,v1,v3 holds
(v0"\/"(v0"/\"(v1"\/"(v2"/\"(v3"\/"v1)))))=(v0"\/"(v0"/\"(v2"/\"(v3"\/"v1))))
proof let v0,v2,v1,v3;
((v0"/\"v2)"/\"(v3"\/"v1))=(v0"/\"(v2"/\"(v3"\/"v1))) by A292;
hence thesis by A1090;
end;
A1099: for v100,v101,v2,v103 holds
(v100"\/"((v101"/\"(v103"/\"v2))"\/"(v103"/\"(v100"\/"v101))))=(v100"\/"(v103
"/\"
(v101"\/"(v101"/\"v2))))
proof let v100,v101,v2,v103;
(v101"/\"(v103"\/"(v103"/\"v2)))=(v103"/\"(v101"\/"(v101"/\"v2))) by A1005;
hence thesis by A106;
end;
A1102: for v2,v3,v1,v0 holds
(v0"\/"(v2"/\"((v0"\/"v1)"\/"(v1"/\"v3))))=(v0"\/"(v2"/\"(v1"\/"(v1"/\"v3))))
proof let v2,v3,v1,v0;
((v1"/\"(v2"/\"v3))"\/"(v2"/\"(v0"\/"v1)))=(v2"/\"((v0"\/"v1)"\/"(v1"/\"v3)))
by A123;
hence thesis by A1099;
end;
A1105: for v1,v0,v3,v2 holds
(v0"\/"(v1"/\"(v0"\/"(v2"\/"(v2"/\"v3)))))=(v0"\/"(v1"/\"(v2"\/"(v2"/\"v3))))
proof let v1,v0,v3,v2;
((v0"\/"v2)"\/"(v2"/\"v3))=(v0"\/"(v2"\/"(v2"/\"v3))) by A181;
hence thesis by A1102;
end;
A1107: for v0,v1,v3,v2 holds
(v0"\/"(v0"\/"(v1"/\"(v2"\/"(v2"/\"v3)))))=(v0"\/"(v1"/\"(v2"\/"(v2"/\"v3))))
proof let v0,v1,v3,v2;
(v0"\/"(v1"/\"(v0"\/"(v2"\/"(v2"/\"v3)))))=(v0"\/"(v0"\/"(v1"/\"(v2"\/"(v2"/\"
v3))))) by
A956;
hence thesis by A1105;
end;
A1109: for v1,v0 holds (v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1)))))=(v0"/\"(v0
"\/"v1))
proof let v1,v0;
(v0"\/"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1))))
by A1107;
hence thesis by A1049;
end;
A1111: for v1,v0 holds (v0"/\"(v0"\/"(v1"/\"(v0"/\"v1))))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1)))))=(v0"/\"(v0"\/"(v1"/\"(v0"/\"v1))))
by A896;
hence thesis by A1109;
end;
A1113: for v1,v0 holds (v0"/\"(v0"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A1111;
end;
A1115: for v1,v0 holds (v0"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v0"\/"(v0"/\"v1)));
hence thesis by A1113;
end;
A1117: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v1"\/"(v1"/\"v2))))=(v0"/\"(v0"\/"(v0"/\"(v1"/\"v2))))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v1"\/"(v1"/\"v2))))
by A1115;
hence thesis by A1061;
end;
A1119: for v0,v2,v1 holds
(v0"/\"(v0"\/"(v1"\/"(v1"/\"v2))))=(v0"/\"(v0"\/"(v1"/\"v2)))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v0"/\"(v1"/\"v2))))=(v0"/\"(v0"\/"(v1"/\"v2))) by A1115;
hence thesis by A1117;
end;
A1121: for v1,v2,v0 holds
(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v1"/\"(v1"\/"(v1"/\"v2)))=(v1"/\"(v1"\/"v2)) by A1115;
hence thesis by A932;
end;
A1126: for v1,v0 holds (v0"/\"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v0"\/"v1)) by A1115;
hence thesis by A534;
end;
A1159: for v102,v1,v100 holds
(v100"/\"((v100"\/"(v100"/\"v1))"/\"v102))=(v102"/\"(v100"/\"(v100"\/"v1)))
proof let v102,v1,v100;
(v100"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1115;
hence thesis by A14;
end;
A1165: for v1,v2,v0 holds
(v0"/\"(v1"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"((v0"\/"v2)"/\"v1))
proof let v1,v2,v0;
(v0"/\"((v0"\/"v2)"/\"v1))=(v1"/\"(v0"/\"(v0"\/"v2))) by A14;
hence thesis by A1159;
end;
A1170: for v101,v1,v100 holds
((v100"\/"v101)"/\"(v101"\/"(v100"\/"(v100"/\"v1))))=(v101"\/"(v100"/\"(v100
"\/"v1)))
proof let v101,v1,v100;
(v100"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1115;
hence thesis by A4;
end;
A1173: for v1,v2,v0 holds
((v0"\/"v1)"/\"(v0"\/"((v0"/\"v2)"\/"v1)))=(v1"\/"(v0"/\"(v0"\/"v2)))
proof let v1,v2,v0;
(v0"\/"((v0"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v2))) by A8;
hence thesis by A1170;
end;
A1177: for v1,v2,v0 holds
(v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))=(v1"\/"(v0"/\"(v0"\/"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v0"/\"v2))))=(v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))
by A4;
hence thesis by A1173;
end;
A1180: for v1,v2,v0 holds
((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1"\/"(v0"/\"v2))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A1115;
end;
A1182: for v1,v2,v0 holds
((v0"\/"v1)"/\"(v1"\/"((v0"/\"v2)"\/"(v0"\/"v1))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
(v1"\/"((v0"/\"v2)"\/"(v0"\/"v1)))=((v0"\/"v1)"\/"(v1"\/"(v0"/\"v2))) by A8;
hence thesis by A1180;
end;
A1184: for v1,v2,v0 holds
((v0"\/"v1)"/\"(v1"\/"(v1"\/"((v0"/\"v2)"\/"v0))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
((v0"/\"v2)"\/"(v0"\/"v1))=(v1"\/"((v0"/\"v2)"\/"v0)) by A8;
hence thesis by A1182;
end;
A1188: for v1,v2,v0 holds
((v0"\/"v1)"/\"(v1"\/"(v0"\/"((v0"/\"v2)"\/"v1))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
(v0"\/"((v0"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v2))) by A8;
hence thesis by A1184;
end;
A1192: for v1,v2,v0 holds
((v0"\/"v1)"/\"(v0"\/"((v1"\/"(v0"/\"v2))"\/"v1)))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
(v0"\/"((v1"\/"(v0"/\"v2))"\/"v1))=(v1"\/"(v0"\/"(v1"\/"(v0"/\"v2)))) by A8;
hence thesis by A1188;
end;
A1196: for v1,v2,v0 holds
(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1
"\/"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"
(v0"/\"v2))))) by A4;
hence thesis by A1192;
end;
A1198: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1"\/"v2)))
proof let v0,v2,v1;
(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"v2))) by A1121;
hence thesis by A1196;
end;
A1200: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"(v2"\/"((v0"\/"v1)"\/"v1)))
proof let v0,v2,v1;
((v0"\/"v1)"\/"(v1"\/"v2))=(v2"\/"((v0"\/"v1)"\/"v1)) by A8;
hence thesis by A1198;
end;
A1204: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"(v2"\/"(v0"\/"(v1"\/"v1))))
proof let v0,v2,v1;
(v0"\/"(v1"\/"v1))=(v1"\/"(v0"\/"v1)) by A8;
hence thesis by A1200;
end;
A1206: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"(v0"\/"((v1"\/"v1)"\/"v2)))
proof let v0,v2,v1;
(v0"\/"((v1"\/"v1)"\/"v2))=(v2"\/"(v0"\/"(v1"\/"v1))) by A8;
hence thesis by A1204;
end;
A1210: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v2"\/"v1))))
proof let v0,v2,v1;
(v2"\/"(v1"\/"v1))=(v1"\/"(v2"\/"v1)) by A8;
hence thesis by A1206;
end;
A1214: for v0,v2,v1 holds
(v0"\/"(v1"/\"(v1"\/"v2)))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2))))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v1"\/"v2))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2))))
by A4;
hence thesis by A1210;
end;
A1267: for v102,v103,v1,v100 holds
((v100"/\"(v100"\/"v1))"/\"(v102"\/"v103))=(v100"/\"((v100"\/"(v100"/\"v1))
"/\"
(v102"\/"v103)))
proof let v102,v103,v1,v100;
(v100"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1115;
hence thesis by A292;
end;
A1270: for v2,v3,v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"(v2"\/"v3)))=(v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2"\/"v3)))
proof let v2,v3,v1,v0;
((v0"/\"(v0"\/"v1))"/\"(v2"\/"v3))=(v0"/\"((v0"\/"v1)"/\"(v2"\/"v3))) by A292;
hence thesis by A1267;
end;
A1272: for v2,v3,v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"(v2"\/"v3)))=(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"v3))))
proof let v2,v3,v1,v0;
(v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2"\/"v3)))=(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"
v3)))) by
A912;
hence thesis by A1270;
end;
A1377: for v102,v1,v100 holds
(v100"\/"(((v100"/\"v1)"/\"v102)"\/"(v100"/\"(v100"\/"v1))))=(v100"\/"((v100
"/\"v1)"/\"
(v100"\/"v102)))
proof let v102,v1,v100;
(v100"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1115;
hence thesis by A106;
end;
A1383: for v2,v0,v1 holds
(v0"\/"((v2"/\"(v1"/\"v0))"\/"(v0"/\"(v0"\/"v2))))=(v0"\/"((v0"/\"v2)"/\"(v0
"\/"v1)))
proof let v2,v0,v1;
(v1"/\"(v0"/\"v2))=(v2"/\"(v1"/\"v0)) by A14;
hence thesis by A1377;
end;
A1388: for v0,v1,v2 holds
(v0"\/"((v0"/\"(v2"/\"v1))"\/"(v0"/\"(v0"\/"v1))))=(v0"\/"((v0"/\"v1)"/\"(v0
"\/"v2)))
proof let v0,v1,v2;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1383;
end;
A1394: for v0,v2,v1 holds
(v0"\/"(v0"/\"((v1"/\"v2)"\/"(v0"\/"v1))))=(v0"\/"((v0"/\"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
((v0"/\"(v1"/\"v2))"\/"(v0"/\"(v0"\/"v1)))=(v0"/\"((v1"/\"v2)"\/"(v0"\/"v1)))
by A6;
hence thesis by A1388;
end;
A1396: for v0,v2,v1 holds
(v0"\/"(v0"/\"(v1"\/"((v1"/\"v2)"\/"v0))))=(v0"\/"((v0"/\"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
((v1"/\"v2)"\/"(v0"\/"v1))=(v1"\/"((v1"/\"v2)"\/"v0)) by A8;
hence thesis by A1394;
end;
A1400: for v0,v2,v1 holds
(v0"\/"(v0"/\"(v0"\/"((v1"/\"v2)"\/"v1))))=(v0"\/"((v0"/\"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
(v0"\/"((v1"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v1"/\"v2))) by A8;
hence thesis by A1396;
end;
A1404: for v0,v2,v1 holds
(v0"\/"(v0"/\"(v0"\/"(v1"/\"v2))))=(v0"\/"((v0"/\"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v1"\/"(v1"/\"v2))))=(v0"/\"(v0"\/"(v1"/\"v2))) by A1119;
hence thesis by A1400;
end;
A1406: for v0,v2,v1 holds
(v0"\/"(v0"/\"(v0"\/"(v1"/\"v2))))=(v0"\/"(v0"/\"(v1"/\"(v0"\/"v2))))
proof let v0,v2,v1;
((v0"/\"v1)"/\"(v0"\/"v2))=(v0"/\"(v1"/\"(v0"\/"v2))) by A292;
hence thesis by A1404;
end;
A1410: for v103,v100,v1,v101 holds
((v100"/\"(v101"/\"(v101"\/"v1)))"\/"(v101"/\"v103))=(v101"/\"(v103"\/"(v100
"/\"
(v101"\/"(v101"/\"v1)))))
proof let v103,v100,v1,v101;
(v101"/\"(v101"\/"(v101"/\"v1)))=(v101"/\"(v101"\/"v1)) by A1115;
hence thesis by A123;
end;
A1413: for v3,v0,v2,v1 holds
(v1"/\"(v3"\/"(v0"/\"(v1"\/"v2))))=(v1"/\"(v3"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))
proof let v3,v0,v2,v1;
((v0"/\"(v1"/\"(v1"\/"v2)))"\/"(v1"/\"v3))=(v1"/\"(v3"\/"(v0"/\"(v1"\/"v2))))
by A123;
hence thesis by A1410;
end;
A1443: for v1,v2,v0 holds
(v0"/\"(v1"/\"(v0"\/"v2)))=(v0"/\"(v0"/\"(v1"/\"(v0"\/"v2))))
proof let v1,v2,v0;
(v0"/\"(v1"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v1"/\"(v0"\/"v2))) by A1165;
hence thesis by A833;
end;
A1455: for v1,v2,v0 holds
(v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))=(v0"\/"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))
by A1214;
hence thesis by A1121;
end;
A1457: for v1,v2,v0 holds (v1"\/"(v0"/\"(v0"\/"v2)))=(v0"\/"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))=(v1"\/"(v0"/\"(v0"\/"v2))) by A1177;
hence thesis by A1455;
end;
A1470: for v2,v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"(v2"\/"(v0"/\"(v1
"/\"v1))))
proof let v2,v1,v0;
(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1))))))=(v0"/\"((v0"\/"v1)
"/\"(v2"\/"
(v0"/\"(v1"/\"v1))))) by A1272;
hence thesis by A714;
end;
A1472: for v3,v1,v2,v0 holds
(v0"/\"((v1"/\"(v0"\/"v2))"\/"(v3"/\"(v0"\/"v2))))=(v0"/\"((v0"\/"v2)"/\"(v1
"\/"
(v3"/\"v0))))
proof let v3,v1,v2,v0;
(v0"/\"((v1"/\"(v0"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v2)))))=(v0"/\"((v1"/\"(v0
"\/"v2))"\/"
(v3"/\"(v0"\/"v2)))) by A1413;
hence thesis by A994;
end;
A1474: for v1,v3,v2,v0 holds
(v0"/\"((v0"\/"v2)"/\"(v1"\/"v3)))=(v0"/\"((v0"\/"v2)"/\"(v1"\/"(v3"/\"v0))))
proof let v1,v3,v2,v0;
((v1"/\"(v0"\/"v2))"\/"(v3"/\"(v0"\/"v2)))=((v0"\/"v2)"/\"(v1"\/"v3)) by A523;
hence thesis by A1472;
end;
A1482: for v1,v0 holds
(v0"\/"(v0"/\"(v1"\/"(v0"/\"(v1"/\"(v0"\/"v1))))))=(v0"/\"(v0"\/"(v1"\/"v1)))
proof let v1,v0;
(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1))))=(v0"/\"(v1"/\"(v0"\/"v1))) by A1443;
hence thesis by A816;
end;
A1484: for v1,v0 holds
(v0"\/"(v0"/\"(v1"\/"(v1"/\"(v0"\/"v1)))))=(v0"/\"(v0"\/"(v1"\/"v1)))
proof let v1,v0;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"(v0"\/"v1)))))=(v0"/\"(v1"\/"(v1"/\"(v0"\/"v1))))
by A378;
hence thesis by A1482;
end;
A1486: for v1,v0 holds (v0"\/"(v0"/\"(v1"/\"(v0"\/"v1))))=(v0"/\"(v0"\/"(v1"\/"
v1)))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"\/"(v1"/\"(v0"\/"v1)))))=(v0"\/"(v0"/\"(v1"/\"(v0"\/"v1))))
by A1096;
hence thesis by A1484;
end;
A1488: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"
v1)))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"/\"(v0"\/"v1))))=(v0"\/"(v0"/\"(v0"\/"(v1"/\"v1)))) by A1406;
hence thesis by A1486;
end;
A1490: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"(v1"\/"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"/\"v1)))=(v0"/\"(v0"\/"v1));
hence thesis by A1488;
end;
A1499: for v2,v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v1"/\"v1))))=(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1))))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"((v0"\/"v1)"/\"(v2
"\/"
(v1"/\"v1)))) by A1474;
hence thesis by A1470;
end;
A1501: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"\/"v1)))=(v0"/\"(v0"\/"v1));
hence thesis by A1490;
end;
A1504: for v102,v1,v100 holds
((v100"/\"(v100"\/"v1))"\/"((v100"/\"(v100"\/"v1))"/\"v102))=((v100"/\"
(v100"\/"v1))"/\"(v100"\/"v102))
proof let v102,v1,v100;
(v100"/\"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"v1)) by A1126;
hence thesis by A6;
end;
A1509: for v2,v1,v0 holds
((v0"/\"(v0"\/"v1))"\/"(v0"/\"((v0"\/"v1)"/\"v2)))=((v0"/\"(v0"\/"v1))"/\"(v0
"\/"v2))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"v2))=(v2"/\"(v0"/\"(v0"\/"v1))) by A14;
hence thesis by A1504;
end;
A1513: for v2,v1,v0 holds
(v0"/\"((v0"\/"v1)"\/"(v2"/\"(v0"\/"v1))))=((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))
proof let v2,v1,v0;
((v0"/\"(v0"\/"v1))"\/"(v0"/\"(v2"/\"(v0"\/"v1))))=(v0"/\"((v0"\/"v1)"\/"(v2
"/\"
(v0"\/"v1)))) by A6;
hence thesis by A1509;
end;
A1515: for v2,v1,v0 holds
(v0"/\"(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))))=((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))
proof let v2,v1,v0;
((v0"\/"v1)"\/"(v2"/\"(v0"\/"v1)))=(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))) by A181;
hence thesis by A1513;
end;
A1517: for v0,v2,v1 holds
(v0"\/"(v0"/\"(v1"/\"v2)))=((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))))=(v0"\/"(v0"/\"(v1"/\"v2))) by A1027;
hence thesis by A1515;
end;
A1519: for v0,v2,v1 holds
(v0"\/"(v0"/\"(v1"/\"v2)))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2))) by A292;
hence thesis by A1517;
end;
A1521: for v0,v2,v1 holds (v0"\/"(v0"/\"(v1"/\"v2)))=(v0"/\"(v0"\/"(v1"/\"v2)))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A1519;
end;
A1580: for v1,v0 holds (v0"\/"(v0"/\"(v0"/\"v1)))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"/\"v1)))=(v0"\/"(v0"/\"(v0"/\"v1))) by A1521;
hence thesis by A1115;
end;
A1582: for v1,v2,v0 holds
(v0"/\"(v1"\/"(v1"/\"(v0"/\"v2))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v1"/\"(v1"\/"(v0"/\"v2)))=(v1"\/"(v1"/\"(v0"/\"v2))) by A1521;
hence thesis by A730;
end;
A1584: for v0,v1,v2 holds
(v0"/\"(v1"\/"(v0"/\"(v2"/\"v1))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v1,v2;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1582;
end;
A1588: for v0,v2,v1 holds (v0"/\"(v1"\/"(v1"/\"v2)))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v2,v1;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"v2))))=(v0"/\"(v1"\/"(v1"/\"v2))) by A378;
hence thesis by A1584;
end;
A1622: for v102,v1,v100 holds
(v100"\/"((v100"/\"(v100"\/"v1))"\/"v102))=(v102"\/"(v100"/\"(v100"\/"v1)))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"v1)) by A1501;
hence thesis by A8;
end;
A1669: for v0,v2,v1 holds
(v0"/\"(v0"/\"(v2"\/"(v1"/\"(v1"\/"v2)))))=(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v0,v2,v1;
(v1"\/"(v2"\/"(v1"/\"(v1"\/"v2))))=(v2"\/"(v1"/\"(v1"\/"v2))) by A1622;
hence thesis by A1037;
end;
A1672: for v0,v1,v2 holds
(v0"/\"(v1"\/"(v0"/\"(v2"/\"(v2"\/"v1)))))=(v0"/\"(v2"\/"(v0"/\"v1)))
proof let v0,v1,v2;
(v0"/\"(v0"/\"(v1"\/"(v2"/\"(v2"\/"v1)))))=(v0"/\"(v1"\/"(v0"/\"(v2"/\"(v2"\/"
v1))))) by
A398;
hence thesis by A1669;
end;
A1674: for v0,v1,v2 holds
(v0"/\"(v1"\/"(v0"/\"(v2"\/"(v2"/\"v1)))))=(v0"/\"(v2"\/"(v0"/\"v1)))
proof let v0,v1,v2;
(v0"/\"(v2"/\"(v2"\/"v1)))=(v0"/\"(v2"\/"(v2"/\"v1))) by A1588;
hence thesis by A1672;
end;
A1677: for v102,v1,v100 holds
((v100"/\"(v100"\/"v1))"/\"((v100"/\"(v1"/\"v1))"\/"v102))=((v100"/\"(v1"/\"v1
))"\/"
(v100"/\"v102))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v1"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1521;
hence thesis by A4;
end;
A1682: for v2,v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1)))))=((v0"/\"(v1"/\"v1))"\/"(v0
"/\"v2))
proof let v2,v1,v0;
((v0"/\"(v0"\/"v1))"/\"(v2"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"((v0"\/"v1)"/\"(v2
"\/"(v0"/\"
(v1"/\"v1))))) by A292;
hence thesis by A1677;
end;
A1684: for v2,v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v1"/\"v1))))=((v0"/\"(v1"/\"v1))"\/"(v0"/\"v2))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"((v0"\/"v1)"/\"(v2
"\/"
(v1"/\"v1)))) by A1474;
hence thesis by A1682;
end;
A1686: for v2,v1,v0 holds
(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1))))=((v0"/\"(v1"/\"v1))"\/"(v0"/\"v2))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v1"/\"v1))))=(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1))))
by A1499;
hence thesis by A1684;
end;
A1689: for v1,v2,v0 holds
(v0"/\"(v1"\/"(v0"/\"(v2"/\"v2))))=(v0"/\"((v2"/\"v2)"\/"v1))
proof let v1,v2,v0;
((v0"/\"(v2"/\"v2))"\/"(v0"/\"v1))=(v0"/\"((v2"/\"v2)"\/"v1)) by A6;
hence thesis by A1686;
end;
A1694: for v101,v103 holds
((v103"/\"v101)"/\"((v103"/\"v101)"\/"v103))=(v103"/\"(v101"\/"(
(v103"/\"v101)"/\"v103)))
proof let v101,v103;
((v103"/\"v101)"\/"((v103"/\"v101)"/\"(v103"/\"v103)))=((v103"/\"v101)"/\"(
(v103"/\"v101)"\/"v103)) by A1521;
hence thesis by A159;
end;
A1699: for v1,v0 holds
(v0"/\"(v1"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"((v0"/\"v1)"/\"v0)))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v1"/\"(v0"\/"(v0"/\"v1)))) by A292;
hence thesis by A1694;
end;
A1701: for v1,v0 holds (v0"/\"(v1"/\"(v0"\/"v1)))=(v0"/\"(v1"\/"((v0"/\"v1)"/\"
v0)))
proof let v1,v0;
(v0"/\"(v1"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"/\"(v0"\/"v1))) by A1165;
hence thesis by A1699;
end;
A1707: for v102,v103,v1,v101 holds
((v101"/\"(v1"/\"v1))"\/"((v101"/\"v102)"\/"(v103"/\"(v101"/\"(v101"\/"v1)))))
=(
(v101"/\"(v1"/\"v1))"\/"(v101"/\"(v103"\/"v102)))
proof let v102,v103,v1,v101;
(v101"\/"(v101"/\"(v1"/\"v1)))=(v101"/\"(v101"\/"v1)) by A1521;
hence thesis by A150;
end;
A1710: for v2,v3,v1,v0 holds
((v0"/\"(v1"/\"v1))"\/"((v0"/\"v2)"\/"(v3"/\"(v0"\/"(v0"/\"v1)))))=((v0"/\"(v1
"/\"v1))"\/"
(v0"/\"(v3"\/"v2)))
proof let v2,v3,v1,v0;
(v3"/\"(v0"/\"(v0"\/"v1)))=(v3"/\"(v0"\/"(v0"/\"v1))) by A1588;
hence thesis by A1707;
end;
A1712: for v3,v0,v2,v1 holds
((v0"/\"((v1"/\"v1)"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=((v0"/\"(v1"/\"v1))
"\/"(v0"/\"
(v3"\/"v2)))
proof let v3,v0,v2,v1;
((v0"/\"(v1"/\"v1))"\/"((v0"/\"v2)"\/"(v3"/\"(v0"\/"(v0"/\"v1)))))=((v0"/\"(
(v1"/\"v1)"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1)))) by A341;
hence thesis by A1710;
end;
A1719: for v3,v0,v2,v1 holds
((v0"/\"(v1"\/"(v2"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"((v2"/\"v2)
"\/"
(v1"\/"v3)))
proof let v3,v0,v2,v1;
((v0"/\"(v2"/\"v2))"\/"(v0"/\"(v1"\/"v3)))=(v0"/\"((v2"/\"v2)"\/"(v1"\/"v3)))
by A6;
hence thesis by A1712;
end;
A1721: for v3,v0,v2,v1 holds
((v0"/\"(v1"\/"(v2"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v3"\/"(
(v2"/\"v2)"\/"v1)))
proof let v3,v0,v2,v1;
((v2"/\"v2)"\/"(v1"\/"v3))=(v3"\/"((v2"/\"v2)"\/"v1)) by A8;
hence thesis by A1719;
end;
A1725: for v3,v0,v2,v1 holds
((v0"/\"(v1"\/"(v2"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v1"\/"(
(v2"/\"v2)"\/"v3)))
proof let v3,v0,v2,v1;
(v1"\/"((v2"/\"v2)"\/"v3))=(v3"\/"(v1"\/"(v2"/\"v2))) by A8;
hence thesis by A1721;
end;
A1729: for v2,v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v1"/\"v1))))=(v0"/\"(v2"\/"(v1"/\"v1)))
proof let v2,v1,v0;
(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v2"\/"(v1"/\"v1))) by A1689;
hence thesis by A1499;
end;
A1732: for v102,v1,v100 holds
(v100"/\"(((v100"/\"v1)"\/"v102)"/\"(v100"/\"(v100"\/"v1))))=(v100"/\"((v100
"/\"v1)"\/"
(v100"/\"v102)))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1580;
hence thesis by A82;
end;
A1738: for v1,v2,v0 holds
(v0"/\"((v0"\/"v2)"/\"((v1"\/"(v0"/\"v2))"/\"v0)))=(v0"/\"((v0"/\"v2)"\/"(v0
"/\"v1)))
proof let v1,v2,v0;
((v1"\/"(v0"/\"v2))"/\"(v0"/\"(v0"\/"v2)))=((v0"\/"v2)"/\"((v1"\/"(v0"/\"v2))
"/\"v0)) by
A14;
hence thesis by A1732;
end;
A1743: for v2,v1,v0 holds
(v0"/\"(v0"/\"((v2"\/"(v0"/\"v1))"/\"(v0"\/"v1))))=(v0"/\"((v0"/\"v1)"\/"(v0
"/\"v2)))
proof let v2,v1,v0;
(v0"/\"((v2"\/"(v0"/\"v1))"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v0"/\"(v2"\/"(v0"/\"
v1)))) by
A14;
hence thesis by A1738;
end;
A1749: for v2,v1,v0 holds
(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"v1))))=(v0"/\"((v0"/\"v1)"\/"(v0"/\"v2)))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"v1))))=(v0"/\"((v0"\/"v1)"/\"(v2"\/"v1)))
by A1474;
hence thesis by A1743;
end;
A1753: for v1,v2,v0 holds
(v0"/\"(v0"/\"(v1"\/"(v0"/\"v2))))=(v0"/\"((v0"/\"v1)"\/"(v0"/\"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A1749;
end;
A1755: for v1,v2,v0 holds
(v0"/\"(v1"\/"(v0"/\"(v0"/\"v2))))=(v0"/\"((v0"/\"v1)"\/"(v0"/\"v2)))
proof let v1,v2,v0;
(v0"/\"(v0"/\"(v1"\/"(v0"/\"v2))))=(v0"/\"(v1"\/"(v0"/\"(v0"/\"v2)))) by A398;
hence thesis by A1753;
end;
A1757: for v1,v2,v0 holds
(v0"/\"(v1"\/"(v0"/\"(v0"/\"v2))))=(v0"/\"(v0"/\"(v1"\/"v2)))
proof let v1,v2,v0;
((v0"/\"v1)"\/"(v0"/\"v2))=(v0"/\"(v1"\/"v2)) by A6;
hence thesis by A1755;
end;
A1795: for v102,v103,v1,v101 holds
((v101"/\"(v101"/\"v1))"\/"((v101"/\"v102)"\/"(v103"/\"(v101"/\"(v101"\/"v1)))
))=(
(v101"/\"(v101"/\"v1))"\/"(v101"/\"(v103"\/"v102)))
proof let v102,v103,v1,v101;
(v101"\/"(v101"/\"(v101"/\"v1)))=(v101"/\"(v101"\/"v1)) by A1580;
hence thesis by A150;
end;
A1798: for v2,v3,v1,v0 holds
((v0"/\"(v0"/\"v1))"\/"((v0"/\"v2)"\/"(v3"/\"(v0"\/"(v0"/\"v1)))))=((v0"/\"(v0
"/\"v1))"\/"
(v0"/\"(v3"\/"v2)))
proof let v2,v3,v1,v0;
(v3"/\"(v0"/\"(v0"\/"v1)))=(v3"/\"(v0"\/"(v0"/\"v1))) by A1588;
hence thesis by A1795;
end;
A1800: for v3,v2,v1,v0 holds
((v0"/\"((v0"/\"v1)"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=((v0"/\"(v0"/\"v1))
"\/"(v0"/\"
(v3"\/"v2)))
proof let v3,v2,v1,v0;
((v0"/\"(v0"/\"v1))"\/"((v0"/\"v2)"\/"(v3"/\"(v0"\/"(v0"/\"v1)))))=((v0"/\"(
(v0"/\"v1)"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1)))) by A341;
hence thesis by A1798;
end;
A1807: for v3,v1,v2,v0 holds
((v0"/\"(v1"\/"(v0"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"((v0"/\"v2)
"\/"
(v1"\/"v3)))
proof let v3,v1,v2,v0;
((v0"/\"(v0"/\"v2))"\/"(v0"/\"(v1"\/"v3)))=(v0"/\"((v0"/\"v2)"\/"(v1"\/"v3)))
by A6;
hence thesis by A1800;
end;
A1809: for v3,v1,v2,v0 holds
((v0"/\"(v1"\/"(v0"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v3"\/"(
(v0"/\"v2)"\/"v1)))
proof let v3,v1,v2,v0;
((v0"/\"v2)"\/"(v1"\/"v3))=(v3"\/"((v0"/\"v2)"\/"v1)) by A8;
hence thesis by A1807;
end;
A1813: for v3,v1,v2,v0 holds
((v0"/\"(v1"\/"(v0"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v1"\/"(
(v0"/\"v2)"\/"v3)))
proof let v3,v1,v2,v0;
(v1"\/"((v0"/\"v2)"\/"v3))=(v3"\/"(v1"\/"(v0"/\"v2))) by A8;
hence thesis by A1809;
end;
A1817: for v1,v0 holds v0"/\"(v0"/\"(v1"\/"v1))=v0"/\"(v1"/\"(v0"\/"v1))
proof let v1,v0;
v0"/\"(v1"\/"(v0"/\"(v0"/\"v1)))=v0"/\"(v0"/\"(v1"\/"v1)) by A1757;
hence thesis by A1701;
end;
A2027: for v1,v0 holds v0"/\"(v0"\/"v1)=v0"\/"(v1"/\"v0)
proof let v1,v0;
v0"\/"(v0"/\"(v1"/\"v1))=v0"/\"(v0"\/"v1) by A1521;
hence thesis;
end;
A2080: for v102,v100 holds
(v102"/\"((v100"\/"v102)"\/"((v100"\/"v102)"/\"(v100"\/"v102))))=(v102"\/"
(v100"/\"v102))
proof let v102,v100;
(v102"/\"((v100"\/"v102)"\/"((v100"\/"v102)"/\"(v100"\/"v102))))=((v100"\/"v102
)"/\"
(v102"\/"v102));
hence thesis by A4;
end;
A2089: for v1,v0 holds (v0"/\"((v0"\/"v1)"\/"(v0"\/"(v1"/\"v1))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
((v0"\/"v1)"/\"(v0"\/"v1))=(v0"\/"(v1"/\"v1));
hence thesis by A2080;
end;
A2091: for v1,v0 holds (v0"/\"(v0"\/"((v1"/\"v1)"\/"(v0"\/"v1))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
(v0"\/"((v1"/\"v1)"\/"(v0"\/"v1)))=((v0"\/"v1)"\/"(v0"\/"(v1"/\"v1))) by A8;
hence thesis by A2089;
end;
A2097: for v1,v0 holds (v0"/\"(v0"\/"(v0"\/"((v1"/\"v1)"\/"v1))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
(v0"\/"((v1"/\"v1)"\/"v1))=(v1"\/"(v0"\/"(v1"/\"v1))) by A8;
hence thesis by A2091;
end;
A2101: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"(v1"\/"(v1"/\"v1)))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"\/"(v1"\/"(v1"/\"v1)))))=(v0"\/"(v0"/\"(v0"\/"(v1"\/"(v1"/\"
v1))))) by
A2027;
hence thesis by A2097;
end;
A2103: for v1,v0 holds (v0"\/"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1)))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"\/"(v1"/\"v1))))=(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1)))) by A2027;
hence thesis by A2101;
end;
A2105: for v1,v0 holds (v0"\/"(v0"\/"(v0"/\"(v1"/\"v1))))=(v0"\/"(v1"/\"v0))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"\/"(v0"/\"(v1"/\"v1)));
hence thesis by A2103;
end;
A2107: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"v1)))=(v0"\/"(v1"/\"v0))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"/\"v1)))=(v0"/\"(v0"\/"v1)) by A1521;
hence thesis by A2105;
end;
A2109: for v1,v0 holds (v0"\/"(v0"\/"(v0"/\"v1)))=(v0"\/"(v1"/\"v0))
proof let v1,v0;
(v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"v1)) by A2027;
hence thesis by A2107;
end;
A2117: for v1,v0 holds ((v0"/\"v1)"\/"(v0"/\"(v1"/\"v0)))=(v0"/\"(v1"\/"v1))
proof let v1,v0;
(v1"/\"(v0"/\"v0))=(v0"/\"(v1"/\"v0)) by A14;
hence thesis;
end;
A2121: for v1,v0 holds (v0"/\"(v1"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v1))
proof let v1,v0;
((v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)))=(v0"/\"(v1"\/"(v0"/\"v1))) by A6;
hence thesis by A2117;
end;
A2148: for v1,v0 holds v0"/\"(v0"/\"(v1"\/"v1))=v1"/\"(v0"\/"v0)
proof let v1,v0;
v1"/\"(v0"\/"(v0"/\"v0))=v1"/\"(v0"\/"v0);
hence thesis by A292;
end;
A2170: for v2,v1,v0 holds
((v0"\/"(v1"/\"(v0"\/"v0)))"/\"(v2"\/"(v0"/\"(v1"\/"v1))))=(v0"/\"(v1"\/"(
(v1"/\"v1)"\/"v2)))
proof let v2,v1,v0;
(v1"\/"((v1"/\"v1)"\/"v2))=(v2"\/"(v1"\/"(v1"/\"v1))) by A8;
hence thesis by A85;
end;
A2178: for v1,v0 holds ((v0"\/"(v0"/\"v1))"/\"(v1"/\"(v0"\/"v1)))=(v1"/\"(v0
"\/"v0))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"((v1"/\"v1)"\/"(v0"/\"v1)))=((v0"\/"(v0"/\"v1))"/\"(v1
"/\"
(v0"\/"v1))) by A336;
hence thesis by A85;
end;
A2180: for v1,v0 holds ((v0"\/"v1)"/\"((v0"\/"(v0"/\"v1))"/\"v1))=(v1"/\"(v0
"\/"v0))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v1"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"((v0"\/"(v0"/\"v1))
"/\"v1)) by A14;
hence thesis by A2178;
end;
A2184: for v1,v0 holds (v1"/\"((v0"\/"(v0"/\"v1))"/\"(v0"\/"v1)))=(v1"/\"(v0
"\/"v0))
proof let v1,v0;
(v1"/\"((v0"\/"(v0"/\"v1))"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v1"/\"(v0"\/"(v0"/\"
v1)))) by A14;
hence thesis by A2180;
end;
A2189: for v0,v1 holds (v0"/\"(v1"\/"(v0"/\"(v1"/\"v0))))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
((v1"\/"v0)"/\"(v1"\/"(v1"/\"v0)))=(v1"\/"(v0"/\"(v1"/\"v0))) by A4;
hence thesis by A2184;
end;
A2191: for v0,v1 holds (v0"/\"(v1"\/"(v1"/\"(v0"/\"v0))))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
(v1"/\"(v0"/\"v0))=(v0"/\"(v1"/\"v0)) by A14;
hence thesis by A2189;
end;
A2193: for v0,v1 holds (v0"/\"(v1"/\"(v1"\/"v0)))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
(v1"\/"(v1"/\"(v0"/\"v0)))=(v1"/\"(v1"\/"v0)) by A1521;
hence thesis by A2191;
end;
A2195: for v0,v1 holds (v0"/\"(v1"\/"(v1"/\"v0)))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
(v1"/\"(v1"\/"v0))=(v1"\/"(v1"/\"v0)) by A2027;
hence thesis by A2193;
end;
A2212: for v101,v100 holds
((v100"/\"v101)"/\"((v100"\/"(v100"/\"v101))"\/"((v100"\/"(v100"/\"v101))"/\"(
v100"\/"
(v100"/\"v101)))))=(v100"/\"(v101"\/"(v100"/\"v101)))
proof let v101,v100;
((v100"/\"v101)"/\"((v100"\/"(v100"/\"v101))"\/"((v100"\/"(v100"/\"v101))"/\"(
v100"\/"
(v100"/\"v101)))))=((v100"\/"(v100"/\"v101))"/\"((v100"/\"v101)"\/"(v100"/\"
v101)));
hence thesis by A85;
end;
A2215: for v1,v0 holds
((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"((v0"/\"v1)"/\"(v0"/\"v1)))))=(v0
"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v0"\/"(v0"/\"v1)))=
(v0"\/"((v0"/\"v1)"/\"(v0"/\"v1)));
hence thesis by A2212;
end;
A2217: for v1,v0 holds
((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v1"/\"((v0"/\"v1)"/\"v0)))))=
(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"/\"v1))=(v1"/\"((v0"/\"v1)"/\"v0)) by A14;
hence thesis by A2215;
end;
A2221: for v1,v0 holds
((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"((v0"/\"v1)"/\"v1)))))=
(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
(v0"/\"((v0"/\"v1)"/\"v1))=(v1"/\"(v0"/\"(v0"/\"v1))) by A14;
hence thesis by A2217;
end;
A2225: for v1,v0 holds
((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"(v0"/\"(v1"/\"v1))))))=
(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A2221;
end;
A2227: for v1,v0 holds
((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"\/"(v1"/\"v1)))))=
v0"/\"(v1"\/"(v0"/\"v1))
proof let v1,v0;
(v0"\/"(v0"/\"(v0"/\"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"/\"v1))) by A1580;
hence thesis by A2225;
end;
A2229: for v1,v0 holds
((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"(v1
"\/"
(v0"/\"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"/\"v1)))=(v0"\/"(v0"/\"(v1"/\"v1))) by A2027;
hence thesis by A2227;
end;
A2231: for v1,v0 holds
((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"\/"v1))))=(v0"/\"(v1"\/"(v0
"/\"v1)))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"/\"v1)))=(v0"/\"(v0"\/"v1)) by A1521;
hence thesis by A2229;
end;
A2233: for v1,v0 holds
((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v0
"/\"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"v1)) by A2027;
hence thesis by A2231;
end;
A2235: for v1,v0 holds
((v0"/\"v1)"/\"((v0"/\"v1)"\/"((v0"\/"(v0"/\"v1))"\/"v0)))=(v0"/\"(v1"\/"(v0
"/\"v1)))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"v1)))=((v0"/\"v1)"\/"((v0"\/"(v0"/\"v1))
"\/"v0)) by
A8;
hence thesis by A2233;
end;
A2239: for v1,v0 holds
((v0"/\"v1)"/\"((v0"/\"v1)"\/"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
(v0"\/"(v0"\/"(v0"/\"v1)))=(v0"\/"(v0"/\"v1)) by A2109;
hence thesis by A2235;
end;
A2241: for v1,v0 holds
((v0"/\"v1)"/\"(v0"\/"((v0"/\"v1)"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
(v0"\/"((v0"/\"v1)"\/"(v0"/\"v1)))=((v0"/\"v1)"\/"(v0"\/"(v0"/\"v1))) by A8;
hence thesis by A2239;
end;
A2243: for v1,v0 holds
((v0"/\"v1)"/\"(v0"\/"(v0"/\"(v1"\/"v1))))=(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
((v0"/\"v1)"\/"(v0"/\"v1))=(v0"/\"(v1"\/"v1));
hence thesis by A2241;
end;
A2245: for v1,v0 holds ((v0"/\"v1)"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"(v0"/\"
v1)))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"\/"v1)))=(v0"\/"(v0"/\"v1));
hence thesis by A2243;
end;
A2247: for v1,v0 holds (v0"/\"(v1"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"
v1)))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v1"/\"(v0"\/"(v0"/\"v1)))) by A292;
hence thesis by A2245;
end;
A2249: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))=(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v0,v1;
(v1"/\"(v0"\/"(v0"/\"v1)))=(v1"/\"(v0"\/"v0)) by A2195;
hence thesis by A2247;
end;
A2251: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
(v0"/\"(v1"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v1)) by A2121;
hence thesis by A2249;
end;
A2340: for v1,v0 holds (v0"\/"(v1"/\"(v0"\/"v1)))=(v0"\/"((v0"/\"v0)"\/"v1))
proof let v1,v0;
(v0"\/"((v0"/\"v0)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v0))) by A8;
hence thesis by A1457;
end;
A2355: for v2,v1,v0 holds
((v0"\/"v1)"/\"(v0"\/"((v0"/\"v0)"\/"v2)))=(v0"\/"(v1"/\"v2))
proof let v2,v1,v0;
(v0"\/"((v0"/\"v0)"\/"v2))=(v2"\/"(v0"\/"(v0"/\"v0))) by A8;
hence thesis by A4;
end;
A2359: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v0"\/"(v0"\/"v2)))=(v0"\/"(v1"/\"v2))
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v0"\/"(v2"\/"(v0"/\"v0))))=((v0"\/"v1)"/\"(v0"\/"(v0"\/"v2)))
;
hence thesis by A2355;
end;
A2361: for v1,v2,v0 holds (v0"\/"(v1"/\"(v0"\/"v2)))=(v0"\/"(v1"/\"v2))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v0"\/"(v0"\/"v2)))=(v0"\/"(v1"/\"(v0"\/"v2))) by A4;
hence thesis by A2359;
end;
A2369: for v1,v0 holds (v0"/\"(v1"/\"(v0"\/"v1)))=(v1"/\"(v0"\/"v0))
proof let v1,v0;
(v0"/\"(v0"/\"(v1"\/"v1)))=(v1"/\"(v0"\/"v0)) by A2148;
hence thesis by A1817;
end;
A2371: for v2,v1,v0 holds
((v0"\/"(v1"/\"v0))"/\"(v2"\/"(v0"/\"(v1"\/"v1))))=(v0"/\"(v1"\/"(v2"\/"(v1
"/\"v1))))
proof let v2,v1,v0;
(v0"\/"(v1"/\"(v0"\/"v0)))=(v0"\/"(v1"/\"v0));
hence thesis by A2170;
end;
A2375: for v2,v1,v0 holds
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"(v1"\/"v1))))=(v0"/\"(v1"\/"(v1"\/"v2)))
proof let v2,v1,v0;
(v0"/\"(v1"\/"(v2"\/"(v1"/\"v1))))=(v0"/\"(v1"\/"(v1"\/"v2)));
hence thesis by A2371;
end;
A2397: for v0,v1 holds (v0"\/"(v1"\/"(v0"/\"v0)))=(v0"\/"(v1"/\"v1))
proof let v0,v1;
(v0"\/"(v1"/\"(v0"\/"v1)))=(v0"\/"(v1"/\"v1)) by A2361;
hence thesis by A2340;
end;
A2408: (c2"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))=(c2"\/"((c3"\/"c4)"/\"(c3"/\"
c4))) by A2361;
A2411: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"((c2"\/"c3)"/\"(
c1"\/"
(c2"/\"c3))))))=((c2"\/"(c4"/\"((c3"\/"c4)"/\"c3)))"/\"(c1"\/"(c2"/\"((c3"\/"c4
)"/\"(c2"\/"
(c3"/\"c4)))))) by A14,A2408,A368;
A2415: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"((c2"\/"c3)"/\"(
c1"\/"
(c2"/\"c3))))))=((c2"\/"(c4"/\"(c3"\/"(c3"/\"c4))))"/\"(c1"\/"(c2"/\"((c3"\/"c4
)"/\"(c2"\/"
(c3"/\"c4)))))) by A2027,A2411;
A2417: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"((c2"\/"c3)"/\"(
c1"\/"
(c2"/\"c3))))))=((c2"\/"(c4"/\"(c3"\/"c3)))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2
"\/"
(c3"/\"c4)))))) by A2195,A2415;
A2431: for v2,v0,v1 holds
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v1"/\"v0)))=(v0"/\"(v1"\/"(v1"\/"v2)))
proof let v2,v0,v1;
(v2"\/"(v0"/\"(v1"\/"v1)))=(v2"\/"(v1"/\"v0));
hence thesis by A2375;
end;
A2435: for v0,v2,v1 holds (v0"/\"(v1"\/"v2))=(v0"/\"(v1"\/"(v1"\/"v2)))
proof let v0,v2,v1;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v2)) by A85;
hence thesis by A2431;
end;
A2490: for v1,v2,v0 holds (v0"/\"(v1"\/"(v0"/\"v2)))=(v0"/\"(v2"\/"(v1"/\"v1)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A1729;
end;
A2492: for v1,v2,v0 holds v0"/\"(v1"\/"(v0"/\"v2)) = v0"/\"(v2"\/"v1)
proof let v1,v2,v0;
v0"/\"(v2"\/"(v1"/\"v1)) = v0"/\"(v2"\/"v1);
hence thesis by A2490;
end;
A2498: for v0,v2,v1 holds
v0"/\"(v1"\/"(v2"\/"(v1"/\"v2))) = v0"/\"(v2"\/"(v0"/\"v1))
proof let v0,v2,v1;
v0"/\"(v1"\/"(v0"/\"(v2"\/"(v1"/\"v2)))) = v0"/\"(v1"\/"(v2"\/"(v1"/\"v2)))
by A2492;
hence thesis by A1674;
end;
A2500: for v0,v2,v1 holds v0"/\"(v1"\/"(v2"\/"(v1"/\"v2))) = v0"/\"(v2"\/"v1)
proof let v0,v2,v1;
v0"/\"(v2"\/"(v0"/\"v1)) = v0"/\"(v2"\/"v1) by A2492;
hence thesis by A2498;
end;
A2504: for v3,v0,v2,v1 holds
(v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v2))) =
v0"/\"(v1"\/"(v3"\/"(v0"/\"v2)))
proof let v3,v0,v2,v1;
v0"/\"(v1"\/"(v0"/\"v2)) = v0"/\"(v1"\/"v2) by A2492;
hence thesis by A1813;
end;
A2506: for v0,v1,v2,v3 holds
v0"/\"(v1"\/"(v3"\/"(v2"/\"v2))) = v0"/\"(v1"\/"(v3"\/"(v0"/\"v2)))
proof let v0,v1,v2,v3;
(v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v2))) =
v0"/\"(v1"\/"(v3"\/"(v2"/\"v2))) by A1725;
hence thesis by A2504;
end;
A2509: for v3,v0,v2,v1 holds
(v0"/\"(v1"\/"(v1"/\"v2)))"\/"(v1"/\"(v2"\/"v3)) =
v1"/\"(v0"\/"(v3"\/"(v2"/\"v2)))
proof let v3,v0,v2,v1;
(v1"/\"(v0"\/"v2))"\/"(v3"/\"(v1"\/"(v1"/\"v2))) =
v1"/\"(v0"\/"(v3"\/"(v2"/\"v2))) by A1725;
hence thesis by A444;
end;
A2512: for v102,v100 holds
Tern(v100,(v100"\/"v102)
,v102)=((v100"\/"v102)"\/"((v100"\/"v102)"/\"(v100"/\"v102)))
proof let v102,v100;
(v100"\/"v102)"/\"((v100"\/"v102)"\/"(v100"/\"v102)) =
(v100"\/"v102)"\/"((v100"\/"v102)"/\"(v100"/\"v102)) by A2027;
hence thesis by A63;
end;
A2515: for v1,v0 holds
((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v0"/\"v1)))=((v0"\/"v1)"\/"((v0"\/"v1)"/\"(v0
"/\"v1)))
proof let v1,v0;
Tern(v0,(v0"\/"v1),v1) = (v0"\/"v1)"/\"((v0"\/"v1)"\/"(v0"/\"v1)) by A63;
hence thesis by A2512;
end;
A2517: for v1,v0 holds
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v0"/\"v1))))=((v0"\/"v1)"\/"((v0"\/"v1)"/\"(v0
"/\"v1)))
proof let v1,v0;
((v0"\/"v1)"\/"(v0"/\"v1))=(v0"\/"(v1"\/"(v0"/\"v1))) by A181;
hence thesis by A2515;
end;
A2519: for v1,v0 holds
((v0"\/"v1)"/\"(v0"\/"v1))=((v0"\/"v1)"\/"((v0"\/"v1)"/\"(v0"/\"v1)))
proof let v1,v0;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v0"/\"v1))))=((v0"\/"v1)"/\"(v0"\/"v1)) by A2500;
hence thesis by A2517;
end;
A2521: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"((v0"\/"v1)"/\"(v0"/\"
v1)))
proof let v1,v0;
((v0"\/"v1)"/\"(v0"\/"v1))=(v0"\/"(v1"/\"v1));
hence thesis by A2519;
end;
A2523: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"(v1"/\"((v0"\/"v1)"/\"
v0)))
proof let v1,v0;
((v0"\/"v1)"/\"(v0"/\"v1))=(v1"/\"((v0"\/"v1)"/\"v0)) by A14;
hence thesis by A2521;
end;
A2527: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"(v1"/\"(v0"\/"(v0"/\"
v1))))
proof let v1,v0;
(v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"v1)) by A2027;
hence thesis by A2523;
end;
A2529: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"(v1"/\"(v0"\/"v0)))
proof let v1,v0;
(v1"/\"(v0"\/"(v0"/\"v1)))=(v1"/\"(v0"\/"v0)) by A2195;
hence thesis by A2527;
end;
A2531: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"(v0"/\"v1))
proof let v1,v0;
((v0"\/"v1)"\/"(v1"/\"(v0"\/"v0)))=((v0"\/"v1)"\/"(v0"/\"v1));
hence thesis by A2529;
end;
A2533: for v1,v0 holds (v0"\/"(v1"/\"v1))=(v0"\/"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
((v0"\/"v1)"\/"(v0"/\"v1))=(v0"\/"(v1"\/"(v0"/\"v1))) by A181;
hence thesis by A2531;
end;
A2549: for v103,v100,v1,v101 holds
((v100"/\"(v101"\/"(v101"/\"v1)))"\/"(v101"/\"v103))=(v101"/\"(v103"\/"(v100
"/\"
(v101"\/"v1))))
proof let v103,v100,v1,v101;
(v101"/\"(v101"\/"v1))=(v101"\/"(v101"/\"v1)) by A2027;
hence thesis by A123;
end;
A2553: for v101,v102,v1,v100 holds
((v100"/\"v101)"\/"(v102"/\"(v100"\/"(v100"/\"v1))))=(v100"/\"(v101"\/"(v102
"/\"
(v100"\/"v1))))
proof let v101,v102,v1,v100;
(v100"/\"(v100"\/"v1))=(v100"\/"(v100"/\"v1)) by A2027;
hence thesis by A159;
end;
A2556: for v3,v0,v2,v1 holds
(v1"/\"((v2"\/"v3)"\/"(v0"/\"(v1"\/"v2))))=(v1"/\"(v0"\/"(v3"\/"(v2"/\"v2))))
proof let v3,v0,v2,v1;
((v0"/\"(v1"\/"(v1"/\"v2)))"\/"(v1"/\"(v2"\/"v3)))=(v1"/\"((v2"\/"v3)"\/"(v0
"/\"
(v1"\/"v2)))) by A2549;
hence thesis by A2509;
end;
A2559: for v2,v3,v1,v0 holds
(v0"/\"(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))))=(v0"/\"(v3"\/"(v2"\/"(v1"/\"v1))))
proof let v2,v3,v1,v0;
((v1"\/"v2)"\/"(v3"/\"(v0"\/"v1)))=(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))) by A181;
hence thesis by A2556;
end;
A2561: for v2,v3,v1,v0 holds
(v0"/\"((v1"\/"v2)"\/"(v3"/\"(v0"\/"v1))))=(v0"/\"(v1"\/"(v2"\/"v3)))
proof let v2,v3,v1,v0;
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"((v1"\/"v2)"\/"(v3
"/\"
(v0"\/"v1)))) by A2553;
hence thesis by A458;
end;
A2563: for v2,v3,v1,v0 holds
(v0"/\"(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))))=(v0"/\"(v1"\/"(v2"\/"v3)))
proof let v2,v3,v1,v0;
((v1"\/"v2)"\/"(v3"/\"(v0"\/"v1)))=(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))) by A181;
hence thesis by A2561;
end;
A2565: for v0,v3,v1,v2 holds
(v0"/\"(v3"\/"(v2"\/"(v1"/\"v1))))=(v0"/\"(v1"\/"(v2"\/"v3)))
proof let v0,v3,v1,v2;
(v0"/\"(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))))=(v0"/\"(v3"\/"(v2"\/"(v1"/\"v1))))
by A2559;
hence thesis by A2563;
end;
A2574: for v0,v3,v2,v1 holds
(v0"/\"(v3"\/"(v1"\/"v2)))=(v0"/\"(v1"\/"(v2"\/"(v0"/\"v3))))
proof let v0,v3,v2,v1;
(v0"/\"(v1"\/"(v2"\/"(v3"/\"v3))))=(v0"/\"(v3"\/"(v1"\/"v2))) by A2565;
hence thesis by A2506;
end;
A2577: for v0,v3,v2,v1 holds
(v0"/\"(v3"\/"(v1"\/"v2)))=(v0"/\"(v2"\/"(v3"\/"(v0"/\"v1))))
proof let v0,v3,v2,v1;
(v1"\/"(v2"\/"v3))=(v3"\/"(v1"\/"v2)) by A8;
hence thesis by A2574;
end;
A2583: for v0,v2,v1,v3 holds
(v0"/\"(v2"\/"(v3"\/"v1)))=(v0"/\"(v2"\/"(v1"\/"(v0"/\"v3))))
proof let v0,v2,v1,v3;
(v2"\/"(v3"\/"v1))=(v1"\/"(v2"\/"v3)) by A8;
hence thesis by A2577;
end;
A2591: for v102,v103,v1,v101 holds
((v101"\/"v1)"/\"((v101"\/"v102)"/\"(v103"\/"(v101"/\"(v101"\/"v1)))))=(v101
"\/"(v1"/\"
(v103"/\"v102)))
proof let v102,v103,v1,v101;
((v101"\/"v1)"/\"(v101"\/"(v103"/\"v102)))=(v101"\/"(v1"/\"(v103"/\"v102))) by
A4;
hence thesis by A241;
end;
A2594: for v2,v3,v1,v0 holds
((v0"\/"v1)"/\"((v0"\/"v2)"/\"(v3"\/"(v0"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v3
"/\"v2)))
proof let v2,v3,v1,v0;
(v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"v1)) by A2027;
hence thesis by A2591;
end;
A2596: for v2,v3,v1,v0 holds
((v0"\/"v1)"/\"((v0"\/"v2)"/\"(v0"\/"((v0"/\"v1)"\/"v3))))=(v0"\/"(v1"/\"(v3
"/\"v2)))
proof let v2,v3,v1,v0;
(v0"\/"((v0"/\"v1)"\/"v3))=(v3"\/"(v0"\/"(v0"/\"v1))) by A8;
hence thesis by A2594;
end;
A2600: for v2,v3,v1,v0 holds
((v0"\/"v1)"/\"(v0"\/"(v2"/\"(v3"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v3"/\"v2)))
proof let v2,v3,v1,v0;
((v0"\/"v2)"/\"(v0"\/"(v3"\/"(v0"/\"v1))))=(v0"\/"(v2"/\"(v3"\/"(v0"/\"v1))))
by A4;
hence thesis by A2596;
end;
A2602: for v2,v3,v1,v0 holds
(v0"\/"(v1"/\"(v2"/\"(v3"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v3"/\"v2)))
proof let v2,v3,v1,v0;
((v0"\/"v1)"/\"(v0"\/"(v2"/\"(v3"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v2"/\"(v3"\/"
(v0"/\"v1))))) by A4;
hence thesis by A2600;
end;
A2618: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))=(v1"/\"(v0"\/"v0))
proof let v0,v1;
(v0"/\"(v1"\/"v1))=(v0"/\"(v1"/\"(v0"\/"v0))) by A2251;
hence thesis;
end;
A2652: for v1,v2,v100,v102,v101 holds
((v100"\/"(v101"\/"v102))"/\"(v101"\/"(v1"/\"v2)))=(v101"\/"((v1"/\"(v101"\/"
v2))"/\"
(v100"\/"v102)))
proof let v1,v2,v100,v102,v101;
(v101"\/"(v1"/\"(v101"\/"v2)))=(v101"\/"(v1"/\"v2)) by A2361;
hence thesis by A109;
end;
A2655: for v1,v0,v2,v4,v3 holds
(v1"\/"((v3"/\"v4)"/\"(v0"\/"v2)))=(v1"\/"((v3"/\"(v1"\/"v4))"/\"(v0"\/"v2)))
proof let v1,v0,v2,v4,v3;
((v0"\/"(v1"\/"v2))"/\"(v1"\/"(v3"/\"v4)))=(v1"\/"((v3"/\"v4)"/\"(v0"\/"v2)))
by A109;
hence thesis by A2652;
end;
A2658: for v0,v1,v2,v4,v3 holds
(v0"\/"(v1"/\"(v2"/\"(v3"\/"v4))))=(v0"\/"((v1"/\"(v0"\/"v2))"/\"(v3"\/"v4)))
proof let v0,v1,v2,v4,v3;
((v1"/\"v2)"/\"(v3"\/"v4))=(v1"/\"(v2"/\"(v3"\/"v4))) by A292;
hence thesis by A2655;
end;
A2660: for v0,v1,v2,v4,v3 holds
(v0"\/"(v1"/\"(v2"/\"(v3"\/"v4))))=(v0"\/"(v1"/\"((v0"\/"v2)"/\"(v3"\/"v4))))
proof let v0,v1,v2,v4,v3;
((v1"/\"(v0"\/"v2))"/\"(v3"\/"v4))=(v1"/\"((v0"\/"v2)"/\"(v3"\/"v4))) by A292;
hence thesis by A2658;
end;
A2663: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"(c3"/\"(c1"\/"(c2
"/\"c3))))))=
((c2"\/"(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by
A2660,A2417;
A2667: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c3"/\"(c4"/\"(c1"\/"(c2
"/\"c3))))))=
((c2"\/"(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by
A2663,A14;
A2669: not
((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c3"/\"(c4"/\"c1))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A2602,
A2667;
A2677: not
((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(
c2"\/"(c3"/\"c4)))))) by A14,A2669;
A2680: for v103,v101,v100 holds
((v101"/\"(v100"\/"v100))"\/"((v100"\/"v101)"/\"v103))=((v100"\/"v101)"/\"(
v103"\/"
(v100"/\"v101)))
proof let v103,v101,v100;
(v100"/\"(v101"/\"(v100"\/"v101)))=(v101"/\"(v100"\/"v100)) by A2369;
hence thesis by A131;
end;
A2692: for v103,v100,v1,v101 holds
((v100"\/"(v101"\/"(v1"/\"v1)))"/\"((v1"\/"(v101"/\"v101))"\/"v103))=((v1"\/"
(v101"/\"v101))"\/"(v103"/\"(v100"\/"v101)))
proof let v103,v100,v1,v101;
(v101"\/"(v1"\/"(v101"/\"v101)))=(v101"\/"(v1"/\"v1)) by A2397;
hence thesis by A117;
end;
A2697: for v3,v0,v2,v1 holds
((v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v2"\/"((v1"/\"v1)"\/"v3)))=((v2"\/"(v1"/\"v1))
"\/"(v3"/\"
(v0"\/"v1)))
proof let v3,v0,v2,v1;
(v2"\/"((v1"/\"v1)"\/"v3))=(v3"\/"(v2"\/"(v1"/\"v1))) by A8;
hence thesis by A2692;
end;
A2701: for v3,v0,v2,v1 holds
((v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v1"\/"(v2"\/"v3)))=((v2"\/"(v1"/\"v1))"\/"(v3
"/\"
(v0"\/"v1)))
proof let v3,v0,v2,v1;
((v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v2"\/"(v3"\/"(v1"/\"v1))))=((v0"\/"(v1"\/"(v2
"/\"v2)))"/\"
(v1"\/"(v2"\/"v3))) by A2565;
hence thesis by A2697;
end;
A2703: for v1,v0,v3,v2 holds
(v1"\/"((v2"\/"v3)"/\"(v0"\/"(v2"/\"v2))))=((v2"\/"(v1"/\"v1))"\/"(v3"/\"(v0
"\/"v1)))
proof let v1,v0,v3,v2;
((v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v1"\/"(v2"\/"v3)))=(v1"\/"((v2"\/"v3)"/\"(v0
"\/"(v2"/\"v2)))) by A109;
hence thesis by A2701;
end;
A2706: for v0,v3,v2,v1 holds
v0"\/"((v1"\/"v2)"/\"(v3"\/"v1)) = (v1"\/"(v0"/\"v0))"\/"(v2"/\"(v3"\/"v0))
proof let v0,v3,v2,v1;
(v1"\/"v2)"/\"(v3"\/"(v1"/\"v1)) = (v1"\/"v2)"/\"(v3"\/"v1);
hence thesis by A2703;
end;
A2708: for v0,v1,v2,v3 holds
v0"\/"(v1"\/"(v3"/\"v2)) = (v1"\/"(v0"/\"v0))"\/"(v2"/\"(v3"\/"v0))
proof let v0,v1,v2,v3;
v0"\/"((v1"\/"v2)"/\"(v3"\/"v1)) = v0"\/"(v1"\/"(v3"/\"v2)) by A223;
hence thesis by A2706;
end;
A2711: for v0,v1,v3,v2 holds
v0"\/"(v1"\/"(v2"/\"v3)) = v1"\/"((v0"/\"v0)"\/"(v3"/\"(v2"\/"v0)))
proof let v0,v1,v3,v2;
(v1"\/"(v0"/\"v0))"\/"(v3"/\"(v2"\/"v0)) =
v1"\/"((v0"/\"v0)"\/"(v3"/\"(v2"\/"v0))) by A181;
hence thesis by A2708;
end;
A2713: for v0,v1,v3,v2 holds
v0"\/"(v1"\/"(v2"/\"v3)) = v1"\/"(v0"\/"(v3"/\"(v2"\/"v0)))
proof let v0,v1,v3,v2;
(v0"/\"v0)"\/"(v3"/\"(v2"\/"v0)) = v0"\/"(v3"/\"(v2"\/"v0));
hence thesis by A2711;
end;
A2715: for v0,v1,v3,v2 holds
(v0"\/"(v1"\/"(v2"/\"v3)))=(v0"\/"((v3"/\"(v2"\/"v0))"\/"v1))
proof let v0,v1,v3,v2;
(v0"\/"((v3"/\"(v2"\/"v0))"\/"v1))=(v1"\/"(v0"\/"(v3"/\"(v2"\/"v0)))) by A8;
hence thesis by A2713;
end;
A2721: for v0,v1 holds (v0"\/"(v1"\/"(v0"/\"v0)))=(v1"\/"(v0"/\"v0))
proof let v0,v1;
(v0"\/"(v1"\/"(v0"/\"v0)))=(v0"\/"(v1"/\"v1)) by A2397;
hence thesis;
end;
A2773: for v2,v1,v0 holds
(v1"/\"v0)"\/"(v2"/\"(v0"\/"v1)) = (v0"\/"v1)"/\"(v2"\/"(v0"/\"v1))
proof let v2,v1,v0;
(v0"/\"(v1"\/"v1))"\/"(v2"/\"(v0"\/"v1)) = (v1"/\"v0)"\/"(v2"/\"(v0"\/"v1));
hence thesis by A2680;
end;
A2780: not
((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A2773,
A2677;
A2782: not
((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"/\"c4)"\/"(c2"/\"(c3"\/"c4)))))) by A2773,
A2780;
A2784: not
((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"/\"c4)"\/"(c3"\/"c4))))) by A2492,A2782;
A2788: not
((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"(c3"\/"(c4"\/"(c3"/\"c4)))))) by A181,A2784;
A2790: not
((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"(c3"\/"(c4"/\"c4))))) by A2533,A2788;
A2795: for v101,v102,v2,v3,v1,v0 holds
(((v0"/\"(v1"/\"v2))"\/"v101)"/\"(v102"\/"(v2"/\"(v3"\/"(v0"/\"v1)))))=((v0
"/\"
(v1"/\"v2))"\/"(v101"/\"(v102"\/"(v2"/\"v3))))
proof let v101,v102,v2,v3,v1,v0;
((v0"/\"(v1"/\"v2))"\/"(v2"/\"v3))=(v2"/\"(v3"\/"(v0"/\"v1))) by A131;
hence thesis by A270;
end;
A2802: for v103,v102,v101 holds
(v101"\/"v102)"/\"(v102"\/"v103) = v102"\/"(v103"/\"((v101"\/"v102)"\/"v101))
proof let v103,v102,v101;
((v101"\/"v102)"\/"(v101"\/"v102))"/\"(v102"\/"v103) =
(v101"\/"v102)"/\"(v102"\/"v103);
hence thesis by A117;
end;
A2805: for v1,v2,v0 holds (v1"\/"(v0"/\"v2))=(v1"\/"(v2"/\"((v0"\/"v1)"\/"v0)))
proof let v1,v2,v0;
(v0"\/"v1)"/\"(v1"\/"v2) = v1"\/"(v0"/\"v2) by A4;
hence thesis by A2802;
end;
A2810: for v0,v2,v1 holds v0"\/"(v1"/\"v2) = v0"\/"(v2"/\"(v1"\/"v0))
proof let v0,v2,v1;
v2"/\"(v1"\/"(v1"\/"v0)) = v2"/\"(v1"\/"v0) by A2435;
hence thesis by A2805;
end;
A2815: for v1,v2,v100,v102,v101 holds
((v100"/\"(v101"/\"v102))"\/"(v101"/\"(v1"\/"v2)))=(v101"/\"((v1"\/"(v101"/\"
v2))"\/"
(v100"/\"v102)))
proof let v1,v2,v100,v102,v101;
(v101"/\"(v1"\/"(v101"/\"v2)))=(v101"/\"(v1"\/"v2)) by A2492;
hence thesis by A123;
end;
A2818: for v1,v0,v2,v4,v3 holds
(v1"/\"((v3"\/"v4)"\/"(v0"/\"v2)))=(v1"/\"((v3"\/"(v1"/\"v4))"\/"(v0"/\"v2)))
proof let v1,v0,v2,v4,v3;
((v0"/\"(v1"/\"v2))"\/"(v1"/\"(v3"\/"v4)))=(v1"/\"((v3"\/"v4)"\/"(v0"/\"v2)))
by A123;
hence thesis by A2815;
end;
A2821: for v0,v1,v2,v4,v3 holds
v0"/\"(v1"\/"(v2"\/"(v3"/\"v4))) = v0"/\"((v1"\/"(v0"/\"v2))"\/"(v3"/\"v4))
proof let v0,v1,v2,v4,v3;
(v1"\/"v2)"\/"(v3"/\"v4) = v1"\/"(v2"\/"(v3"/\"v4)) by A181;
hence thesis by A2818;
end;
A2823: for v0,v1,v2,v4,v3 holds
(v0"/\"(v1"\/"(v2"\/"(v3"/\"v4))))=(v0"/\"(v1"\/"((v0"/\"v2)"\/"(v3"/\"v4))))
proof let v0,v1,v2,v4,v3;
((v1"\/"(v0"/\"v2))"\/"(v3"/\"v4))=(v1"\/"((v0"/\"v2)"\/"(v3"/\"v4))) by A181;
hence thesis by A2821;
end;
A2838: for v102,v100,v1 holds
(v1"/\"(v100"\/"v100))"\/"(v100"/\"v102) =
v100"/\"((v1"/\"(v100"\/"v100))"\/"v102)
proof let v102,v100,v1;
v100"/\"(v1"/\"(v100"\/"v100)) = v1"/\"(v100"\/"v100) by A2618;
hence thesis by A6;
end;
A2847: for v1,v2,v0 holds v1"/\"(v0"\/"v2) = v1"/\"((v0"/\"(v1"\/"v1))"\/"v2)
proof let v1,v2,v0;
(v0"/\"v1)"\/"(v1"/\"v2) = v1"/\"(v0"\/"v2) by A6;
hence thesis by A2838;
end;
A2852: for v0,v2,v1 holds v0"/\"(v1"\/"v2) = v0"/\"(v2"\/"(v0"/\"v1))
proof let v0,v2,v1;
v2"\/"(v1"/\"(v0"\/"v0)) = v2"\/"(v0"/\"v1);
hence thesis by A2847;
end;
A2859: for v103,v100,v101,v1 holds
(v100"/\"(v1"/\"(v101"\/"v101)))"\/"(v101"/\"v103) =
v101"/\"(v103"\/"(v100"/\"(v1"/\"(v101"\/"v101))))
proof let v103,v100,v101,v1;
v101"/\"(v1"/\"(v101"\/"v101)) = v1"/\"(v101"\/"v101) by A2618;
hence thesis by A123;
end;
A2862: for v2,v3,v1,v0 holds
(v2"/\"(v3"\/"(v0"/\"v1)))=(v2"/\"(v3"\/"(v0"/\"(v1"/\"(v2"\/"v2)))))
proof let v2,v3,v1,v0;
((v0"/\"(v1"/\"(v2"\/"v2)))"\/"(v2"/\"v3))=(v2"/\"(v3"\/"(v0"/\"v1))) by A123;
hence thesis by A2859;
end;
A2865: for v0,v1,v3,v2 holds
(v0"/\"(v1"\/"(v2"/\"v3)))=(v0"/\"(v1"\/"(v0"/\"(v2"/\"v3))))
proof let v0,v1,v3,v2;
(v1"\/"(v2"/\"(v3"/\"(v0"\/"v0))))=(v1"\/"(v0"/\"(v2"/\"v3))) by A14;
hence thesis by A2862;
end;
A2867: for v0,v1,v3,v2 holds
(v0"/\"(v1"\/"(v2"/\"v3)))=(v0"/\"(v1"\/"(v3"/\"(v0"/\"v2))))
proof let v0,v1,v3,v2;
(v0"/\"(v2"/\"v3))=(v3"/\"(v0"/\"v2)) by A14;
hence thesis by A2865;
end;
A2886: for v3,v2,v1,v0 holds
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v2"\/"(v0"/\"v1))))=((v0"/\"v1)"\/"(v2"/\"(v0
"\/"v3)))
proof let v3,v2,v1,v0;
((v2"\/"(v0"/\"v1))"/\"(v0"\/"(v3"\/"(v0"/\"v1))))=((v0"/\"v1)"\/"(v2"/\"(v0
"\/"v3))) by A305;
hence thesis by A511;
end;
A2889: for v103,v100,v101,v1 holds
(v100"\/"(v1"\/"(v101"/\"v101)))"/\"(v101"\/"v103) =
v101"\/"(v103"/\"(v100"\/"(v1"\/"(v101"/\"v101))))
proof let v103,v100,v101,v1;
v101"\/"(v1"\/"(v101"/\"v101)) = v1"\/"(v101"/\"v101) by A2721;
hence thesis by A109;
end;
A2892: for v2,v3,v1,v0 holds
(v2"\/"(v3"/\"(v0"\/"v1)))=(v2"\/"(v3"/\"(v0"\/"(v1"\/"(v2"/\"v2)))))
proof let v2,v3,v1,v0;
(v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v2"\/"v3) = v2"\/"(v3"/\"(v0"\/"v1)) by A109;
hence thesis by A2889;
end;
A2895: for v0,v1,v3,v2 holds
v0"\/"(v1"/\"(v2"\/"v3)) = v0"\/"(v1"/\"(v0"\/"(v2"\/"v3)))
proof let v0,v1,v3,v2;
v1"/\"(v2"\/"(v3"\/"(v0"/\"v0))) = v1"/\"(v0"\/"(v2"\/"v3)) by A2565;
hence thesis by A2892;
end;
A2897: for v0,v1,v3,v2 holds
v0"\/"(v1"/\"(v2"\/"v3)) = v0"\/"(v1"/\"(v3"\/"(v0"\/"v2)))
proof let v0,v1,v3,v2;
v0"\/"(v2"\/"v3) = v3"\/"(v0"\/"v2) by A8;
hence thesis by A2895;
end;
A2907: for v102,v1,v100,v2 holds
((v100"/\"(v2"\/"v1))"\/"((v1"\/"(v2"/\"v100))"/\"v102))=((v1"\/"(v2"/\"v100))
"/\"
(v100"\/"v102))
proof let v102,v1,v100,v2;
v100"/\"(v1"\/"(v2"/\"v100)) = v100"/\"(v2"\/"v1) by A2852;
hence thesis by A6;
end;
A2914: for v1,v2,v3,v0 holds
(v0"/\"v1)"\/"(v2"/\"(v0"\/"v3)) = (v2"\/"(v1"/\"v0))"/\"(v0"\/"v3)
proof let v1,v2,v3,v0;
(v0"/\"(v1"\/"v2))"\/"(v3"/\"(v2"\/"(v0"/\"v1))) =
(v0"/\"v1)"\/"(v2"/\"(v0"\/"v3)) by A2886;
hence thesis by A2907;
end;
A2921: for v102,v101,v1,v0 holds
((v102"/\"v101)"\/"(v101"/\"(v0"\/"v1)))=(v101"/\"((v0"\/"(v1"\/"(v102"/\"v101
)))"\/"(
(v0"\/"(v1"\/"(v102"/\"v101)))"/\"v102)))
proof let v102,v101,v1,v0;
((v0"\/"(v1"\/"(v102"/\"v101)))"/\"(v101"\/"(v102"/\"v101)))=((v102"/\"v101)
"\/"
(v101"/\"(v0"\/"v1))) by A346;
hence thesis by A1005;
end;
A2924: for v1,v0,v3,v2 holds
v1"/\"(v0"\/"(v2"\/"v3)) =
v1"/\"((v2"\/"(v3"\/"(v0"/\"v1)))"\/"((v2"\/"(v3"\/"(v0"/\"v1)))"/\"v0))
proof let v1,v0,v3,v2;
(v0"/\"v1)"\/"(v1"/\"(v2"\/"v3)) = v1"/\"(v0"\/"(v2"\/"v3)) by A6;
hence thesis by A2921;
end;
A2929: for v0,v1,v3,v2 holds
v0"/\"(v1"\/"(v2"\/"v3)) =
v0"/\"((v2"\/"(v3"\/"(v1"/\"v0)))"\/"(v1"/\"(v2"\/"(v3"\/"v0))))
proof let v0,v1,v3,v2;
v1"/\"(v2"\/"(v3"\/"(v1"/\"v0))) = v1"/\"(v2"\/"(v3"\/"v0)) by A2583;
hence thesis by A2924;
end;
A2933: for v0,v1,v3,v2 holds
v0"/\"(v1"\/"(v2"\/"v3)) =
v0"/\"((v2"\/"(v3"\/"(v1"/\"v0)))"\/"(v1"/\"(v0"\/"(v3"\/"v2))))
proof let v0,v1,v3,v2;
v0"\/"(v3"\/"v2) = v2"\/"(v0"\/"v3) by A8;
hence thesis by A2929;
end;
A2937: for v0,v1,v3,v2 holds
v0"/\"(v1"\/"(v2"\/"v3)) =
v0"/\"(v2"\/"((v3"\/"(v1"/\"v0))"\/"(v1"/\"(v0"\/"(v2"\/"v3)))))
proof let v0,v1,v3,v2;
(v2"\/"(v3"\/"(v1"/\"v0)))"\/"(v1"/\"(v0"\/"(v2"\/"v3))) =
v2"\/"((v3"\/"(v1"/\"v0))"\/"(v1"/\"(v0"\/"(v2"\/"v3)))) by A181;
hence thesis by A2933;
end;
A2939: for v0,v1,v3,v2 holds
v0"/\"(v1"\/"(v2"\/"v3)) =
v0"/\"(v2"\/"(v3"\/"((v1"/\"v0)"\/"(v1"/\"(v0"\/"(v2"\/"v3))))))
proof let v0,v1,v3,v2;
(v3"\/"(v1"/\"v0))"\/"(v1"/\"(v0"\/"(v2"\/"v3))) =
v3"\/"((v1"/\"v0)"\/"(v1"/\"(v0"\/"(v2"\/"v3)))) by A181;
hence thesis by A2937;
end;
A2941: for v0,v1,v3,v2 holds v0"/\"(v1"\/"(v2"\/"v3)) =
v0"/\"(v2"\/"(v3"\/"(v1"/\"(v0"\/"(v0"\/"(v2"\/"v3))))))
proof let v0,v1,v3,v2;
(v1"/\"v0)"\/"(v1"/\"(v0"\/"(v2"\/"v3))) =
v1"/\"(v0"\/"(v0"\/"(v2"\/"v3))) by A6;
hence thesis by A2939;
end;
A2943: for v0,v1,v3,v2 holds
v0"/\"(v1"\/"(v2"\/"v3)) = v0"/\"(v2"\/"(v3"\/"(v1"/\"(v0"\/"(v2"\/"v3)))))
proof let v0,v1,v3,v2;
v1"/\"(v0"\/"(v0"\/"(v2"\/"v3))) = v1"/\"(v0"\/"(v2"\/"v3)) by A2435;
hence thesis by A2941;
end;
A2945: for v0,v1,v3,v2 holds
v0"/\"(v1"\/"(v2"\/"v3)) = v0"/\"(v2"\/"(v3"\/"(v1"/\"(v0"\/"v2))))
proof let v0,v1,v3,v2;
v3"\/"(v1"/\"(v0"\/"(v2"\/"v3))) = v3"\/"(v1"/\"(v0"\/"v2)) by A2897;
hence thesis by A2943;
end;
A2947: for v0,v1,v3,v2 holds
v0"/\"(v1"\/"(v2"\/"v3)) = v0"/\"(v2"\/"(v3"\/"(v0"/\"v1)))
proof let v0,v1,v3,v2;
v2"\/"(v3"\/"(v1"/\"(v0"\/"v2))) = v2"\/"(v3"\/"(v0"/\"v1)) by A2715;
hence thesis by A2945;
end;
A2969: not
((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"/\"
(c3"\/"c4))"\/"(c1"/\"(c2"\/"(c3"/\"c4)))) by A2914,A2790;
A2972: for v101,v102,v1,v3,v2 holds
(v1"\/"(v2"/\"(v3"/\"v102)))"/\"(v101"\/"(v102"/\"(v1"\/"(v2"/\"v3)))) =
(v1"\/"(v2"/\"(v3"/\"v102)))"/\"(v102"\/"v101)
proof let v101,v102,v1,v3,v2;
v102"/\"(v1"\/"(v2"/\"(v3"/\"v102))) = v102"/\"(v1"\/"(v2"/\"v3)) by A2867;
hence thesis by A2852;
end;
A2975: for v0,v4,v1,v3,v2 holds
(v1"/\"(v2"/\"v3))"\/"(v0"/\"(v4"\/"(v3"/\"v0))) =
(v0"\/"(v1"/\"(v2"/\"v3)))"/\"(v3"\/"v4)
proof let v0,v4,v1,v3,v2;
(v0"\/"(v1"/\"(v2"/\"v3)))"/\"(v4"\/"(v3"/\"(v0"\/"(v1"/\"v2)))) =
(v1"/\"(v2"/\"v3))"\/"(v0"/\"(v4"\/"(v3"/\"v0))) by A2795;
hence thesis by A2972;
end;
A2980: for v4,v3,v0,v2,v1 holds
(v0"/\"(v1"/\"v2))"\/"(v3"/\"(v4"\/"v2)) =
(v3"\/"(v0"/\"(v1"/\"v2)))"/\"(v2"\/"v4)
proof let v4,v3,v0,v2,v1;
v3"/\"(v4"\/"(v3"/\"v2)) = v3"/\"(v4"\/"v2) by A2492;
hence thesis by A2975;
end;
A2986: not
((c1"/\"(c3"/\"c4))"\/"(c2"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3))))))=((
c2"/\"
(c3"\/"c4))"\/"(c1"/\"(c2"\/"(c3"/\"c4)))) by A2980,A2969;
A2987:
(c2"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=(c2"/\"(c4"\/"(c3"\/"(c1
"/\"
(c2"\/"c3))))) by A2823;
A2992: not
((c1"/\"(c3"/\"c4))"\/"(c2"/\"(c4"\/"(c3"\/"(c1"/\"c2)))))=((c2"/\"(c3"\/"c4))
"\/"(c1"/\"
(c2"\/"(c3"/\"c4)))) by A2810,A2987,A2986;
A2998: not
((c1"/\"(c3"/\"c4))"\/"(c2"/\"(c1"\/"(c3"\/"c4))))=((c2"/\"(c3"\/"c4))"\/"(c1
"/\"(c2"\/"
(c3"/\"c4)))) by A2947,A2992;
A3002: for v2,v100,v102,v101 holds
((v100"\/"(v101"/\"v102))"/\"(v101"\/"(v100"/\"v2)))=((v101"/\"v102)"\/"(v100
"/\"
(v101"\/"v2)))
proof let v2,v100,v102,v101;
(v100"/\"(v101"\/"(v100"/\"v2)))=(v100"/\"(v101"\/"v2)) by A2492;
hence thesis by A2914;
end;
A3005: for v3,v0,v2,v1 holds
((v0"/\"v3)"\/"(v1"/\"(v0"\/"(v1"/\"v2))))=((v1"/\"v2)"\/"(v0"/\"(v1"\/"v3)))
proof let v3,v0,v2,v1;
((v0"\/"(v1"/\"v2))"/\"(v1"\/"(v0"/\"v3)))=((v0"/\"v3)"\/"(v1"/\"(v0"\/"(v1"/\"
v2)))) by
A2914;
hence thesis by A3002;
end;
for v1,v2,v3,v0 holds
(v0"/\"v1)"\/"(v2"/\"(v0"\/"v3)) = (v2"/\"v3)"\/"(v0"/\"(v2"\/"v1))
proof let v1,v2,v3,v0;
v2"/\"(v0"\/"(v2"/\"v3)) = v2"/\"(v0"\/"v3) by A2492;
hence thesis by A3005;
end;
hence thesis by A2998;
end;
LemacikA:
for B being Boolean Lattice
for v2,v1,v0 being Element of BA2TBAA B holds Tern(v0,v1,v2)=Tern(v2,v0,v1)
proof
let B be Boolean Lattice;
let v2,v1,v0 be Element of BA2TBAA B;
reconsider aa = v0, bb = v1, cc = v2 as Element of B;
Tern (v0,v1,v2) = Ros (aa,bb,cc) by RosTrnDef
.= Ros (cc,aa,bb) by LATTICES:def 5
.= Tern (v2,v0,v1) by RosTrnDef;
hence thesis;
end;
LemacikB:
for B being Boolean Lattice
for v2,v1,v0 being Element of BA2TBAA B holds Tern(v0,v1,v2)=Tern(v0,v2,v1)
proof
let B be Boolean Lattice;
let v2,v1,v0 be Element of BA2TBAA B;
reconsider aa = v0, bb = v1, cc = v2 as Element of B;
Tern (v0,v1,v2) = Ros (aa,bb,cc) by RosTrnDef
.= Ros (aa,cc,bb) by LATTICES:def 5
.= Tern (v0,v2,v1) by RosTrnDef;
hence thesis;
end;
theorem
for B being Boolean Lattice
for v0,v1 being Element of BA2TBAA B,
a,b being Element of B st a = v0 & b = v1 holds
v0 "\/" v1 = a "\/" b;
LemacikD:
for B being Boolean Lattice
for v0,v2,v1 being Element of BA2TBAA B
holds v0"/\"(v1"\/"v2) = (v0"/\"v1)"\/"(v0"/\"v2)
proof
let B be Boolean Lattice;
let v0,v2,v1 be Element of BA2TBAA B;
reconsider cc = v2, aa = v0, bb = v1 as Element of B;
v0"/\"(v1"\/"v2) = aa"/\"(bb"\/"cc)
.= (aa"/\"bb)"\/"(aa"/\"cc) by LATTICES:def 11
.= (v0"/\"v1)"\/"(v0"/\"v2);
hence thesis;
end;
LemacikE:
for B being Boolean Lattice
for v0,v2,v1 being Element of BA2TBAA B
holds v0"\/"(v1"/\"v2) = (v0"\/"v1)"/\"(v0"\/"v2)
proof
let B be Boolean Lattice;
let v0,v2,v1 be Element of BA2TBAA B;
reconsider cc = v2, aa = v0, bb = v1 as Element of B;
v0"\/"(v1"/\"v2) = aa"\/"(bb"/\"cc)
.= (aa"\/"bb)"/\"(aa"\/"cc) by LATTICES:11
.= (v0"\/"v1)"/\"(v0"\/"v2);
hence thesis;
end;
LemacikC:
for B being Boolean Lattice
for v3,v2,v1,v0 being Element of BA2TBAA B holds
Tern(Tern(v0,v1,v2),v1,v3) = Tern(v0,v1,Tern(v2,v1,v3))
proof
let B be Boolean Lattice;
let v3,v2,v1,v0 be Element of BA2TBAA B;
A1: for v2,v1,v0 being Element of BA2TBAA B
holds Tern(v0,v1,v2)=((v0"\/"v1)"/\"(v1"\/"v2))"/\"(v0"\/"v2)
proof
let v2,v1,v0 be Element of BA2TBAA B;
reconsider aa = v0, bb = v1, cc = v2 as Element of B;
Tern(v0,v1,v2) = Ros (aa,bb,cc) by RosTrnDef
.= ((aa"\/"bb)"/\"(bb"\/"cc))"/\"(cc"\/"aa)
by LATTICES:13
.= ((v0"\/"v1)"/\"(v1"\/"v2))"/\"(v2"\/"v0);
hence thesis;
end;
A3:
(for v0,v2,v1 being Element of BA2TBAA B
holds v0"\/"(v1"/\"v2) = (v0"\/"v1)"/\"(v0"\/"v2)) &
(for v0,v2,v1 being Element of BA2TBAA B
holds v0"/\"(v1"\/"v2) = (v0"/\"v1)"\/"(v0"/\"v2)) by LemacikD,LemacikE;
(for v2,v1,v0 being Element of BA2TBAA B
holds (v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2)) &
(for v2,v1,v0 being Element of BA2TBAA B
holds (v0"/\"v1)"/\"v2 = v0"/\"(v1"/\"v2)) by LATTICES:def 5,def 7;
hence thesis by A1,A3,TBA2;
end;
registration
let B be Boolean Lattice;
cluster BA2TBAA B -> ternary-distributive;
coherence
proof
set T = BA2TBAA B;
set ff = RosTrn B;
A1: (for v1,v0 being Element of T holds Tern(v0,v0,v1)=v0)
by TLIDef;
A2: (for v2,v1,v0 being Element of T holds Tern(v0,v1,v2)=Tern(v2,v0,v1))
by LemacikA;
A3: (for v2,v1,v0 being Element of T holds Tern(v0,v1,v2)=Tern(v0,v2,v1))
by LemacikB;
(for v3,v2,v1,v0 being Element of T holds
Tern(Tern(v0,v1,v2),v1,v3)=Tern(v0,v1,Tern(v2,v1,v3)))
by LemacikC;
hence thesis by TBA1,A1,A2,A3;
end;
end;
registration let T be Ternary_Boolean_Algebra;
let p be Element of T;
cluster the LattStr of TBA2BA (T,p) -> distributive;
coherence
proof
set L = the LattStr of TBA2BA (T,p);
for x,y,z being Element of L holds
x "/\" (y "\/" z) = (x "/\" y) "\/" (x "/\" z)
proof
let x,y,z be Element of L;
reconsider xx = x, yy = y, zz = z as Element of T;
R1: y "\/" z = Tern (yy,p,zz) by JoinDef;
R2: x "/\" y = Tern (xx,p`,yy) by MeetDef;
R3: x "/\" z = Tern (xx,p`,zz) by MeetDef;
reconsider xxzz = x "/\" z as Element of T;
reconsider xxyy = x "/\" y as Element of T;
reconsider yyzz = y "\/" z as Element of T;
x "/\" (y "\/" z) = Tern (xx,p`,yyzz) by MeetDef
.= Tern (Tern(xx,p`,yy),p,Tern(xx,p`,zz)) by TDis,R1
.= (the L_join of L).(xxyy,xxzz) by R2,R3,JoinDef;
hence thesis;
end;
hence thesis by LATTICES:def 11;
end;
end;
registration let T be Ternary_Boolean_Algebra;
let p be Element of T;
cluster the LattStr of TBA2BA (T,p) -> bounded;
coherence
proof
set L = the LattStr of TBA2BA (T,p);
ex c being Element of L st
for a being Element of L holds c"/\"a = c & a"/\"c = c
proof
reconsider pp = p as Element of L;
reconsider t = p` as Element of L;
take t;
reconsider tt = t as Element of T;
let a be Element of L;
reconsider aa = a as Element of T;
a "/\" t = Tern (aa,p`,tt) by MeetDef
.= tt by TRIDef;
hence thesis;
end; then
A1: L is lower-bounded by LATTICES:def 13;
ex c being Element of L st
for a being Element of L holds c"\/"a = c & a"\/"c = c
proof
reconsider pp = p as Element of L;
take t = pp;
reconsider tt = t as Element of T;
let a be Element of L;
reconsider aa = a as Element of T;
t "\/" a = Tern (tt,p,aa) by JoinDef
.= tt by TLIDef;
hence thesis;
end; then
L is upper-bounded by LATTICES:def 14;
hence thesis by A1;
end;
end;
theorem TopTBA:
for T being Ternary_Boolean_Algebra,
p being Element of T holds
Top the LattStr of TBA2BA (T,p) = p
proof
let T be Ternary_Boolean_Algebra,
p be Element of T;
set L = the LattStr of TBA2BA (T,p);
reconsider t = p as Element of L;
reconsider tt = t as Element of T;
for a being Element of L holds t "\/" a = t & a "\/" t = t
proof
let a be Element of L;
reconsider aa = a as Element of T;
a "\/" t = Tern (aa,p,tt) by JoinDef
.= tt by TRIDef;
hence thesis;
end;
hence thesis by LATTICES:def 17;
end;
theorem BotTBA:
for T being Ternary_Boolean_Algebra,
p being Element of T holds
Bottom the LattStr of TBA2BA (T,p) = p`
proof
let T be Ternary_Boolean_Algebra,
p be Element of T;
set L = the LattStr of TBA2BA (T,p);
reconsider t = p` as Element of L;
reconsider tt = t as Element of T;
for a being Element of L holds t "/\" a = t & a "/\" t = t
proof
let a be Element of L;
reconsider aa = a as Element of T;
a "/\" t = Tern (aa,p`,tt) by MeetDef
.= tt by TRIDef;
hence thesis;
end;
hence thesis by LATTICES:def 16;
end;
registration let T be Ternary_Boolean_Algebra;
let p be Element of T;
cluster the LattStr of TBA2BA (T,p) -> complemented;
coherence
proof
set L = the LattStr of TBA2BA (T,p);
for b being Element of L
ex a being Element of L st a is_a_complement_of b
proof
let b be Element of L;
reconsider bb = b as Element of T;
reconsider aa = bb` as Element of T;
reconsider a = aa as Element of L;
A1: a "/\" b = Tern (aa,p`,bb) by MeetDef
.= Tern (bb`,bb,p`) by Th36a
.= p` by TLADef
.= Bottom L by BotTBA;
a "\/" b = Tern (aa,p,bb) by JoinDef
.= Tern (bb`,bb,p) by Th36a
.= p by TLADef
.= Top L by TopTBA;
hence thesis by A1,LATTICES:def 18;
end;
hence thesis by LATTICES:def 19;
end;
end;
registration let T;
let p be Element of T;
cluster the LattStr of TBA2BA (T,p) -> Boolean;
coherence;
end;
begin :: Single Axioms for TBA
reserve T for non empty TBAStruct;
reserve v0,v1,v2,v3,v4,v5,v6,u,w,v,v100,v101,v102,v103,v104 for Element of T;
definition let T be non empty TBAStruct;
attr T is satisfying_TBA1 means
for x,y,z,u,v,v6,w being Element of T holds
Tern(Tern(x, x`, y), (Tern(Tern(z, u, v), w, Tern(z, u, v6)))`,
Tern(u, Tern(v6, w, v), z)) = y;
end;
theorem TBALemma: :: TBA-1
(for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,v4)) = Tern(v0,v1,Tern(v2,v3,v4))) &
(for v1,v0 holds Tern(v0,v1,v1) = v1) &
(for v1,v0 holds Tern(v0,v1,v1`) = v0) &
(for v1,v0 holds Tern(v0,v0,v1) = v0) implies
for x,y,z,u,v,v6,w being Element of T holds
Tern(Tern(x, x`, y), (Tern(Tern(z, u, v), w, Tern(z, u, v6)))`,
Tern(u, Tern(v6, w, v), z)) = y
proof
assume A2: for v4,v3,v2,v1,v0 holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,v4)) = Tern(v0,v1,Tern(v2,v3,v4));
assume A3: for v1,v0 holds Tern(v0,v1,v1) = v1;
assume A4: for v1,v0 holds Tern(v0,v1,v1`) = v0;
assume A5: for v1,v0 holds Tern(v0,v0,v1) = v0;
A11: for v103,v104,v102,v100 holds
Tern(v102,v103,Tern(v100,v102,v104)) = Tern(v100,v102,Tern(v102,v103,v104))
proof let v103,v104,v102,v100;
Tern(v100,v102,v102) = v102 by A3;
hence thesis by A2;
end;
A15: for v103,v102,v104,v100 holds
Tern(Tern(v100,v104,v102),v103,v104) = Tern(v100,v104,Tern(v102,v103,v104))
proof let v103,v102,v104,v100;
Tern(v100,v104,v104) = v104 by A3;
hence thesis by A2;
end;
A19: for v103,v104,v101,v100 holds
Tern(v100,v103,Tern(v100,v101,v104)) = Tern(v100,v101,Tern(v101`,v103,v104))
proof let v103,v104,v101,v100;
Tern(v100,v101,v101`) = v100 by A4;
hence thesis by A2;
end;
A25: for v103,v100,v102 holds
Tern(v100,v103,Tern(v102,v100,v103)) = Tern(v102,v100,v103)
proof let v103,v100,v102;
Tern(v100,v103,v103) = v103 by A3;
hence thesis by A11;
end;
A29: for v102,v101,v100 holds
Tern(v100,v101,v102) = Tern(v102,v100,Tern(v100,v101,v100`))
proof let v102,v101,v100;
Tern(v102,v100,v100`) = v102 by A4;
hence thesis by A11;
end;
A35: for v102,v100 holds Tern(v100,v100`,v102) = Tern(v102,v100,v100`)
proof let v102,v100;
Tern(v102,v100,v100`) = v102 by A4;
hence thesis by A25;
end;
A38: for v1,v0 holds Tern(v0,v0`,v1) = v1
proof let v1,v0;
Tern(v1,v0,v0`) = v1 by A4;
hence thesis by A35;
end;
A43: for v101,v103,v100 holds
Tern(v100,v103,v101) = Tern(v100,v101,Tern(v101`,v103,v101))
proof let v101,v103,v100;
Tern(v100,v101,v101`) = v100 by A4;
hence thesis by A15;
end;
A49: for v101,v100 holds
Tern(v100,v100,Tern(v100,v101,v101)) = Tern(v101`,v100,v101)
proof let v101,v100;
Tern(v100,v101,Tern(v101`,v100,v101)) =
Tern(v100,v100,Tern(v100,v101,v101))
by A19;
hence thesis by A25;
end;
A52: for v1,v0 holds Tern(v0,v0,v1) = Tern(v1`,v0,v1)
proof let v1,v0;
Tern(v0,v1,v1) = v1 by A3;
hence thesis by A49;
end;
A54: for v0,v1 holds v0 = Tern(v1`,v0,v1)
proof let v0,v1;
Tern(v0,v0,v1) = v0 by A5;
hence thesis by A52;
end;
A58: for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v0,v2,v1)
proof let v2,v1,v0;
Tern(v1`,v2,v1) = v2 by A54;
hence thesis by A43;
end;
A64: for v1,v0 holds Tern(v0,v1,v0`) = v1
proof let v1,v0;
Tern(v0,v0`,v1) = Tern(v0,v1,v0`) by A58;
hence thesis by A38;
end;
A66: for v2,v1,v0 holds Tern(v0,v1,v2) = Tern(v1,v2,v0)
proof let v2,v1,v0;
Tern(v1,v2,v1`) = v2 by A64;
hence thesis by A29;
end;
let x,y,z,u,v,v6,w be Element of T;
Tern(v,w,v6) = Tern(w,v6,v) by A66
.= Tern(w,v,v6) by A58
.= Tern(v6,w,v) by A66; then
VV: Tern(z, u, Tern(v6, w, v)) = Tern(Tern(z, u, v), w, Tern(z, u, v6)) by A2;
Tern(Tern(x, x`, y), (Tern(Tern(z, u, v), w, Tern(z, u, v6)))`,
Tern(u, Tern(v6, w, v), z))
= Tern(y, (Tern(Tern(z, u, v), w, Tern(z, u, v6)))`,
Tern(u, Tern(v6, w, v), z)) by A38
.= Tern(y, (
Tern(Tern(z, u, v), w, Tern(z, u, v6)))`, Tern(z, u, Tern(v6, w, v)))
by A66
.= Tern(y, Tern(z, u, Tern(v6, w, v)),
(Tern(Tern(z, u, v), w, Tern(z, u, v6)))`) by A58
.= Tern(Tern(z, u, Tern(v6, w, v)),
(Tern(Tern(z, u, v), w, Tern(z, u, v6))`), y) by A66
.= y by A38,VV;
hence thesis;
end;
definition let T be non empty TBAStruct;
attr T is TBA-like means
T is ternary-distributive ternary-left-idempotent
ternary-right-idempotent ternary-left-absorbing ternary-right-absorbing;
end;
registration
cluster ternary-distributive ternary-left-idempotent
ternary-right-idempotent ternary-left-absorbing
ternary-right-absorbing -> TBA-like for non empty TBAStruct;
coherence;
cluster TBA-like -> ternary-distributive ternary-left-idempotent
ternary-right-idempotent ternary-left-absorbing
ternary-right-absorbing for non empty TBAStruct;
coherence;
end;
registration
cluster TBA-like -> satisfying_TBA1 for non empty TBAStruct;
coherence
proof
let T be non empty TBAStruct;
assume T is TBA-like; then
T is ternary-distributive ternary-left-idempotent
ternary-right-idempotent ternary-left-absorbing
ternary-right-absorbing; then
(for v4,v3,v2,v1,v0 being Element of T holds
Tern(Tern(v0,v1,v2),v3,Tern(v0,v1,v4)) = Tern(v0,v1,Tern(v2,v3,v4))) &
(for v1,v0 being Element of T holds Tern(v0,v1,v1) = v1) &
(for v1,v0 being Element of T holds Tern(v0,v1,v1`) = v0) &
(for v1,v0 being Element of T holds Tern(v0,v0,v1) = v0);
hence thesis by TBALemma;
end;
end;