:: On Weakly Associative Lattices and Near Lattices
:: by Damian Sawicki and Adam Grabowski
::
:: Received June 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 EQREL_1, LATTICES, PBOOLE, CARD_1, FUNCT_1, XXREAL_0, ZFMISC_1,
SHEFFER1, LATWAL_1, ROBBINS3, XBOOLE_0, SUBSET_1, ROBBINS1, BINOP_1;
notations ENUMSET1, XXREAL_0, SUBSET_1, ORDINAL1, STRUCT_0, BINOP_1, LATTICES,
ROBBINS1, SHEFFER1, ROBBINS3;
constructors BINOP_1, ENUMSET1, XREAL_0, SHEFFER1, ROBBINS3;
registrations RELSET_1, LATTICES, XREAL_0, SUBSET_1, LATTAD_1, LATQUASI;
requirements SUBSET, NUMERALS, BOOLE, REAL;
definitions LATTICES;
equalities LATTICES;
expansions ROBBINS1, SHEFFER1;
theorems LATTICES, XXREAL_0, ENUMSET1, BINOP_1, STRUCT_0, ROBBINS3;
schemes BINOP_1;
begin :: Preliminaries
reserve L for non empty LattStr;
reserve v100,v102,v2,v1,v0,v3,v101 for Element of L;
:: WAL + v0"/\"(v1"\/"(v0"\/"v2)) = v0 => LT
:: WAL-1
theorem
(for v0 holds v0"/\"v0 = v0) &
(for v1,v0 holds v0"/\"v1 = v1"/\"v0) &
(for v0 holds v0"\/"v0 = v0) &
(for v1,v0 holds v0"\/"v1 = v1"\/"v0) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1) &
(for v1,v2,v0 holds v0"/\"(v1"\/"(v0"\/"v2)) = v0) implies
for v0,v1,v2 holds (v0"/\"v1)"/\"v2 = v0"/\"(v1"/\"v2)
proof
assume
A2: for v0 holds v0"/\"v0 = v0;
assume
A3: for v1,v0 holds v0"/\"v1 = v1"/\"v0;
assume
A4: for v0 holds v0"\/"v0 = v0;
assume
A5: for v1,v0 holds v0"\/"v1 = v1"\/"v0;
assume
A6: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1;
A8: for v2,v1,v0 holds v1"/\"((v0"\/"v1)"/\"(v2"\/"v1)) = v1
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 =
v1"/\"((v0"\/"v1)"/\"(v2"\/"v1)) by A3;
hence thesis by A6;
end;
assume
A10:for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1;
A12:for v2,v1,v0 holds v1"\/"((v0"/\"v1)"\/"(v2"/\"v1)) = v1
proof let v2,v1,v0;
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 =
v1"\/"((v0"/\"v1)"\/"(v2"/\"v1)) by A5;
hence thesis by A10;
end;
assume
A14:for v1,v2,v0 holds v0"/\"(v1"\/"(v0"\/"v2)) = v0;
A20:for v100,v102 holds v100"/\"(v102"\/"v100) = v100
proof let v100,v102;
(v102"\/"v100)"/\"(v102"\/"v100) = v102"\/"v100 by A2;
hence thesis by A8;
end;
A23:for v2,v1,v0 holds v0"\/"((v0"/\"v1)"\/"(v2"/\"v0)) = v0
proof let v2,v1,v0;
v1"/\"v0 = v0"/\"v1 by A3;
hence thesis by A12;
end;
A25:for v2,v0,v1 holds v0"\/"((v1"/\"v0)"\/"(v0"/\"v2)) = v0
proof let v2,v0,v1;
v2"/\"v0 = v0"/\"v2 by A3;
hence thesis by A12;
end;
A28:for v100,v102 holds v100"\/"(v102"/\"v100) = v100
proof let v100,v102;
(v102"/\"v100)"\/"(v102"/\"v100) = v102"/\"v100 by A4;
hence thesis by A12;
end;
A32:for v102,v2,v101,v1 holds
((v1"/\"v101)"\/"(v2"/\"v101))"/\"(v101"/\"
(v102"\/"((v1"/\"v101)"\/"(v2"/\"v101)))) =
(v1"/\"v101)"\/"(v2"/\"v101)
proof let v102,v2,v101,v1;
v101"\/"((v1"/\"v101)"\/"(v2"/\"v101)) = v101 by A12;
hence thesis by A8;
end;
A35:for v1,v0,v2 holds v0"/\"(v1"\/"(v2"\/"v0)) = v0
proof let v1,v0,v2;
v0"\/"v2 = v2"\/"v0 by A5;
hence thesis by A14;
end;
A38:for v102,v101,v1 holds
(v1"\/"v101)"\/"(v101"\/"(v102"/\"(v1"\/"v101))) = v1"\/"v101
proof let v102,v101,v1;
v101"/\"(v1"\/"v101) = v101 by A20;
hence thesis by A12;
end;
A41:for v1,v0 holds v0"\/"(v0"/\"v1) = v0
proof let v1,v0;
v1"/\"v0 = v0"/\"v1 by A3;
hence thesis by A28;
end;
A44:for v102,v1,v101 holds
(v101"/\"v1)"/\"(v101"/\"(v102"\/"(v101"/\"v1))) = v101"/\"v1
proof let v102,v1,v101;
v101"\/"(v101"/\"v1) = v101 by A41;
hence thesis by A8;
end;
A47:for v1,v0,v2 holds v0"/\"((v2"\/"v0)"\/"v1) = v0
proof let v1,v0,v2;
v1"\/"(v2"\/"v0) = (v2"\/"v0)"\/"v1 by A5;
hence thesis by A35;
end;
A51:for v101,v102,v1 holds (v1"/\"v102)"/\"(v101"\/"v102) = v1"/\"v102
proof let v101,v102,v1;
v102"\/"(v1"/\"v102) = v102 by A28;
hence thesis by A35;
end;
A55:for v102,v101,v1 holds (v1"/\"v101)"/\"(v101"\/"v102) = v1"/\"v101
proof let v102,v101,v1;
v101"\/"(v1"/\"v101) = v101 by A28;
hence thesis by A47;
end;
A58:for v2,v1,v0 holds v0"\/"((v0"/\"v1)"\/"(v0"/\"v2)) = v0
proof let v2,v1,v0;
v2"/\"v0 = v0"/\"v2 by A3;
hence thesis by A23;
end;
A61:for v102,v2,v101,v1 holds
((v1"/\"v101)"\/"(v101"/\"v2))"/\"(v101"/\"(v102"\/"
((v1"/\"v101)"\/"(v101"/\"v2)))) = (v1"/\"v101)"\/"(v101"/\"v2)
proof let v102,v2,v101,v1;
v101"\/"((v1"/\"v101)"\/"(v101"/\"v2)) = v101 by A25;
hence thesis by A8;
end;
A65:for v0,v1,v2 holds (v2"\/"v1)"\/"(v0"/\"v1) = v2"\/"v1
proof let v0,v1,v2;
(v0"/\"v1)"/\"(v2"\/"v1) = v0"/\"v1 by A51;
hence thesis by A28;
end;
A69:for v100,v1,v102 holds
(v100"/\"(v102"/\"v1))"/\"v102 = v100"/\"(v102"/\"v1)
proof let v100,v1,v102;
v102"\/"(v102"/\"v1) = v102 by A41;
hence thesis by A51;
end;
A72:for v0,v2,v1 holds v1"/\"(v0"/\"(v1"/\"v2)) = v0"/\"(v1"/\"v2)
proof let v0,v2,v1;
(v0"/\"(v1"/\"v2))"/\"v1 = v1"/\"(v0"/\"(v1"/\"v2)) by A3;
hence thesis by A69;
end;
A76: for v101,v102 holds
((v102"/\"v101)"\/"(v102"/\"v101))"/\"(v101"/\"v102) =
(v102"/\"v101)"\/"(v102"/\"v101)
proof let v101,v102;
v102"\/"((v102"/\"v101)"\/"(v102"/\"v101)) = v102 by A58;
hence thesis by A32;
end;
A79: for v1,v0 holds (v0"/\"v1)"/\"(v1"/\"v0) = (v0"/\"v1)"\/"(v0"/\"v1)
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"v1) = v0"/\"v1 by A4;
hence thesis by A76;
end;
A81: for v1,v0 holds (v0"/\"v1)"/\"(v1"/\"v0) = v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"v1) = v0"/\"v1 by A4;
hence thesis by A79;
end;
A84: for v102,v100,v1 holds
v100"\/"(v102"/\"(v1"/\"v100)) = v100"\/"(v1"/\"v100)
proof let v102,v100,v1;
v100"\/"(v1"/\"v100) = v100 by A28;
hence thesis by A65;
end;
A87: for v1,v0,v2 holds v0"\/"(v1"/\"(v2"/\"v0)) = v0
proof let v1,v0,v2;
v0"\/"(v2"/\"v0) = v0 by A28;
hence thesis by A84;
end;
A90: for v102,v1,v100 holds
v100"\/"(v102"/\"(v100"/\"v1)) = v100"\/"(v100"/\"v1)
proof let v102,v1,v100;
v100"\/"(v100"/\"v1) = v100 by A41;
hence thesis by A65;
end;
A93: for v1,v2,v0 holds v0"\/"(v1"/\"(v0"/\"v2)) = v0
proof let v1,v2,v0;
v0"\/"(v0"/\"v2) = v0 by A41;
hence thesis by A90;
end;
A95: for v1,v0,v2 holds v0"\/"((v2"/\"v0)"/\"v1) = v0
proof let v1,v0,v2;
v1"/\"(v2"/\"v0) = (v2"/\"v0)"/\"v1 by A3;
hence thesis by A87;
end;
A99: for v102,v2,v100,v1 holds
v100"\/"(((v1"/\"v100)"/\"v2)"\/"
(v102"/\"(v100"\/"((v1"/\"v100)"/\"v2)))) =
v100"\/"((v1"/\"v100)"/\"v2)
proof let v102,v2,v100,v1;
v100"\/"((v1"/\"v100)"/\"v2) = v100 by A95;
hence thesis by A38;
end;
A102: for v3,v2,v0,v1 holds
v0"\/"(((v1"/\"v0)"/\"v2)"\/"(v3"/\"v0)) = v0"\/"((v1"/\"v0)"/\"v2)
proof let v3,v2,v0,v1;
v0"\/"((v1"/\"v0)"/\"v2) = v0 by A95;
hence thesis by A99;
end;
A104: for v3,v2,v0,v1 holds v0"\/"(((v1"/\"v0)"/\"v2)"\/"(v3"/\"v0)) = v0
proof let v3,v2,v0,v1;
v0"\/"((v1"/\"v0)"/\"v2) = v0 by A95;
hence thesis by A102;
end;
A107: for v102,v0,v1 holds
(v0"/\"v1)"/\"((v1"/\"v0)"\/"v102) = (v0"/\"v1)"/\"(v1"/\"v0)
proof let v102,v0,v1;
(v0"/\"v1)"/\"(v1"/\"v0) = v0"/\"v1 by A81;
hence thesis by A55;
end;
A110: for v2,v0,v1 holds (v0"/\"v1)"/\"((v1"/\"v0)"\/"v2) = v0"/\"v1
proof let v2,v0,v1;
(v0"/\"v1)"/\"(v1"/\"v0) = v0"/\"v1 by A81;
hence thesis by A107;
end;
A113: for v100,v101,v0 holds
(v100"/\"v101)"/\"(v100"/\"(v0"\/"v101)) = v100"/\"v101
proof let v100,v101,v0;
(v0"\/"v101)"\/"(v100"/\"v101) = v0"\/"v101 by A65;
hence thesis by A44;
end;
A117: for v100,v2,v102 holds
(v100"/\"(v102"/\"v2))"/\"(v100"/\"v102) = v100"/\"(v102"/\"v2)
proof let v100,v2,v102;
v102"\/"(v100"/\"(v102"/\"v2)) = v102 by A93;
hence thesis by A44;
end;
A120: for v0,v2,v1 holds (v0"/\"v1)"/\"(v0"/\"(v1"/\"v2)) = v0"/\"(v1"/\"v2)
proof let v0,v2,v1;
(v0"/\"(v1"/\"v2))"/\"(v0"/\"v1) = (v0"/\"v1)"/\"(v0"/\"(v1"/\"v2)) by A3;
hence thesis by A117;
end;
A123: for v101,v1,v2,v100 holds
v100"\/"((v100"/\"v101)"\/"(v1"/\"(v100"/\"v2))) = v100
proof let v101,v1,v2,v100;
v100"/\"(v1"/\"(v100"/\"v2)) = v1"/\"(v100"/\"v2) by A72;
hence thesis by A58;
end;
A127: for v101,v102,v1 holds
(((v1"/\"v102)"/\"v101)"\/"(v101"/\"v102))"/\"(v101"/\"v102) =
((v1"/\"v102)"/\"v101)"\/"(v101"/\"v102)
proof let v101,v102,v1;
v102"\/"(((v1"/\"v102)"/\"v101)"\/"(v101"/\"v102)) = v102 by A104;
hence thesis by A61;
end;
A130: for v2,v1,v0 holds
(v2"/\"v1)"/\"(((v0"/\"v1)"/\"v2)"\/"(v2"/\"v1)) =
((v0"/\"v1)"/\"v2)"\/"(v2"/\"v1)
proof let v2,v1,v0;
(((v0"/\"v1)"/\"v2)"\/"(v2"/\"v1))"/\"(v2"/\"v1) =
(v2"/\"v1)"/\"(((v0"/\"v1)"/\"v2)"\/"(v2"/\"v1)) by A3;
hence thesis by A127;
end;
A133: for v0,v1,v2 holds v0"/\"v1 = ((v2"/\"v1)"/\"v0)"\/"(v0"/\"v1)
proof let v0,v1,v2;
(v0"/\"v1)"/\"(((v2"/\"v1)"/\"v0)"\/"(v0"/\"v1)) = v0"/\"v1 by A20;
hence thesis by A130;
end;
A138: for v101,v3,v100 holds
((v100"/\"v101)"\/"(v101"/\"(v100"/\"v3)))"/\"(v101"/\"v100) =
(v100"/\"v101)"\/"(v101"/\"(v100"/\"v3))
proof let v101,v3,v100;
v100"\/"((v100"/\"v101)"\/"(v101"/\"(v100"/\"v3))) = v100 by A123;
hence thesis by A61;
end;
A141: for v1,v2,v0 holds
(v1"/\"v0)"/\"((v0"/\"v1)"\/"(v1"/\"(v0"/\"v2))) =
(v0"/\"v1)"\/"(v1"/\"(v0"/\"v2))
proof let v1,v2,v0;
((v0"/\"v1)"\/"(v1"/\"(v0"/\"v2)))"/\"(v1"/\"v0) =
(v1"/\"v0)"/\"((v0"/\"v1)"\/"(v1"/\"(v0"/\"v2))) by A3;
hence thesis by A138;
end;
A144: for v0,v2,v1 holds v0"/\"v1 = (v1"/\"v0)"\/"(v0"/\"(v1"/\"v2))
proof let v0,v2,v1;
(v0"/\"v1)"/\"((v1"/\"v0)"\/"(v0"/\"(v1"/\"v2))) = v0"/\"v1 by A110;
hence thesis by A141;
end;
A149: for v100,v101,v2 holds
(v100"/\"v101)"\/"((v100"/\"(v2"\/"v101))"/\"v101) =
(v100"/\"(v2"\/"v101))"/\"v101
proof let v100,v101,v2;
(v100"/\"v101)"/\"(v100"/\"(v2"\/"v101)) = v100"/\"v101 by A113;
hence thesis by A133;
end;
A152: for v0,v1,v2 holds
(v0"/\"v1)"\/"(v1"/\"(v0"/\"(v2"\/"v1))) = (v0"/\"(v2"\/"v1))"/\"v1
proof let v0,v1,v2;
(v0"/\"(v2"\/"v1))"/\"v1 = v1"/\"(v0"/\"(v2"\/"v1)) by A3;
hence thesis by A149;
end;
A154: for v0,v1,v2 holds v1"/\"v0 = (v0"/\"(v2"\/"v1))"/\"v1
proof let v0,v1,v2;
(v0"/\"v1)"\/"(v1"/\"(v0"/\"(v2"\/"v1))) = v1"/\"v0 by A144;
hence thesis by A152;
end;
A157: for v1,v0,v2 holds v0"/\"v1 = v0"/\"(v1"/\"(v2"\/"v0))
proof let v1,v0,v2;
(v1"/\"(v2"\/"v0))"/\"v0 = v0"/\"(v1"/\"(v2"\/"v0)) by A3;
hence thesis by A154;
end;
A160: for v1,v0,v2 holds v0"/\"((v2"\/"v0)"/\"v1) = v0"/\"v1
proof let v1,v0,v2;
v1"/\"(v2"\/"v0) = (v2"\/"v0)"/\"v1 by A3;
hence thesis by A157;
end;
A164: for v102,v101,v1 holds
(v1"/\"v101)"/\"(v101"/\"v102) = (v1"/\"v101)"/\"v102
proof let v102,v101,v1;
v101"\/"(v1"/\"v101) = v101 by A28;
hence thesis by A160;
end;
A168: for v102,v1,v101 holds
(v101"/\"v1)"/\"(v101"/\"v102) = (v101"/\"v1)"/\"v102
proof let v102,v1,v101;
v101"\/"(v101"/\"v1) = v101 by A41;
hence thesis by A160;
end;
A171: for v2,v1,v0 holds (v0"/\"v1)"/\"(v1"/\"v2) = v0"/\"(v1"/\"v2)
proof let v2,v1,v0;
(v0"/\"v1)"/\"(v0"/\"(v1"/\"v2)) = (v0"/\"v1)"/\"(v1"/\"v2) by A168;
hence thesis by A120;
end;
A173: for v2,v1,v0 holds (v0"/\"v1)"/\"v2 = v0"/\"(v1"/\"v2)
proof let v2,v1,v0;
(v0"/\"v1)"/\"(v1"/\"v2) = (v0"/\"v1)"/\"v2 by A164;
hence thesis by A171;
end;
A175: for v1,v2,v0 holds v0"/\"(v1"/\"(v0"/\"v2)) = (v0"/\"v1)"/\"v2
proof let v1,v2,v0;
(v0"/\"v1)"/\"(v0"/\"v2) = v0"/\"(v1"/\"(v0"/\"v2)) by A173;
hence thesis by A168;
end;
A177: for v1,v2,v0 holds v1"/\"(v0"/\"v2) = (v0"/\"v1)"/\"v2
proof let v1,v2,v0;
v0"/\"(v1"/\"(v0"/\"v2)) = v1"/\"(v0"/\"v2) by A72;
hence thesis by A175;
end;
A180: for v0,v2,v1 holds v0"/\"(v1"/\"v2) = v1"/\"(v0"/\"v2)
proof let v0,v2,v1;
(v1"/\"v0)"/\"v2 = v1"/\"(v0"/\"v2) by A173;
hence thesis by A177;
end;
let v0,v2,v1;
v1"/\"(v0"/\"v2) = v0"/\"(v1"/\"v2) by A180; then
v1"/\"(v0"/\"v2) = v0"/\"(v2"/\"v1) by A3;
hence thesis by A3;
end;
:: Associativity
theorem
(for v0 holds v0"/\"v0 = v0) &
(for v1,v0 holds v0"/\"v1 = v1"/\"v0) &
(for v0 holds v0"\/"v0 = v0) &
(for v1,v0 holds v0"\/"v1 = v1"\/"v0) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1) &
(for v1,v2,v0 holds v0"/\"(v1"\/"(v0"\/"v2)) = v0) implies
for v0,v1,v2 holds (v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2)
proof
assume A2: for v0 holds v0"/\"v0 = v0;
assume A3: for v1,v0 holds v0"/\"v1 = v1"/\"v0;
assume A4: for v0 holds v0"\/"v0 = v0;
assume A5: for v1,v0 holds v0"\/"v1 = v1"\/"v0;
assume A6: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1;
A8: for v2,v1,v0 holds v1"/\"((v0"\/"v1)"/\"(v2"\/"v1)) = v1
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 =
v1"/\"((v0"\/"v1)"/\"(v2"\/"v1)) by A3;
hence thesis by A6;
end;
assume A10: for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1;
A12: for v2,v1,v0 holds v1"\/"((v0"/\"v1)"\/"(v2"/\"v1)) = v1
proof let v2,v1,v0;
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1"\/"((v0"/\"v1)"\/"(v2"/\"v1)) by A5;
hence thesis by A10;
end;
assume A14: for v1,v2,v0 holds v0"/\"(v1"\/"(v0"\/"v2)) = v0;
A20: for v100,v102 holds v100"/\"(v102"\/"v100) = v100
proof let v100,v102;
(v102"\/"v100)"/\"(v102"\/"v100) = v102"\/"v100 by A2;
hence thesis by A8;
end;
A23: for v2,v0,v1 holds v0"/\"((v1"\/"v0)"/\"(v0"\/"v2)) = v0
proof let v2,v0,v1;
v2"\/"v0 = v0"\/"v2 by A5;
hence thesis by A8;
end;
A25: for v2,v1,v0 holds v0"\/"((v0"/\"v1)"\/"(v2"/\"v0)) = v0
proof let v2,v1,v0;
v1"/\"v0 = v0"/\"v1 by A3;
hence thesis by A12;
end;
A28: for v100,v102 holds v100"\/"(v102"/\"v100) = v100
proof let v100,v102;
(v102"/\"v100)"\/"(v102"/\"v100) = v102"/\"v100 by A4;
hence thesis by A12;
end;
A32: for v102,v100 holds v100"/\"(v100"\/"v102) = v100
proof let v102,v100;
(v100"\/"v102)"\/"(v100"\/"v102) = v100"\/"v102 by A4;
hence thesis by A14;
end;
A35: for v1,v0,v2 holds v0"/\"(v1"\/"(v2"\/"v0)) = v0
proof let v1,v0,v2;
v0"\/"v2 = v2"\/"v0 by A5;
hence thesis by A14;
end;
A37: for v1,v2,v0 holds v0"/\"((v0"\/"v2)"\/"v1) = v0
proof let v1,v2,v0;
v1"\/"(v0"\/"v2) = (v0"\/"v2)"\/"v1 by A5;
hence thesis by A14;
end;
A41: for v102,v101,v1 holds
(v1"\/"v101)"\/"(v101"\/"(v102"/\"(v1"\/"v101))) = v1"\/"v101
proof let v102,v101,v1;
v101"/\"(v1"\/"v101) = v101 by A20;
hence thesis by A12;
end;
A45: for v102,v101,v1 holds
(v1"/\"v101)"/\"(v101"/\"(v102"\/"(v1"/\"v101))) = v1"/\"v101
proof let v102,v101,v1;
v101"\/"(v1"/\"v101) = v101 by A28;
hence thesis by A8;
end;
A49: for v1,v2,v101 holds
(v1"\/"(v101"\/"v2))"\/"v101 = v1"\/"(v101"\/"v2)
proof let v1,v2,v101;
v101"/\"(v1"\/"(v101"\/"v2)) = v101 by A14;
hence thesis by A28;
end;
A52: for v0,v2,v1 holds v1"\/"(v0"\/"(v1"\/"v2)) = v0"\/"(v1"\/"v2)
proof let v0,v2,v1;
(v0"\/"(v1"\/"v2))"\/"v1 = v1"\/"(v0"\/"(v1"\/"v2)) by A5;
hence thesis by A49;
end;
A56: for v102,v1,v101 holds
(v101"\/"v1)"\/"(v101"\/"(v102"/\"(v101"\/"v1))) = v101"\/"v1
proof let v102,v1,v101;
v101"/\"(v101"\/"v1) = v101 by A32;
hence thesis by A12;
end;
A60: for v1,v101 holds (v101"\/"v1)"\/"v101 = v101"\/"v1
proof let v1,v101;
v101"/\"(v101"\/"v1) = v101 by A32;
hence thesis by A28;
end;
A63: for v1,v0 holds v0"\/"(v0"\/"v1) = v0"\/"v1
proof let v1,v0;
(v0"\/"v1)"\/"v0 = v0"\/"(v0"\/"v1) by A5;
hence thesis by A60;
end;
A65: for v1,v0,v2 holds v0"/\"((v2"\/"v0)"\/"v1) = v0
proof let v1,v0,v2;
v1"\/"(v2"\/"v0) = (v2"\/"v0)"\/"v1 by A5;
hence thesis by A35;
end;
A69: for v102,v2,v101,v1 holds
((v1"\/"v101)"/\"(v101"\/"v2))"\/"(v101"\/"
(v102"/\"((v1"\/"v101)"/\"(v101"\/"v2)))) =
(v1"\/"v101)"/\"(v101"\/"v2)
proof let v102,v2,v101,v1;
v101"/\"((v1"\/"v101)"/\"(v101"\/"v2)) = v101 by A23;
hence thesis by A12;
end;
A73: for v102,v101,v1 holds (v1"/\"v101)"/\"(v101"\/"v102) = v1"/\"v101
proof let v102,v101,v1;
v101"\/"(v1"/\"v101) = v101 by A28;
hence thesis by A65;
end;
A77: for v101,v1,v2,v102 holds
(v1"\/"(v102"\/"v2))"\/"(((v1"\/"(v102"\/"v2))"/\"v101)"\/"v102) =
v1"\/"(v102"\/"v2)
proof let v101,v1,v2,v102;
v102"/\"(v1"\/"(v102"\/"v2)) = v102 by A14;
hence thesis by A25;
end;
A80: for v3,v0,v2,v1 holds
(v0"\/"(v1"\/"v2))"\/"(v1"\/"((v0"\/"(v1"\/"v2))"/\"v3)) = v0"\/"(v1"\/"v2)
proof let v3,v0,v2,v1;
((v0"\/"(v1"\/"v2))"/\"v3)"\/"v1 = v1"\/"((v0"\/"(v1"\/"v2))"/\"v3) by A5;
hence thesis by A77;
end;
A83: for v101,v2,v1,v102 holds
((v102"\/"v1)"\/"v2)"\/"((((v102"\/"v1)"\/"v2)"/\"v101)"\/"v102) =
(v102"\/"v1)"\/"v2
proof let v101,v2,v1,v102;
v102"/\"((v102"\/"v1)"\/"v2) = v102 by A37;
hence thesis by A25;
end;
A86: for v3,v2,v1,v0 holds
((v0"\/"v1)"\/"v2)"\/"(v0"\/"(((v0"\/"v1)"\/"v2)"/\"v3)) = (v0"\/"v1)"\/"v2
proof let v3,v2,v1,v0;
(((v0"\/"v1)"\/"v2)"/\"v3)"\/"v0 = v0"\/"(((v0"\/"v1)"\/"v2)"/\"v3) by A5;
hence thesis by A83;
end;
A89: for v101,v100,v0 holds
(v100"\/"v101)"\/"(v101"\/"(v0"/\"v100)) = v100"\/"v101
proof let v101,v100,v0;
(v0"/\"v100)"/\"(v100"\/"v101) = v0"/\"v100 by A73;
hence thesis by A41;
end;
A93: for v102,v2,v1,v100 holds
v100"/\"(((v100"\/"v1)"\/"v2)"/\"
(v102"\/"(v100"/\"((v100"\/"v1)"\/"v2)))) =
v100"/\"((v100"\/"v1)"\/"v2)
proof let v102,v2,v1,v100;
v100"/\"((v100"\/"v1)"\/"v2) = v100 by A37;
hence thesis by A45;
end;
A96: for v3,v2,v1,v0 holds
v0"/\"(((v0"\/"v1)"\/"v2)"/\"(v3"\/"v0)) = v0"/\"((v0"\/"v1)"\/"v2)
proof let v3,v2,v1,v0;
v0"/\"((v0"\/"v1)"\/"v2) = v0 by A37;
hence thesis by A93;
end;
A98: for v3,v2,v1,v0 holds v0"/\"(((v0"\/"v1)"\/"v2)"/\"(v3"\/"v0)) = v0
proof let v3,v2,v1,v0;
v0"/\"((v0"\/"v1)"\/"v2) = v0 by A37;
hence thesis by A96;
end;
A101: for v100,v2,v102 holds
(v100"\/"(v102"\/"v2))"\/"(v100"\/"v102) = v100"\/"(v102"\/"v2)
proof let v100,v2,v102;
v102"/\"(v100"\/"(v102"\/"v2)) = v102 by A14;
hence thesis by A56;
end;
A104: for v0,v2,v1 holds
(v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)) = v0"\/"(v1"\/"v2)
proof let v0,v2,v1;
(v0"\/"(v1"\/"v2))"\/"(v0"\/"v1) = (v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)) by A5;
hence thesis by A101;
end;
A106: for v3,v0,v2,v1 holds
(v0"\/"(v2"\/"v1))"\/"(v1"\/"((v0"\/"(v1"\/"v2))"/\"v3)) = v0"\/"(v1"\/"v2)
proof let v3,v0,v2,v1;
v1"\/"v2 = v2"\/"v1 by A5;
hence thesis by A80;
end;
A110: for v101,v1,v102 holds
(((v102"\/"v1)"\/"v101)"/\"(v101"\/"v102))"\/"(v101"\/"v102) =
((v102"\/"v1)"\/"v101)"/\"(v101"\/"v102)
proof let v101,v1,v102;
v102"/\"(((v102"\/"v1)"\/"v101)"/\"(v101"\/"v102)) = v102 by A98;
hence thesis by A69;
end;
A113: for v2,v1,v0 holds
(v2"\/"v0)"\/"(((v0"\/"v1)"\/"v2)"/\"(v2"\/"v0)) =
((v0"\/"v1)"\/"v2)"/\"(v2"\/"v0)
proof let v2,v1,v0;
(((v0"\/"v1)"\/"v2)"/\"(v2"\/"v0))"\/"(v2"\/"v0) =
(v2"\/"v0)"\/"(((v0"\/"v1)"\/"v2)"/\"(v2"\/"v0)) by A5;
hence thesis by A110;
end;
A116: for v0,v2,v1 holds v0"\/"v1 = ((v1"\/"v2)"\/"v0)"/\"(v0"\/"v1)
proof let v0,v2,v1;
(v0"\/"v1)"\/"(((v1"\/"v2)"\/"v0)"/\"(v0"\/"v1)) = v0"\/"v1 by A28;
hence thesis by A113;
end;
A120: for v3,v2,v0,v1 holds
((v0"\/"v1)"\/"v2)"\/"(v0"\/"(((v1"\/"v0)"\/"v2)"/\"v3)) =
(v0"\/"v1)"\/"v2
proof let v3,v2,v0,v1;
v0"\/"v1 = v1"\/"v0 by A5;
hence thesis by A86;
end;
A122: for v2,v1,v0 holds (v2"\/"(v0"\/"v1))"/\"(v2"\/"v0) = v2"\/"v0
proof let v2,v1,v0;
(v0"\/"v1)"\/"v2 = v2"\/"(v0"\/"v1) by A5;
hence thesis by A116;
end;
A125: for v0,v2,v1 holds (v0"\/"v1)"/\"(v0"\/"(v1"\/"v2)) = v0"\/"v1
proof let v0,v2,v1;
(v0"\/"(v1"\/"v2))"/\"(v0"\/"v1) = (v0"\/"v1)"/\"(v0"\/"(v1"\/"v2)) by A3;
hence thesis by A122;
end;
A128: for v101,v100,v2 holds
(v100"\/"v101)"/\"((v101"\/"(v2"/\"v100))"\/"v100) =
(v101"\/"(v2"/\"v100))"\/"v100
proof let v101,v100,v2;
(v100"\/"v101)"\/"(v101"\/"(v2"/\"v100)) = v100"\/"v101 by A89;
hence thesis by A116;
end;
A131: for v1,v0,v2 holds
(v0"\/"v1)"/\"(v0"\/"(v1"\/"(v2"/\"v0))) = (v1"\/"(v2"/\"v0))"\/"v0
proof let v1,v0,v2;
(v1"\/"(v2"/\"v0))"\/"v0 = v0"\/"(v1"\/"(v2"/\"v0)) by A5;
hence thesis by A128;
end;
A133: for v1,v0,v2 holds v0"\/"v1 = (v1"\/"(v2"/\"v0))"\/"v0
proof let v1,v0,v2;
(v0"\/"v1)"/\"(v0"\/"(v1"\/"(v2"/\"v0))) = v0"\/"v1 by A125;
hence thesis by A131;
end;
A135: for v1,v0,v2 holds v0"\/"v1 = v0"\/"(v1"\/"(v2"/\"v0))
proof let v1,v0,v2;
(v1"\/"(v2"/\"v0))"\/"v0 = v0"\/"(v1"\/"(v2"/\"v0)) by A5;
hence thesis by A133;
end;
A138: for v1,v0,v2 holds v0"\/"((v2"/\"v0)"\/"v1) = v0"\/"v1
proof let v1,v0,v2;
v1"\/"(v2"/\"v0) = (v2"/\"v0)"\/"v1 by A5;
hence thesis by A135;
end;
A142: for v102,v101,v1 holds
(v1"\/"v101)"\/"(v101"\/"v102) = (v1"\/"v101)"\/"v102
proof let v102,v101,v1;
v101"/\"(v1"\/"v101) = v101 by A20;
hence thesis by A138;
end;
A146: for v102,v1,v101 holds
(v101"\/"v1)"\/"(v101"\/"v102) = (v101"\/"v1)"\/"v102
proof let v102,v1,v101;
v101"/\"(v101"\/"v1) = v101 by A32;
hence thesis by A138;
end;
A149: for v2,v1,v0 holds (v0"\/"v1)"\/"(v1"\/"v2) = v0"\/"(v1"\/"v2)
proof let v2,v1,v0;
(v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)) = (v0"\/"v1)"\/"(v1"\/"v2) by A146;
hence thesis by A104;
end;
A151: for v2,v1,v0 holds (v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2)
proof let v2,v1,v0;
(v0"\/"v1)"\/"(v1"\/"v2) = (v0"\/"v1)"\/"v2 by A142;
hence thesis by A149;
end;
A153: for v3,v0,v1,v2 holds
v0"\/"((v1"\/"v2)"\/"(v2"\/"((v0"\/"(v2"\/"v1))"/\"v3))) =
v0"\/"(v2"\/"v1)
proof let v3,v0,v1,v2;
(v0"\/"(v1"\/"v2))"\/"(v2"\/"((v0"\/"(v2"\/"v1))"/\"v3)) =
v0"\/"((v1"\/"v2)"\/"(v2"\/"((v0"\/"(v2"\/"v1))"/\"v3))) by A151;
hence thesis by A106;
end;
A155: for v3,v0,v1,v2 holds
v0"\/"(v1"\/"(v2"\/"(v2"\/"((v0"\/"(v2"\/"v1))"/\"v3)))) = v0"\/"(v2"\/"v1)
proof let v3,v0,v1,v2;
(v1"\/"v2)"\/"(v2"\/"((v0"\/"(v2"\/"v1))"/\"v3)) =
v1"\/"(v2"\/"(v2"\/"((v0"\/"(v2"\/"v1))"/\"v3))) by A151;
hence thesis by A153;
end;
A157: for v3,v0,v1,v2 holds
v0"\/"(v1"\/"(v2"\/"((v0"\/"(v2"\/"v1))"/\"v3))) = v0"\/"(v2"\/"v1)
proof let v3,v0,v1,v2;
v2"\/"(v2"\/"((v0"\/"(v2"\/"v1))"/\"v3)) =
v2"\/"((v0"\/"(v2"\/"v1))"/\"v3) by A63;
hence thesis by A155;
end;
A159: for v3,v2,v0,v1 holds
(v0"\/"(v1"\/"v2))"\/"(v0"\/"(((v1"\/"v0)"\/"v2)"/\"v3)) = (v0"\/"v1)"\/"v2
proof let v3,v2,v0,v1;
(v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2) by A151;
hence thesis by A120;
end;
A161: for v3,v1,v2,v0 holds
(v0"\/"(v1"\/"v2))"\/"(v0"\/"((v1"\/"(v0"\/"v2))"/\"v3)) = (v0"\/"v1)"\/"v2
proof let v3,v1,v2,v0;
(v1"\/"v0)"\/"v2 = v1"\/"(v0"\/"v2) by A151;
hence thesis by A159;
end;
A163: for v3,v1,v2,v0 holds
v0"\/"((v1"\/"v2)"\/"(v0"\/"((v1"\/"(v0"\/"v2))"/\"v3))) = (v0"\/"v1)"\/"v2
proof let v3,v1,v2,v0;
(v0"\/"(v1"\/"v2))"\/"(v0"\/"((v1"\/"(v0"\/"v2))"/\"v3)) =
v0"\/"((v1"\/"v2)"\/"(v0"\/"((v1"\/"(v0"\/"v2))"/\"v3))) by A151;
hence thesis by A161;
end;
A165: for v3,v1,v2,v0 holds
v0"\/"(v1"\/"(v2"\/"(v0"\/"((v1"\/"(v0"\/"v2))"/\"v3)))) = (v0"\/"v1)"\/"v2
proof let v3,v1,v2,v0;
(v1"\/"v2)"\/"(v0"\/"((v1"\/"(v0"\/"v2))"/\"v3)) =
v1"\/"(v2"\/"(v0"\/"((v1"\/"(v0"\/"v2))"/\"v3))) by A151;
hence thesis by A163;
end;
A167: for v1,v2,v0 holds v0"\/"(v1"\/"(v0"\/"v2)) = (v0"\/"v1)"\/"v2
proof
now let v3,v1,v2,v0;
v1"\/"(v2"\/"(v0"\/"((v1"\/"(v0"\/"v2))"/\"v3))) = v1"\/"(v0"\/"v2)
by A157;
hence v0"\/"(v1"\/"(v0"\/"v2)) = (v0"\/"v1)"\/"v2 by A165;
end;
hence thesis;
end;
A169: for v1,v2,v0 holds v1"\/"(v0"\/"v2) = (v0"\/"v1)"\/"v2
proof let v1,v2,v0;
v0"\/"(v1"\/"(v0"\/"v2)) = v1"\/"(v0"\/"v2) by A52;
hence thesis by A167;
end;
A172: for v0,v2,v1 holds v0"\/"(v1"\/"v2) = v1"\/"(v0"\/"v2)
proof let v0,v2,v1;
(v1"\/"v0)"\/"v2 = v1"\/"(v0"\/"v2) by A151;
hence thesis by A169;
end;
let v0,v2,v1;
v1"\/"(v0"\/"v2) = v0"\/"(v1"\/"v2) by A172; then
(v0"\/"v2)"\/"v1 = v0"\/"(v1"\/"v2) by A5;
hence thesis by A5;
end;
:: Third
theorem
(for v0 holds v0"\/"v0 = v0) &
(for v1,v2,v0 holds v0"/\"(v1"\/"(v0"\/"v2)) = v0) implies
for v1,v2 holds v1"/\"(v1"\/"v2) = v1
proof
assume A1: for v0 holds v0"\/"v0 = v0;
assume A2: for v1,v2,v0 holds v0"/\"(v1"\/"(v0"\/"v2)) = v0;
for v102,v100 holds v100"/\"(v100"\/"v102) = v100
proof
let v102,v100;
(v100"\/"v102)"\/"(v100"\/"v102) = v100"\/"v102 by A1;
hence thesis by A2;
end;
hence thesis;
end;
:: Fourth
theorem Lemma4:
(for v1,v0 holds v0"/\"v1 = v1"/\"v0) &
(for v0 holds v0"\/"v0 = v0) &
(for v1,v0 holds v0"\/"v1 = v1"\/"v0) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1) implies
for v1,v2 holds v1"\/"(v1"/\"v2) = v1
proof
assume A1: for v1,v0 holds v0"/\"v1 = v1"/\"v0;
assume A2: for v0 holds v0"\/"v0 = v0;
assume A3: for v1,v0 holds v0"\/"v1 = v1"\/"v0;
assume A4: for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1;
A6: for v2,v1,v0 holds v1"\/"((v0"/\"v1)"\/"(v2"/\"v1)) = v1
proof let v2,v1,v0;
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1"\/"((v0"/\"v1)"\/"(v2"/\"v1)) by A3;
hence thesis by A4;
end;
A11: for v100,v102 holds v100"\/"(v102"/\"v100) = v100
proof let v100,v102;
(v102"/\"v100)"\/"(v102"/\"v100) = v102"/\"v100 by A2;
hence thesis by A6;
end;
for v1,v0 holds v0"\/"(v0"/\"v1) = v0
proof let v1,v0;
v1"/\"v0 = v0"/\"v1 by A1;
hence thesis by A11;
end;
hence thesis;
end;
begin :: Definition of Attributes
definition let L be non empty LattStr;
attr L is satisfying_W3 means :DefW3:
for v2,v1,v0 being Element of L holds
((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1;
attr L is satisfying_W3' means :DefW33:
for v2,v1,v0 being Element of L holds
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1;
end;
definition let L be meet-absorbing join-absorbing meet-commutative
non empty LattStr;
redefine attr L is satisfying_W3 means :defW3: :: redefines satisfying_W3 (LATWAL_1, definition)
for v2,v1,v0 being Element of L holds
v1 [= (v0"\/"v1)"/\"(v2"\/"v1);
compatibility
proof
hereby assume
A1: L is satisfying_W3;
let v2,v1,v0 be Element of L;
((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1 by A1;
hence v1 [= (v0"\/"v1)"/\"(v2"\/"v1) by LATTICES:4;
end;
assume
A1: for v2,v1,v0 being Element of L holds v1 [= (v0"\/"v1)"/\"(v2"\/"v1);
let v2,v1,v0 be Element of L;
((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1 by LATTICES:4,A1;
hence thesis;
end;
end;
definition let L;
redefine attr L is satisfying_W3' means :defW33: :: redefines satisfying_W3' (LATWAL_1, definition)
for v2,v1,v0 holds (v0"/\"v1)"\/"(v2"/\"v1) [= v1;
compatibility
proof
hereby assume
A1: L is satisfying_W3';
let v2,v1,v0;
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1 by A1;
hence (v0"/\"v1)"\/"(v2"/\"v1) [= v1 by LATTICES:def 3;
end;
assume
for v2,v1,v0 holds (v0"/\"v1)"\/"(v2"/\"v1) [= v1;
hence thesis by LATTICES:def 3;
end;
end;
Lemma44:
L is meet-commutative join-idempotent join-commutative satisfying_W3' implies
L is meet-Absorbing
proof
assume L is meet-commutative join-idempotent join-commutative
satisfying_W3'; then
(for v1,v0 holds v0"/\"v1 = v1"/\"v0) &
(for v0 holds v0"\/"v0 = v0) &
(for v1,v0 holds v0"\/"v1 = v1"\/"v0) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1)
by LATTICES:def 4,def 6; then
for v1,v2 holds v1"\/"(v1"/\"v2) = v1 by Lemma4;
hence thesis by ROBBINS3:def 3;
end;
registration
cluster meet-commutative join-idempotent join-commutative
satisfying_W3' -> meet-Absorbing for non empty LattStr;
coherence by Lemma44;
end;
Lemma441:
L is meet-commutative meet-idempotent join-commutative satisfying_W3 implies
L is join-absorbing
proof
assume L is meet-commutative meet-idempotent
join-commutative satisfying_W3; then
Z1: (for v1,v0 holds v0"/\"v1 = v1"/\"v0) &
(for v0 holds v0"/\"v0 = v0) &
(for v1,v0 holds v0"\/"v1 = v1"\/"v0) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1)
by LATTICES:def 4,def 6;
for v1,v2 holds v1"/\"(v1"\/"v2) = v1
proof
let v1, v2;
((v2"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1 by Z1; then
z2: ((v1"\/"v2)"/\"(v2"\/"v1))"/\"v1 = v1 by Z1;
v1"/\"(v1"\/"v2) = (v1"\/"v2)"/\"v1 by Z1
.= ((v1"\/"v2)"/\"(v1"\/"v2))"/\"v1 by Z1
.= v1 by z2,Z1;
hence thesis;
end;
hence thesis by LATTICES:def 9;
end;
registration
cluster meet-commutative meet-idempotent join-commutative
satisfying_W3 -> join-absorbing for non empty LattStr;
coherence by Lemma441;
end;
registration
cluster trivial -> satisfying_W3' for non empty LattStr;
coherence by STRUCT_0:def 10;
end;
registration
cluster satisfying_W3 satisfying_W3' join-idempotent meet-idempotent
join-commutative meet-commutative for non empty LattStr;
existence
proof
take L = the trivial Lattice;
thus thesis by STRUCT_0:def 10;
end;
end;
definition
mode WeaklyAssociativeLattice is
join-idempotent meet-idempotent join-commutative meet-commutative
satisfying_W3 satisfying_W3' non empty LattStr;
end;
:: The above definition is taken from Padmanabhan and Rudeanu, Chapter 6
:: x ^ x = x x v x = x
:: x ^ y = y ^ x x v y = y v x
:: ((x v z) ^ (y v z)) ^ z = z ((x ^ z) v (y ^ z)) v z = z
::
:: but
::
:: Fried and Gratzer Some Examples of Weakly Associative Lattices states that
:: x ^ x = x x v x = x
:: x ^ y = y ^ x x v y = y v x
:: x ^ (x v y) = x x v (x ^ y) = x
:: ((x v z) ^ (y v z)) ^ z = z ((x ^ z) v (y ^ z)) v z = z
:: weak-associative identities
:: Absorption law can be derived from these
definition
mode WA_Lattice is WeaklyAssociativeLattice;
end;
:: Every lattice is weakly associative lattice
registration
cluster -> satisfying_W3' for join-associative meet-absorbing Lattice;
coherence
proof
let L be join-associative meet-absorbing Lattice;
for v2,v1,v0 be Element of L holds
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1
proof
let v2,v1,v0 be Element of L;
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 =
(v0"/\"v1)"\/"((v2"/\"v1)"\/"v1) by LATTICES:def 5
.= (v0"/\"v1)"\/"v1 by LATTICES:def 8
.= v1 by LATTICES:def 8;
hence thesis;
end;
hence thesis;
end;
end;
definition let L be non empty LattStr;
attr L is satisfying_WA means
for x,y,z being Element of L holds x"/\"(y"\/"(x"\/"z)) = x;
end;
begin :: Defining WALs in terms of the ordering
registration
cluster meet-Absorbing meet-commutative join-commutative -> meet-absorbing
for non empty LattStr;
coherence
proof
let L be non empty LattStr;
assume
A1: L is meet-Absorbing meet-commutative join-commutative;
let a,b be Element of L;
b "\/" (b "/\" a) = b by A1,ROBBINS3:def 3; then
b "\/" (a "/\" b) = b by A1,LATTICES:def 6;
hence thesis by A1,LATTICES:def 4;
end;
end;
registration
cluster -> meet-absorbing for WA_Lattice;
coherence;
end;
begin :: On the Ordering Relation Generated by Weakly Associated Lattices
reserve L for WA_Lattice;
reserve x,y,z,u for Element of L;
theorem
x "\/" y = y iff x [= y by LATTICES:def 3;
theorem
x "/\" y = x iff x [= y by LATTICES:4;
theorem
x [= x;
theorem
x [= y & y [= x implies x = y by LATTICES:8;
theorem LemmaSum:
x [= x "\/" y
proof
set v1 = x "\/" y;
A1: x "/\" v1 = x by LATTICES:def 9;
((x"/\"v1)"\/"(x"/\"v1))"\/"v1 = v1 by DefW33;
hence thesis by LATTICES:def 3,A1;
end; :: LATTICES:5 but without associativity
theorem Lemacik3:
x "/\" y [= x
proof
(x "/\" y) "\/" x = x by LATTICES:def 8;
hence thesis by LATTICES:def 3;
end; :: LATTICES:5 but without associativity
theorem Lemacik1:
x [= z & y [= z implies x "\/" y [= z
proof
assume x [= z & y [= z; then
x "/\" z = x & y "/\" z = y by LATTICES:4;
hence thesis by defW33;
end;
theorem
ex z st x [= z & y [= z &
for u st x [= u & y [= u holds z [= u
proof
take z = x "\/" y;
thus thesis by Lemacik1,LemmaSum;
end;
theorem Lemacik2:
z [= x & z [= y implies z [= x "/\" y
proof
assume z [= x & z [= y; then
z "\/" x = x & z "\/" y = y by LATTICES:def 3;
hence thesis by defW3;
end;
theorem
ex z st z [= x & z [= y &
for u st u [= x & u [= y holds u [= z
proof
take z = x "/\" y;
thus thesis by Lemacik2,Lemacik3;
end;
:: Under the assumption of (4) the following is true:
theorem
x [= z & y [= z implies (x "\/" y) "\/" z = x "\/" (y "\/" z)
proof
assume
AA: x [= z & y [= z; then
A0: x "\/" z = z & y "\/" z = z by LATTICES:def 3;
x "/\" z = x & y "/\" z = y by LATTICES:4,AA;
hence thesis by A0,DefW33;
end;
theorem
z [= x & z [= y implies (x "/\" y) "/\" z = x "/\" (y "/\" z)
proof
assume
AA: z [= x & z [= y; then
A0: z "\/" x = x & z "\/" y = y by LATTICES:def 3;
z "/\" x = z & z "/\" y = z by LATTICES:4,AA;
hence thesis by A0,DefW3;
end;
:: WA-Lattice is a lattice iff [= is transitive
theorem
L is distributive & x [= y [= z implies x [= z
proof
assume
A0: L is distributive;
assume
A1: x [= y [= z;
x "/\" z = x "/\" (y "\/" z) by A1,LATTICES:def 3
.= (x "/\" y) "\/" (x "/\" z) by A0,LATTICES:def 11
.= x "\/" (x "/\" z) by A1,LATTICES:4
.= x by LATTICES:def 8;
hence thesis by LATTICES:4;
end;
begin :: Distributivity Gives Associativity
reserve L for non empty LattStr;
reserve v100,v101,v102,v0,v1,v2 for Element of L;
theorem WALDistri: :: WAL + Distributivity -> Associativity
(for v0 holds v0"/\"v0 = v0) &
(for v1,v0 holds v0"/\"v1 = v1"/\"v0) &
(for v0 holds v0"\/"v0 = v0) &
(for v1,v0 holds v0"\/"v1 = v1"\/"v0) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1) &
(for v1,v0 holds v0"/\"(v0"\/"v1) = v0) &
(for v0,v2,v1 holds v0"\/"(v1"/\"v2) = (v0"\/"v1)"/\"(v0"\/"v2)) implies
for v0,v1,v2 holds (v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2)
proof
assume A1: for v0 holds v0"/\"v0 = v0;
assume A2: for v1,v0 holds v0"/\"v1 = v1"/\"v0;
assume A3: for v0 holds v0"\/"v0 = v0;
assume A4: for v1,v0 holds v0"\/"v1 = v1"\/"v0;
assume A5: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1;
A7: for v2,v1,v0 holds v1"/\"((v0"\/"v1)"/\"(v2"\/"v1)) = v1
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1"/\"((v0"\/"v1)"/\"(v2"\/"v1)) by A2;
hence thesis by A5;
end;
assume A9: for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1;
A11: for v2,v1,v0 holds v1"\/"((v0"/\"v1)"\/"(v2"/\"v1)) = v1
proof let v2,v1,v0;
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1"\/"((v0"/\"v1)"\/"(v2"/\"v1)) by A4;
hence thesis by A9;
end;
assume A13: for v1,v0 holds v0"/\"(v0"\/"v1) = v0;
assume A15: for v0,v2,v1 holds v0"\/"(v1"/\"v2) = (v0"\/"v1)"/\"(v0"\/"v2);
A22: for v100,v102 holds v100"/\"(v102"\/"v100) = v100
proof let v100,v102;
(v102"\/"v100)"/\"(v102"\/"v100) = v102"\/"v100 by A1;
hence thesis by A7;
end;
A26: for v100,v102 holds v100"\/"(v102"/\"v100) = v100
proof let v100,v102;
(v102"/\"v100)"\/"(v102"/\"v100) = v102"/\"v100 by A3;
hence thesis by A11;
end;
A29: for v2,v0,v1 holds (v1"\/"v0)"/\"(v0"\/"v2) = v0"\/"(v1"/\"v2)
proof let v2,v0,v1;
v0"\/"v1 = v1"\/"v0 by A4;
hence thesis by A15;
end;
A36: for v1,v101 holds (v101"\/"v1)"\/"v101 = v101"\/"v1
proof let v1,v101;
v101"/\"(v101"\/"v1) = v101 by A13;
hence thesis by A26;
end;
A39: for v1,v0 holds v0"\/"(v0"\/"v1) = v0"\/"v1
proof let v1,v0;
(v0"\/"v1)"\/"v0 = v0"\/"(v0"\/"v1) by A4;
hence thesis by A36;
end;
A51: for v0,v2,v1 holds (v0"\/"v2)"\/"(v0"\/"(v1"/\"v2)) = v0"\/"v2
proof let v0,v2,v1;
(v0"\/"v1)"/\"(v0"\/"v2) = v0"\/"(v1"/\"v2) by A15;
hence thesis by A26;
end;
A55: for v102,v1,v100 holds
(v100"\/"v1)"/\"(v100"\/"v102) = v100"\/"((v100"\/"v1)"/\"v102)
proof let v102,v1,v100;
v100"\/"(v100"\/"v1) = v100"\/"v1 by A39;
hence thesis by A15;
end;
A58: for v0,v2,v1 holds v0"\/"(v1"/\"v2) = v0"\/"((v0"\/"v1)"/\"v2)
proof let v0,v2,v1;
(v0"\/"v1)"/\"(v0"\/"v2) = v0"\/"(v1"/\"v2) by A15;
hence thesis by A55;
end;
A86: for v100,v1,v102 holds
(v100"\/"(v102"\/"v1))"\/"(v100"\/"v102) = v100"\/"(v102"\/"v1)
proof let v100,v1,v102;
v102"/\"(v102"\/"v1) = v102 by A13;
hence thesis by A51;
end;
A89: for v0,v2,v1 holds (v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)) = v0"\/"(v1"\/"v2)
proof let v0,v2,v1;
(v0"\/"(v1"\/"v2))"\/"(v0"\/"v1) = (v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)) by A4;
hence thesis by A86;
end;
A92: for v1,v101,v100 holds
v100"\/"((v100"\/"v101)"/\"(v101"\/"v1)) = v100"\/"v101
proof let v1,v101,v100;
v101"/\"(v101"\/"v1) = v101 by A13;
hence thesis by A58;
end;
A95: for v1,v2,v0 holds v0"\/"(v1"\/"(v0"/\"v2)) = v0"\/"v1
proof let v1,v2,v0;
(v0"\/"v1)"/\"(v1"\/"v2) = v1"\/"(v0"/\"v2) by A29;
hence thesis by A92;
end;
A97: for v1,v0,v2 holds v0"\/"(v1"\/"(v2"/\"v0)) = v0"\/"v1
proof let v1,v0,v2;
v0"/\"v2 = v2"/\"v0 by A2;
hence thesis by A95;
end;
A99: for v1,v0,v2 holds v0"\/"((v2"/\"v0)"\/"v1) = v0"\/"v1
proof let v1,v0,v2;
v1"\/"(v2"/\"v0) = (v2"/\"v0)"\/"v1 by A4;
hence thesis by A97;
end;
A103: for v102,v1,v101 holds
(v101"\/"v1)"\/"(v101"\/"v102) = (v101"\/"v1)"\/"v102
proof let v102,v1,v101;
v101"/\"(v101"\/"v1) = v101 by A13;
hence thesis by A99;
end;
A107: for v102,v101,v1 holds
(v1"\/"v101)"\/"(v101"\/"v102) = (v1"\/"v101)"\/"v102
proof let v102,v101,v1;
v101"/\"(v1"\/"v101) = v101 by A22;
hence thesis by A99;
end;
A110: for v2,v1,v0 holds (v0"\/"v1)"\/"(v1"\/"v2) = v0"\/"(v1"\/"v2)
proof let v2,v1,v0;
(v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)) = (v0"\/"v1)"\/"(v1"\/"v2) by A103;
hence thesis by A89;
end;
for v2,v1,v0 holds (v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2)
proof
let v2,v1,v0;
(v0"\/"v1)"\/"(v1"\/"v2) = (v0"\/"v1)"\/"v2 by A107;
hence thesis by A110;
end;
hence thesis;
end;
:: If we assume distributivity (actually one of them), we get full
:: lattice (via the associativity).
registration
cluster distributive' -> join-associative for WA_Lattice;
coherence
proof
let L be WA_Lattice;
assume
A0: L is distributive';
L is join-idempotent meet-idempotent join-commutative meet-commutative
satisfying_W3 satisfying_W3'; then
(for v0 being Element of L holds v0"/\"v0 = v0) &
(for v1,v0 being Element of L holds v0"/\"v1 = v1"/\"v0) &
(for v0 being Element of L holds v0"\/"v0 = v0) &
(for v1,v0 being Element of L holds v0"\/"v1 = v1"\/"v0) &
(for v2,v1,v0 being Element of L holds
((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1) &
(for v2,v1,v0 being Element of L holds
((v0"/\"v1)"\/"(v2"/\"v1))"\/"v1 = v1) &
(for v1,v0 being Element of L holds v0"/\"(v0"\/"v1) = v0) &
(for v1,v0 being Element of L holds v0"\/"(v0"/\"v1) = v0) &
(for v0,v2,v1 being Element of L holds
v0"\/"(v1"/\"v2) = (v0"\/"v1)"/\"(v0"\/"v2))
by A0,ROBBINS3:def 3,LATTICES:def 9; then
for v0,v1,v2 being Element of L holds (v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2)
by WALDistri;
hence thesis by LATTICES:def 5;
end;
end;
begin :: Near Lattices
Lmx2: 2 in {0,1,2} & for x,y being Element of {0,1,2} holds
min (x,y) in {0,1,2}
proof
now let x,y be Element of {0,1,2};
min (x,y) = x or min (x,y) = y by XXREAL_0:15;
hence min (x,y) in {0,1,2};
end;
hence thesis by ENUMSET1:def 1;
end;
Lmy2: 2 in {0,1,2} & for x,y being Element of {0,1,2} holds
max (x,y) in {0,1,2}
proof
now let x,y be Element of {0,1,2};
max (x,y) = x or max (x,y) = y by XXREAL_0:16;
hence max (x,y) in {0,1,2};
end;
hence thesis by ENUMSET1:def 1;
end;
definition
let x,y be Element of {0,1,2};
func x ex123"/\" y -> Element of {0,1,2} equals :ExMeetDef:
2 if (x = 0 & y = 2) or (x = 2 & y = 0),
min (x,y) if not ((x = 0 & y = 2) or (x = 2 & y = 0));
coherence by Lmx2;
consistency;
func x ex123"\/" y -> Element of {0,1,2} equals :UPDef:
0 if (x = 0 & y = 2) or (x = 2 & y = 0),
max (x,y) if not ((x = 0 & y = 2) or (x = 2 & y = 0));
coherence by Lmy2;
consistency;
end;
definition
func ex123\/ -> BinOp of {0,1,2} means :EXUDef:
for x,y being Element of {0,1,2} holds it.(x,y) = x ex123"\/" y;
existence
proof
deffunc O(Element of {0,1,2}, Element of {0,1,2}) = $1 ex123"\/" $2;
ex o being BinOp of {0,1,2} st for a,b being Element of {0,1,2} holds
o.(a,b) = O(a,b) from BINOP_1:sch 4;
hence thesis;
end;
uniqueness
proof
let o1,o2 be BinOp of {0,1,2} such that
A1: for x,y being Element of {0,1,2} holds o1.(x,y) = x ex123"\/" y and
A2: for x,y being Element of {0,1,2} holds o2.(x,y) = x ex123"\/" y;
now
let x,y be Element of {0,1,2};
thus o1.(x,y) = x ex123"\/" y by A1
.= o2.(x,y) by A2;
end;
hence thesis by BINOP_1:2;
end;
func ex123/\ -> BinOp of {0,1,2} means :EXNDef:
for x,y being Element of {0,1,2} holds it.(x,y) = x ex123"/\" y;
existence
proof
deffunc O(Element of {0,1,2}, Element of {0,1,2}) = $1 ex123"/\" $2;
ex o being BinOp of {0,1,2} st for a,b being Element of {0,1,2} holds
o.(a,b) = O(a,b) from BINOP_1:sch 4;
hence thesis;
end;
uniqueness
proof
let o1,o2 be BinOp of {0,1,2} such that
A1: for x,y being Element of {0,1,2} holds o1.(x,y) = x ex123"/\" y and
A2: for x,y being Element of {0,1,2} holds o2.(x,y) = x ex123"/\" y;
now
let x,y be Element of {0,1,2};
thus o1.(x,y) = x ex123"/\" y by A1
.= o2.(x,y) by A2;
end;
hence thesis by BINOP_1:2;
end;
end;
begin :: Near Lattices
:: Here the example of the near lattice. We should show
:: that it breaks one of the lattice axioms
definition
func ExNearLattice -> non empty LattStr equals
LattStr (#{0,1,2}, ex123\/, ex123/\ #);
coherence;
end;
:: We should show that the lattice doesn't satisfy lattice axioms
:: (see similar work in LATQUASI)
:: but obviously it's an example of a near lattice
:: (0 v 1) v 2 = 1 v 2 = 2
:: 0 v (1 v 2) = 0 v 2 = 0
:: (0 ^ 1) ^ 2 = 0 ^ 2 = 2
:: 0 ^ (1 ^ 2) = 0 ^ 1 = 0
:: function(^(_,_), [
:: 0,0,2,
:: 0,1,1,
:: 2,1,2]),
:: function(v(_,_), [
:: 0,1,0,
:: 1,1,2,
:: 0,2,2]),
ExJoinAbs:
ExNearLattice is join-absorbing
proof
set L = ExNearLattice;
for a,b being Element of L holds a "/\" (a"\/"b) = a
proof
let a,b be Element of L;
reconsider aa = a, bb = b as Element of {0,1,2};
per cases;
suppose
B1: a = 0 & b = 2; then
aa ex123"\/" bb = aa by UPDef; then
a "/\" (a "\/" b) = a "/\" a by EXUDef
.= aa ex123"/\" aa by EXNDef
.= min(aa,aa) by ExMeetDef,B1
.= aa;
hence thesis;
end;
suppose
B1: a = 2 & b = 0; then
aa ex123"\/" bb = bb by UPDef; then
a "/\" (a "\/" b) = a "/\" b by EXUDef
.= aa ex123"/\" bb by EXNDef
.= aa by ExMeetDef,B1;
hence thesis;
end;
suppose
B1: not ((a = 0 & b = 2) or (a = 2 & b = 0));
per cases by XXREAL_0:16;
suppose
E: max(aa,bb) = aa;
A3: a "\/"b = aa ex123"\/" bb by EXUDef
.= aa by B1,UPDef,E;
WW: not ((a = 0 & a = 2) or (a = 2 & a = 0));
a "/\"(a "\/" b) = aa ex123"/\" aa by EXNDef,A3
.= min(aa,aa) by ExMeetDef,WW
.= aa;
hence thesis;
end;
suppose
E: max(aa,bb)=bb;
A3: a "\/"b = aa ex123"\/" bb by EXUDef
.= bb by E,B1,UPDef;
a "/\"(a "\/" b) = aa ex123"/\" bb by EXNDef,A3
.= min(aa,bb) by ExMeetDef,B1
.= aa by E,XXREAL_0:def 9,XXREAL_0:25;
hence thesis;
end;
end;
end;
hence thesis by LATTICES:def 9;
end;
ExMeetAbs:
ExNearLattice is meet-absorbing
proof
set L = ExNearLattice;
for a,b being Element of L holds (a "/\"b)"\/"b = b
proof
let a,b be Element of L;
reconsider aa = a, bb = b as Element of {0,1,2};
a0: a "/\" b = aa ex123"/\" bb by EXNDef;
per cases;
suppose
B1: a = 0 & b = 2; then
aa ex123"/\" bb = bb by ExMeetDef; then
(a"/\"b)"\/"b = b "\/" b by EXNDef
.= bb ex123"\/" bb by EXUDef
.= max(bb,bb) by UPDef, B1
.= bb;
hence thesis;
end;
suppose
B1: a = 2 & b = 0; then
(a"/\"b)"\/"b = a "\/" b by a0,ExMeetDef
.= aa ex123"\/" bb by EXUDef
.= bb by UPDef, B1;
hence thesis;
end;
suppose
B1: not ((a = 0 & b = 2) or (a = 2 & b = 0));
per cases by XXREAL_0:15;
suppose
B2: min(aa,bb)=aa; then
(a"/\"b)"\/"b = a "\/" b by a0,B1,ExMeetDef
.= aa ex123"\/" bb by EXUDef
.= max(aa,bb) by UPDef,B1
.= bb by B2,XXREAL_0:def 10,17;
hence thesis;
end;
suppose
B4: min(aa,bb) = bb;
A5: not ((b = 0 & b = 2) or (b = 2 & b = 0));
(a"/\"b)"\/"b = b "\/" b by B4,a0,B1,ExMeetDef
.= bb ex123"\/" bb by EXUDef
.= max(bb,bb) by UPDef,A5
.= bb;
hence thesis;
end;
end;
end;
hence thesis by LATTICES:def 8;
end;
Lemacik1:
for x,y being Element of ExNearLattice holds
ex123/\.(x,y) = ex123/\.(y,x)
proof
let x,y be Element of ExNearLattice;
reconsider xx = x, yy = y as Element of {0,1,2};
per cases;
suppose
x = 0 & y = 0;
hence thesis;
end;
suppose
X1: x = 0 & y = 2;
ex123/\.(x,y) = xx ex123"/\" yy by EXNDef
.= 2 by ExMeetDef,X1
.= yy ex123"/\" xx by ExMeetDef,X1
.= ex123/\.(y,x) by EXNDef;
hence thesis;
end;
suppose
X1: x = 2 & y = 0;
ex123/\.(x,y) = xx ex123"/\" yy by EXNDef
.= 2 by ExMeetDef,X1
.= yy ex123"/\" xx by ExMeetDef,X1
.= ex123/\.(y,x) by EXNDef;
hence thesis;
end;
suppose
X1: not ((x = 0 & y = 2) or (x = 2 & y = 0));
ex123/\.(x,y) = xx ex123"/\" yy by EXNDef
.= min (xx,yy) by ExMeetDef,X1
.= yy ex123"/\" xx by ExMeetDef,X1
.= ex123/\.(y,x) by EXNDef;
hence thesis;
end;
end;
Lemacik1A:
for x,y being Element of ExNearLattice holds
ex123\/.(x,y) = ex123\/.(y,x)
proof
let x,y be Element of ExNearLattice;
reconsider xx = x, yy = y as Element of {0,1,2};
per cases;
suppose
V1: not ((x = 0 & y = 2) or (x = 2 & y = 0)); then
xx ex123"\/" yy = max (xx,yy) by UPDef; then
V3: ex123\/.(x,y) = max (xx,yy) by EXUDef;
yy ex123"\/" xx = max (yy,xx) by V1,UPDef;
hence thesis by V3,EXUDef;
end;
suppose
V1: x = 0 & y = 2 or (x = 2 & y = 0); then
xx ex123"\/" yy = 0 by UPDef; then
V3: ex123\/.(x,y) = 0 by EXUDef;
yy ex123"\/" xx = 0 by V1,UPDef;
hence thesis by V3,EXUDef;
end;
end;
Cosik1:
not ExNearLattice is join-associative
proof
set L = ExNearLattice;
reconsider x = 0, y = 1, z = 2 as Element of L by ENUMSET1:def 1;
reconsider xx = x, yy = y, zz = z as Element of {0,1,2};
yy ex123"\/" zz = max(yy,zz) by UPDef
.= 2 by XXREAL_0:def 10; then
t1: x "\/" (y "\/" z) = x "\/" z by EXUDef
.= xx ex123"\/" zz by EXUDef
.= 0 by UPDef;
xx ex123"\/" yy = max(xx,yy) by UPDef
.= 1 by XXREAL_0:def 10; then
(x "\/" y) "\/" z = y "\/" z by EXUDef
.= yy ex123"\/" zz by EXUDef
.= max(yy,zz) by UPDef
.= 2 by XXREAL_0:def 10;
hence thesis by LATTICES:def 5,t1;
end;
Cosik2:
not ExNearLattice is meet-associative
proof
set L = ExNearLattice;
reconsider x = 0, y = 1, z = 2 as Element of L by ENUMSET1:def 1;
reconsider xx = x, yy = y, zz = z as Element of {0,1,2};
yy ex123"/\" zz = min(yy,zz) by ExMeetDef
.= 1 by XXREAL_0:def 9; then
t1: x "/\" (y "/\" z) = x "/\" y by EXNDef
.= xx ex123"/\" yy by EXNDef
.= min (xx,yy) by ExMeetDef
.= 0 by XXREAL_0:def 9;
xx ex123"/\" yy = min(xx,yy) by ExMeetDef
.= 0 by XXREAL_0:def 9; then
(x "/\" y) "/\" z = x "/\" z by EXNDef
.= xx ex123"/\" zz by EXNDef
.= 2 by ExMeetDef;
hence thesis by LATTICES:def 7,t1;
end;
registration
cluster ExNearLattice -> non join-associative non meet-associative;
coherence by Cosik1,Cosik2;
end;
registration
cluster trivial -> meet-idempotent join-commutative
meet-Absorbing join-absorbing for non empty LattStr;
coherence;
end;
definition
mode NearLattice is join-idempotent meet-idempotent join-commutative
meet-commutative meet-Absorbing join-absorbing non empty LattStr;
end;
ExJoinComm: ExNearLattice is join-commutative
proof
set L = ExNearLattice;
for x,y being Element of L holds x "\/" y = y "\/" x by Lemacik1A;
hence thesis by LATTICES:def 4;
end;
ExMeetComm: ExNearLattice is meet-commutative
proof
set L = ExNearLattice;
for x,y being Element of L holds x "/\" y = y "/\" x by Lemacik1;
hence thesis by LATTICES:def 6;
end;
registration
cluster ExNearLattice -> join-commutative meet-commutative
join-idempotent meet-idempotent join-absorbing meet-absorbing;
coherence by ExJoinComm,ExMeetComm,ExMeetAbs,ExJoinAbs;
end;
registration
cluster meet-absorbing -> meet-Absorbing
for join-commutative meet-commutative non empty LattStr;
coherence
proof
let L be join-commutative meet-commutative non empty LattStr;
assume L is meet-absorbing; then
for x, y being Element of L holds x "\/" (x "/\" y) = x
by LATTICES:def 8;
hence thesis by ROBBINS3:def 3;
end;
cluster meet-Absorbing -> meet-absorbing
for join-commutative meet-commutative non empty LattStr;
coherence;
end;
theorem :: automatically accepted thanks to registrations of clusters
ExNearLattice is NearLattice &
not ExNearLattice is Lattice;
begin :: Alternative Axioms for WAL
::: WAL-3
:: (x ^ y) v (x ^ (x v y)) = x
:: (x ^ x) v (y ^ (x v x)) = x
:: (x ^ y) v (y ^ (x v y)) = y
:: ((x v y) ^ (z v x)) ^ x = x
:: ((x ^ y) v (z ^ x)) v x = x
:: implies
:: x ^ x = x
:: x v x = x
:: x ^ y = y ^ x
:: x v y = y v x
reserve v101,v100,v2,v1,v0,v102,v103,v3 for Element of L;
Lemma1:
(for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0) implies
for v0 holds v0 "/\" v0 = v0
proof
assume A1: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0;
assume A4: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0;
assume A5: for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0;
A13: for v101,v100 holds ((v100"\/"v101)"/\"v100)"/\"v100 = v100
proof
now let v101,v2,v1,v100;
((v100"/\"v1)"\/"(v2"/\"v100))"\/"v100 = v100 by A5;
hence ((v100"\/"v101)"/\"v100)"/\"v100 = v100 by A4;
end;
hence thesis;
end;
A21: for v1,v0 holds (v0"/\"(v0"/\"v1))"/\"(v0"/\"v1) = v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
hence thesis by A13;
end;
A32: for v2,v1,v101 holds
(((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101)"/\"
(((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101) =
((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101
proof let v2,v1,v101;
((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
hence thesis by A21;
end;
A35: for v2,v1,v0 holds
v0"/\"(((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0) = ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0 by A4;
hence thesis by A32;
end;
A37: for v2,v1,v0 holds v0"/\"v0 = ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0 by A4;
hence thesis by A35;
end;
now let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0 by A4;
hence v0"/\"v0 = v0 by A37;
end;
hence thesis;
end;
theorem Lemma2:
(for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0) &
(for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0) &
(for v1,v0 holds (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0) implies
for v0 holds v0 "\/" v0 = v0
proof
assume A1: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0;
assume A2: for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0;
assume A3: for v1,v0 holds (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1;
assume A4: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0;
assume A5: for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0;
assume not thesis; then
consider C being Element of L such that
A6: C"\/"C <> C;
A9: for v100 holds (v100"/\"v100)"\/"(v100"\/"v100) = v100
proof
now let v2,v1,v100;
(((v100"\/"v100)"\/"v1)"/\"(v2"\/"(v100"\/"v100)))"/\"(v100"\/"v100) =
v100"\/"v100 by A4;
hence (v100"/\"v100)"\/"(v100"\/"v100) = v100 by A2;
end;
hence thesis;
end;
A13: for v101,v100 holds ((v100"\/"v101)"/\"v100)"/\"v100 = v100
proof
now let v101,v2,v1,v100;
((v100"/\"v1)"\/"(v2"/\"v100))"\/"v100 = v100 by A5;
hence ((v100"\/"v101)"/\"v100)"/\"v100 = v100 by A4;
end;
hence thesis;
end;
A17: for v0 holds ((v0"/\"v0)"/\"(v0"\/"v0))"\/"((v0"/\"v0)"/\"v0) = v0"/\"v0
proof let v0;
(v0"/\"v0)"\/"(v0"\/"v0) = v0 by A9;
hence thesis by A1;
end;
A20: for v0 holds ((v0"/\"v0)"/\"(v0"\/"v0))"\/"((v0"\/"v0)"/\"v0) = v0"\/"v0
proof let v0;
(v0"/\"v0)"\/"(v0"\/"v0) = v0 by A9;
hence thesis by A3;
end;
A23: for v1,v0 holds (v0"/\"(v0"/\"v1))"/\"(v0"/\"v1) = v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
hence thesis by A13;
end;
A26: for v2,v1,v101 holds
(((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101)"/\"(((v101"\/"v1)"/\"
(v2"\/"v101))"/\"v101) = ((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101
proof let v2,v1,v101;
((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
hence thesis by A23;
end;
A29: for v2,v1,v0 holds
v0"/\"(((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0) = ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0 by A4;
hence thesis by A26;
end;
A31: for v2,v1,v0 holds v0"/\"v0 = ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0 by A4;
hence thesis by A29;
end;
A33: for v0 holds v0"/\"v0 = v0
proof
now let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0 by A4;
hence v0"/\"v0 = v0 by A31;
end;
hence thesis;
end;
A35: for v0 holds (v0"/\"(v0"\/"v0))"\/"((v0"\/"v0)"/\"v0) = v0"\/"v0
proof let v0;
v0"/\"v0 = v0 by A33;
hence thesis by A20;
end;
A37: for v0 holds (v0"/\"(v0"\/"v0))"\/"((v0"/\"v0)"/\"v0) = v0"/\"v0
proof let v0;
v0"/\"v0 = v0 by A33;
hence thesis by A17;
end;
A39: for v0 holds (v0"/\"(v0"\/"v0))"\/"(v0"/\"v0) = v0"/\"v0
proof let v0;
v0"/\"v0 = v0 by A33;
hence thesis by A37;
end;
A41: for v0 holds (v0"/\"(v0"\/"v0))"\/"v0 = v0"/\"v0
proof let v0;
v0"/\"v0 = v0 by A33;
hence thesis by A39;
end;
A43: for v0 holds (v0"/\"(v0"\/"v0))"\/"v0 = v0
proof let v0;
v0"/\"v0 = v0 by A33;
hence thesis by A41;
end;
A46: for v102 holds (v102"\/"v102)"/\"v102 = v102
proof let v102;
(v102"\/"v102)"/\"(v102"\/"v102) = v102"\/"v102 by A33;
hence thesis by A4;
end;
A49: for v0 holds (v0"/\"(v0"\/"v0))"\/"v0 = v0"\/"v0
proof let v0;
(v0"\/"v0)"/\"v0 = v0 by A46;
hence thesis by A35;
end;
for v0 holds v0 = v0"\/"v0
proof let v0;
(v0"/\"(v0"\/"v0))"\/"v0 = v0 by A43;
hence thesis by A49;
end;
hence thesis by A6;
end;
theorem Lemma3:
(for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0) &
(for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0) &
(for v1,v0 holds (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0) implies
for v0,v1 holds v0 "/\" v1 = v1 "/\" v0
proof
assume A1: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0;
assume A2: for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0;
assume A3: for v1,v0 holds (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1;
assume A4: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0;
assume A5: for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0;
assume not thesis; then
consider C,D being Element of L such that
A6: C"/\"D <> D"/\"C;
A9: for v1,v0 holds
((v0"/\"v1)"/\"(v0"/\"(v0"\/"v1)))"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
hence thesis by A1;
end;
A12: for v2,v1,v101 holds
v101"\/"(((v101"\/"v1)"/\"(v2"\/"v101))"/\"(((v101"\/"v1)"/\"
(v2"\/"v101))"\/"v101)) = (v101"\/"v1)"/\"(v2"\/"v101)
proof let v2,v1,v101;
((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
hence thesis by A1;
end;
A16: for v102,v1,v0 holds (v0"/\"(v102"\/"(v0"/\"v1)))"/\"(v0"/\"v1) = v0"/\"v1
proof let v102,v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
hence thesis by A4;
end;
A24: for v102,v1,v0 holds
(v1"/\"(v102"\/"(v0"/\"v1)))"/\"(v0"/\"v1) = v0"/\"v1
proof let v102,v1,v0;
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1 by A3;
hence thesis by A4;
end;
A28: for v101,v100 holds ((v100"\/"v101)"/\"v100)"/\"v100 = v100
proof
now let v101,v2,v1,v100;
((v100"/\"v1)"\/"(v2"/\"v100))"\/"v100 = v100 by A5;
hence ((v100"\/"v101)"/\"v100)"/\"v100 = v100 by A4;
end;
hence thesis;
end;
A32: for v101,v100 holds ((v100"/\"v101)"\/"v100)"\/"v100 = v100
proof
now let v101,v2,v1,v100;
((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100 = v100 by A4;
hence ((v100"/\"v101)"\/"v100)"\/"v100 = v100 by A5;
end;
hence thesis;
end;
A42: for v1,v0 holds (v0"/\"(v0"/\"v1))"/\"(v0"/\"v1) = v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
hence thesis by A28;
end;
A45: for v1,v101 holds
(((v101"/\"v1)"\/"v101)"/\"v101)"\/"(((v101"/\"v1)"\/"v101)"/\"v101) =
(v101"/\"v1)"\/"v101
proof let v1,v101;
((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A32;
hence thesis by A1;
end;
A49: for v1,v101 holds
(v101"\/"((v101"\/"v1)"/\"v101))"\/"((v101"\/"v1)"/\"v101) =
(v101"\/"v1)"/\"v101
proof let v1,v101;
((v101"\/"v1)"/\"v101)"/\"v101 = v101 by A28;
hence thesis by A32;
end;
A60: for v0 holds v0"/\"v0 = v0 by A1,A4,A5,Lemma1;
A63: for v1,v0 holds
((v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)))"\/"(v0"/\"(v0"/\"v1)) = v0"/\"(v0"/\"v1)
proof let v1,v0;
(v0"/\"(v0"/\"v1))"/\"(v0"/\"v1) = v0"/\"v1 by A42;
hence thesis by A32;
end;
A75: for v0,v1 holds v0"\/"(v1"/\"(v0"\/"v0)) = v0
proof let v0,v1;
v0"/\"v0 = v0 by A60;
hence thesis by A2;
end;
A83: for v0 holds v0 = v0"\/"v0 by A1,A2,A3,A4,A5,Lemma2;
A86: for v0,v1 holds v0"\/"(v1"/\"v0) = v0
proof let v0,v1;
v0"\/"v0 = v0 by A83;
hence thesis by A75;
end;
A88: for v1,v0 holds ((v0"/\"v1)"\/"v0)"/\"v0 = (v0"/\"v1)"\/"v0
proof let v1,v0;
(((v0"/\"v1)"\/"v0)"/\"v0)"\/"(((v0"/\"v1)"\/"v0)"/\"v0) =
((v0"/\"v1)"\/"v0)"/\"v0 by A83;
hence thesis by A45;
end;
A90: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"(v0"/\"v1)
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"v1 by A86;
hence thesis by A63;
end;
A92: for v1,v0 holds v0"/\"v1 = v0"/\"(v0"/\"v1)
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"v1 by A86;
hence thesis by A90;
end;
A95: for v1,v0 holds v0"\/"((v0"\/"v1)"/\"v0) = (v0"\/"v1)"/\"v0
proof let v1,v0;
v0"\/"((v0"\/"v1)"/\"v0) = v0 by A86;
hence thesis by A49;
end;
A97: for v1,v0 holds v0 = (v0"\/"v1)"/\"v0
proof let v1,v0;
v0"\/"((v0"\/"v1)"/\"v0) = v0 by A86;
hence thesis by A95;
end;
A101: for v101,v102 holds (v101"/\"(v102"\/"v101))"/\"v101 = v101
proof let v101,v102;
v101"\/"v101 = v101 by A83;
hence thesis by A4;
end;
A105: for v1,v101 holds v101"/\"((v101"/\"v1)"\/"v101) = (v101"/\"v1)"\/"v101
proof let v1,v101;
((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A32;
hence thesis by A97;
end;
A109: for v1,v100 holds
(v100"/\"v1)"\/"(v100"/\"(v100"\/"(v100"/\"v1))) = v100
proof let v1,v100;
v100"/\"(v100"/\"v1) = v100"/\"v1 by A92;
hence thesis by A1;
end;
A113: for v1,v100 holds
((v100"/\"v1)"/\"(v100"/\"(v100"\/"(v100"/\"v1))))"\/"((v100"/\"
(v100"/\"v1))"/\"v100) = v100"/\"(v100"/\"v1)
proof let v1,v100;
v100"/\"(v100"/\"v1) = v100"/\"v1 by A92;
hence thesis by A9;
end;
A116: for v1,v0 holds
((v0"/\"v1)"/\"(v0"/\"(v0"\/"(v0"/\"v1))))"\/"((v0"/\"v1)"/\"v0) =
v0"/\"(v0"/\"v1)
proof let v1,v0;
v0"/\"(v0"/\"v1) = v0"/\"v1 by A92;
hence thesis by A113;
end;
A118: for v1,v0 holds
((v0"/\"v1)"/\"(v0"/\"(v0"\/"(v0"/\"v1))))"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
v0"/\"(v0"/\"v1) = v0"/\"v1 by A92;
hence thesis by A116;
end;
A121: for v102,v1,v101 holds
((v101"/\"v1)"\/"v101)"\/"((v101"/\"(v102"\/"((v101"/\"v1)"\/"v101)))"/\"
(((((v101"/\"v1)"\/"v101)"\/"v101)"/\"(v102"\/"((v101"/\"v1)"\/"v101)))"\/"(
(v101"/\"v1)"\/"v101))) =
(((v101"/\"v1)"\/"v101)"\/"v101)"/\"(v102"\/"((v101"/\"v1)"\/"v101))
proof let v102,v1,v101;
((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A32;
hence thesis by A12;
end;
A124: for v2,v1,v0 holds
((v0"/\"v1)"\/"v0)"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"
((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
(((v0"/\"v1)"\/"v0)"\/"v0)"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
((v0"/\"v1)"\/"v0)"\/"v0 = v0 by A32;
hence thesis by A121;
end;
A126: for v2,v1,v0 holds
((v0"/\"v1)"\/"v0)"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"((v0"/\"
(v2"\/"((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
v0"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
((v0"/\"v1)"\/"v0)"\/"v0 = v0 by A32;
hence thesis by A124;
end;
A129: for v1,v100 holds ((v100"/\"v1)"\/"v100)"/\"v100 = v100
proof let v1,v100;
v100"/\"((v100"/\"v1)"\/"v100) = (v100"/\"v1)"\/"v100 by A105;
hence thesis by A101;
end;
A132: for v1,v0 holds (v0"/\"v1)"\/"v0 = v0
proof let v1,v0;
((v0"/\"v1)"\/"v0)"/\"v0 = (v0"/\"v1)"\/"v0 by A88;
hence thesis by A129;
end;
A135: for v1,v2,v0 holds
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
((v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2))"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2) = v0"/\"v2 by A16;
hence thesis by A105;
end;
A137: for v1,v2,v0 holds
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
(v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2) = v0"/\"v2 by A16;
hence thesis by A135;
end;
A139: for v2,v1,v0 holds
v0"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"((v0"/\"(v2"\/"
((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
v0"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
(v0"/\"v1)"\/"v0 = v0 by A132;
hence thesis by A126;
end;
A142: for v1,v2,v0 holds
(v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"((v0"/\"v2)"\/"v0)))"\/"
((v0"/\"v2)"\/"v0)))) = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
(v0"/\"v2)"\/"v0 = v0 by A132;
hence thesis by A139;
end;
A144: for v2,v0,v1 holds
v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"v0))"\/"((v0"/\"v2)"\/"v0))) =
v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v2,v0,v1;
(v0"/\"v2)"\/"v0 = v0 by A132;
hence thesis by A142;
end;
A146: for v1,v2,v0 holds
v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"v0))"\/"v0)) =
v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
(v0"/\"v2)"\/"v0 = v0 by A132;
hence thesis by A144;
end;
A148: for v1,v2,v0 holds
v0"\/"((v0"/\"(v1"\/"v0))"/\"v0) = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
(v0"/\"(v1"\/"v0))"\/"v0 = v0 by A132;
hence thesis by A146;
end;
A150: for v1,v2,v0 holds v0"\/"v0 = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
(v0"/\"(v1"\/"v0))"/\"v0 = v0 by A101;
hence thesis by A148;
end;
A152: for v1,v2,v0 holds v0 = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
v0"\/"v0 = v0 by A83;
hence thesis by A150;
end;
A154: for v0,v1 holds v0 = v0"/\"(v1"\/"v0)
proof
now let v1,v2,v0;
(v0"/\"v2)"\/"v0 = v0 by A132;
hence v0 = v0"/\"(v1"\/"v0) by A152;
end;
hence thesis;
end;
A157: for v1,v2,v0 holds
v0"/\"(v1"\/"(v0"/\"v2)) = (v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
v0"/\"(v1"\/"(v0"/\"v2)) by A154;
hence thesis by A137;
end;
A161: for v1,v0 holds v0"/\"(v0"\/"(v0"/\"v1)) = v0
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"(v0"/\"v1))) =
v0"/\"(v0"\/"(v0"/\"v1)) by A157;
hence thesis by A109;
end;
A163: for v1,v0 holds ((v0"/\"v1)"/\"v0)"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
v0"/\"(v0"\/"(v0"/\"v1)) = v0 by A161;
hence thesis by A118;
end;
A165: for v1,v0 holds (v0"/\"v1)"/\"v0 = v0"/\"v1
proof let v1,v0;
((v0"/\"v1)"/\"v0)"\/"((v0"/\"v1)"/\"v0) = (v0"/\"v1)"/\"v0 by A83;
hence thesis by A163;
end;
A168: for v1,v100 holds v100"\/"(v100"/\"v1) = v100
proof let v1,v100;
(v100"/\"v1)"/\"v100 = v100"/\"v1 by A165;
hence thesis by A86;
end;
A172: for v102,v100 holds (v100"/\"v102)"/\"(v102"/\"v100) = v102"/\"v100
proof let v102,v100;
v102"\/"(v102"/\"v100) = v102 by A168;
hence thesis by A24;
end;
A176: for v0,v1 holds (v1"/\"v0)"/\"(v0"/\"v1) = (v0"/\"v1)"/\"(v1"/\"v0)
proof let v0,v1;
(v0"/\"v1)"/\"(v1"/\"v0) = v1"/\"v0 by A172;
hence thesis by A165;
end;
A179: for v0,v1 holds v1"/\"v0 = (v1"/\"v0)"/\"(v0"/\"v1)
proof let v0,v1;
(v0"/\"v1)"/\"(v1"/\"v0) = v1"/\"v0 by A172;
hence thesis by A176;
end;
for v1,v0 holds v0"/\"v1 = v1"/\"v0
proof let v1,v0;
(v0"/\"v1)"/\"(v1"/\"v0) = v1"/\"v0 by A172;
hence thesis by A179;
end;
hence thesis by A6;
end;
theorem Lemma4:
(for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0) &
(for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0) &
(for v1,v0 holds (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0) implies
for v0,v1 holds v0 "\/" v1 = v1 "\/" v0
proof
assume A1: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0;
assume A2: for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0;
assume A3: for v1,v0 holds (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1;
assume A4: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0;
assume A5: for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0;
assume not thesis; then
consider C,D being Element of L such that
A6: C"\/"D <> D"\/"C;
A9: for v1,v0 holds
((v0"/\"v1)"/\"(v0"/\"(v0"\/"v1)))"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
hence thesis by A1;
end;
A12: for v0,v1 holds
((v0"/\"v0)"/\"(v1"/\"(v0"\/"v0)))"\/"((v0"/\"v0)"/\"v0) = v0"/\"v0
proof let v0,v1;
(v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0 by A2;
hence thesis by A1;
end;
A15: for v2,v1,v101 holds
v101"\/"(((v101"\/"v1)"/\"(v2"\/"v101))"/\"(((v101"\/"v1)"/\"
(v2"\/"v101))"\/"v101)) = (v101"\/"v1)"/\"(v2"\/"v101)
proof let v2,v1,v101;
((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
hence thesis by A1;
end;
A19: for v102,v1,v0 holds
(v0"/\"(v102"\/"(v0"/\"v1)))"/\"(v0"/\"v1) = v0"/\"v1
proof let v102,v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
hence thesis by A4;
end;
A27: for v102,v1,v0 holds
(v1"/\"(v102"\/"(v0"/\"v1)))"/\"(v0"/\"v1) = v0"/\"v1
proof let v102,v1,v0;
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1 by A3;
hence thesis by A4;
end;
A31: for v101,v100 holds ((v100"\/"v101)"/\"v100)"/\"v100 = v100
proof
now let v101,v2,v1,v100;
((v100"/\"v1)"\/"(v2"/\"v100))"\/"v100 = v100 by A5;
hence ((v100"\/"v101)"/\"v100)"/\"v100 = v100 by A4;
end;
hence thesis;
end;
A35: for v102,v2,v1,v101 holds
(v101"\/"(v102"/\"((v101"\/"v1)"/\"(v2"\/"v101))))"\/"((v101"\/"v1)"/\"
(v2"\/"v101)) = (v101"\/"v1)"/\"(v2"\/"v101)
proof let v102,v2,v1,v101;
((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
hence thesis by A5;
end;
A39: for v101,v100 holds ((v100"/\"v101)"\/"v100)"\/"v100 = v100
proof
now let v101,v2,v1,v100;
((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100 = v100 by A4;
hence ((v100"/\"v101)"\/"v100)"\/"v100 = v100 by A5;
end;
hence thesis;
end;
A49: for v1,v0 holds (v0"/\"(v0"/\"v1))"/\"(v0"/\"v1) = v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
hence thesis by A31;
end;
A52: for v1,v101 holds
(((v101"/\"v1)"\/"v101)"/\"v101)"\/"(((v101"/\"v1)"\/"v101)"/\"v101) =
(v101"/\"v1)"\/"v101
proof let v1,v101;
((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A39;
hence thesis by A1;
end;
A56: for v1,v101 holds
(v101"\/"((v101"\/"v1)"/\"v101))"\/"((v101"\/"v1)"/\"v101) =
(v101"\/"v1)"/\"v101
proof let v1,v101;
((v101"\/"v1)"/\"v101)"/\"v101 = v101 by A31;
hence thesis by A39;
end;
A67: for v0 holds v0"/\"v0 = v0 by A1,A4,A5,Lemma1;
A70: for v1,v0 holds
((v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)))"\/"(v0"/\"(v0"/\"v1)) = v0"/\"(v0"/\"v1)
proof let v1,v0;
(v0"/\"(v0"/\"v1))"/\"(v0"/\"v1) = v0"/\"v1 by A49;
hence thesis by A39;
end;
A82: for v0,v1 holds
(v0"/\"(v1"/\"(v0"\/"v0)))"\/"((v0"/\"v0)"/\"v0) = v0"/\"v0
proof let v0,v1;
v0"/\"v0 = v0 by A67;
hence thesis by A12;
end;
A84: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))"\/"(v0"/\"v0) = v0"/\"v0
proof let v0,v1;
v0"/\"v0 = v0 by A67;
hence thesis by A82;
end;
A86: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))"\/"v0 = v0"/\"v0
proof let v0,v1;
v0"/\"v0 = v0 by A67;
hence thesis by A84;
end;
A88: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))"\/"v0 = v0
proof let v0,v1;
v0"/\"v0 = v0 by A67;
hence thesis by A86;
end;
A90: for v0,v1 holds v0"\/"(v1"/\"(v0"\/"v0)) = v0
proof let v0,v1;
v0"/\"v0 = v0 by A67;
hence thesis by A2;
end;
A98: for v0 holds v0 = v0"\/"v0 by A1,A2,A3,A4,A5,Lemma2;
A101: for v0,v1 holds v0"\/"(v1"/\"v0) = v0
proof let v0,v1;
v0"\/"v0 = v0 by A98;
hence thesis by A90;
end;
A103: for v0,v1 holds (v0"/\"(v1"/\"v0))"\/"v0 = v0
proof let v0,v1;
v0"\/"v0 = v0 by A98;
hence thesis by A88;
end;
A105: for v1,v0 holds ((v0"/\"v1)"\/"v0)"/\"v0 = (v0"/\"v1)"\/"v0
proof let v1,v0;
(((v0"/\"v1)"\/"v0)"/\"v0)"\/"(((v0"/\"v1)"\/"v0)"/\"v0) =
((v0"/\"v1)"\/"v0)"/\"v0 by A98;
hence thesis by A52;
end;
A107: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"(v0"/\"v1)
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"v1 by A101;
hence thesis by A70;
end;
A109: for v1,v0 holds v0"/\"v1 = v0"/\"(v0"/\"v1)
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"v1 by A101;
hence thesis by A107;
end;
A112: for v1,v0 holds v0"\/"((v0"\/"v1)"/\"v0) = (v0"\/"v1)"/\"v0
proof let v1,v0;
v0"\/"((v0"\/"v1)"/\"v0) = v0 by A101;
hence thesis by A56;
end;
A114: for v1,v0 holds v0 = (v0"\/"v1)"/\"v0
proof let v1,v0;
v0"\/"((v0"\/"v1)"/\"v0) = v0 by A101;
hence thesis by A112;
end;
A118: for v101,v102 holds (v101"/\"(v102"\/"v101))"/\"v101 = v101
proof let v101,v102;
v101"\/"v101 = v101 by A98;
hence thesis by A4;
end;
A122: for v1,v101 holds
v101"\/"((v101"\/"v1)"/\"((v101"\/"v1)"\/"v101)) = v101"\/"v1
proof let v1,v101;
(v101"\/"v1)"/\"v101 = v101 by A114;
hence thesis by A1;
end;
A126: for v1,v0 holds v1"/\"(v0"/\"v1) = v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1 by A3;
hence thesis by A114;
end;
A130: for v1,v101 holds
(v101"/\"((v101"\/"v1)"/\"((v101"\/"v1)"\/"v101)))"\/"
(((v101"\/"v1)"/\"v101)"/\"(v101"\/"v1)) = (v101"\/"v1)"/\"v101
proof let v1,v101;
(v101"\/"v1)"/\"v101 = v101 by A114;
hence thesis by A9;
end;
A133: for v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"((v0"\/"v1)"\/"v0)))"\/"(v0"/\"(v0"\/"v1)) =
(v0"\/"v1)"/\"v0
proof let v1,v0;
(v0"\/"v1)"/\"v0 = v0 by A114;
hence thesis by A130;
end;
A135: for v1,v0 holds
(v0"/\"((v0"\/"v1)"/\"((v0"\/"v1)"\/"v0)))"\/"(v0"/\"(v0"\/"v1)) = v0
proof let v1,v0;
(v0"\/"v1)"/\"v0 = v0 by A114;
hence thesis by A133;
end;
A138: for v1,v101 holds v101"/\"((v101"/\"v1)"\/"v101) = (v101"/\"v1)"\/"v101
proof let v1,v101;
((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A39;
hence thesis by A114;
end;
A141: for v0,v1 holds (v1"/\"v0)"\/"v0 = v0
proof let v0,v1;
v0"/\"(v1"/\"v0) = v1"/\"v0 by A126;
hence thesis by A103;
end;
A145: for v1,v100 holds
(v100"/\"v1)"\/"(v100"/\"(v100"\/"(v100"/\"v1))) = v100
proof let v1,v100;
v100"/\"(v100"/\"v1) = v100"/\"v1 by A109;
hence thesis by A1;
end;
A149: for v1,v100 holds
((v100"/\"v1)"/\"(v100"/\"(v100"\/"(v100"/\"v1))))"\/"((v100"/\"
(v100"/\"v1))"/\"v100) = v100"/\"(v100"/\"v1)
proof let v1,v100;
v100"/\"(v100"/\"v1) = v100"/\"v1 by A109;
hence thesis by A9;
end;
A152: for v1,v0 holds
((v0"/\"v1)"/\"(v0"/\"(v0"\/"(v0"/\"v1))))"\/"((v0"/\"v1)"/\"v0) =
v0"/\"(v0"/\"v1)
proof let v1,v0;
v0"/\"(v0"/\"v1) = v0"/\"v1 by A109;
hence thesis by A149;
end;
A154: for v1,v0 holds
((v0"/\"v1)"/\"(v0"/\"(v0"\/"(v0"/\"v1))))"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
v0"/\"(v0"/\"v1) = v0"/\"v1 by A109;
hence thesis by A152;
end;
A157: for v102,v1,v101 holds
((v101"/\"v1)"\/"v101)"\/"((v101"/\"(v102"\/"((v101"/\"v1)"\/"v101)))"/\"
(((((v101"/\"v1)"\/"v101)"\/"v101)"/\"(v102"\/"((v101"/\"v1)"\/"v101)))"\/"
((v101"/\"v1)"\/"v101))) =
(((v101"/\"v1)"\/"v101)"\/"v101)"/\"(v102"\/"((v101"/\"v1)"\/"v101))
proof let v102,v1,v101;
((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A39;
hence thesis by A15;
end;
A160: for v2,v1,v0 holds
((v0"/\"v1)"\/"v0)"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"((v0"/\"(v2"\/"
((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
(((v0"/\"v1)"\/"v0)"\/"v0)"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
((v0"/\"v1)"\/"v0)"\/"v0 = v0 by A39;
hence thesis by A157;
end;
A162: for v2,v1,v0 holds
((v0"/\"v1)"\/"v0)"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"((v0"/\"(v2"\/"
((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
v0"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
((v0"/\"v1)"\/"v0)"\/"v0 = v0 by A39;
hence thesis by A160;
end;
A165: for v2,v1,v101 holds
((v101"\/"v1)"/\"(v2"\/"v101))"/\"(v101"\/"((v101"\/"v1)"/\"(v2"\/"v101))) =
(((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101)"\/"((v101"\/"v1)"/\"(v2"\/"v101))
proof let v2,v1,v101;
((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
hence thesis by A138;
end;
A168: for v2,v1,v0 holds
((v0"\/"v1)"/\"(v2"\/"v0))"/\"(v0"\/"((v0"\/"v1)"/\"(v2"\/"v0))) =
v0"\/"((v0"\/"v1)"/\"(v2"\/"v0))
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0 by A4;
hence thesis by A165;
end;
A171: for v1,v100 holds ((v100"/\"v1)"\/"v100)"/\"v100 = v100
proof let v1,v100;
v100"/\"((v100"/\"v1)"\/"v100) = (v100"/\"v1)"\/"v100 by A138;
hence thesis by A118;
end;
A174: for v1,v0 holds (v0"/\"v1)"\/"v0 = v0
proof let v1,v0;
((v0"/\"v1)"\/"v0)"/\"v0 = (v0"/\"v1)"\/"v0 by A105;
hence thesis by A171;
end;
A177: for v1,v2,v0 holds
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
((v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2))"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2) = v0"/\"v2 by A19;
hence thesis by A138;
end;
A179: for v1,v2,v0 holds
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
(v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2) = v0"/\"v2 by A19;
hence thesis by A177;
end;
A181: for v2,v1,v0 holds
v0"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"((v0"/\"(v2"\/"
((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
v0"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
(v0"/\"v1)"\/"v0 = v0 by A174;
hence thesis by A162;
end;
A184: for v1,v2,v0 holds
v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"((v0"/\"v2)"\/"v0)))"\/"
((v0"/\"v2)"\/"v0))) = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
(v0"/\"v2)"\/"v0 = v0 by A174;
hence thesis by A181;
end;
A186: for v2,v0,v1 holds
v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"v0))"\/"((v0"/\"v2)"\/"v0))) =
v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v2,v0,v1;
(v0"/\"v2)"\/"v0 = v0 by A174;
hence thesis by A184;
end;
A188: for v1,v2,v0 holds
v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"v0))"\/"v0)) =
v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
(v0"/\"v2)"\/"v0 = v0 by A174;
hence thesis by A186;
end;
A190: for v1,v2,v0 holds
v0"\/"((v0"/\"(v1"\/"v0))"/\"v0) = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
(v0"/\"(v1"\/"v0))"\/"v0 = v0 by A174;
hence thesis by A188;
end;
A192: for v1,v2,v0 holds v0"\/"v0 = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
(v0"/\"(v1"\/"v0))"/\"v0 = v0 by A118;
hence thesis by A190;
end;
A194: for v1,v2,v0 holds v0 = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
v0"\/"v0 = v0 by A98;
hence thesis by A192;
end;
A196: for v0,v1 holds v0 = v0"/\"(v1"\/"v0)
proof
now let v1,v2,v0;
(v0"/\"v2)"\/"v0 = v0 by A174;
hence v0 = v0"/\"(v1"\/"v0) by A194;
end;
hence thesis;
end;
A199: for v1,v2,v0 holds
v0"/\"(v1"\/"(v0"/\"v2)) = (v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
(v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
v0"/\"(v1"\/"(v0"/\"v2)) by A196;
hence thesis by A179;
end;
A203: for v2,v1,v0 holds
(v0"\/"v1)"/\"(v2"\/"v0) = v0"\/"((v0"\/"v1)"/\"(v2"\/"v0))
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"(v0"\/"((v0"\/"v1)"/\"(v2"\/"v0))) =
(v0"\/"v1)"/\"(v2"\/"v0) by A196;
hence thesis by A168;
end;
A206: for v1,v0 holds v0"/\"(v0"\/"(v0"/\"v1)) = v0
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"(v0"/\"v1))) = v0"/\"(v0"\/"(v0"/\"v1)) by A199;
hence thesis by A145;
end;
A208: for v1,v0 holds (v0"\/"v1)"/\"((v0"\/"v1)"\/"v0) = v0"\/"v1
proof let v1,v0;
v0"\/"((v0"\/"v1)"/\"((v0"\/"v1)"\/"v0)) =
(v0"\/"v1)"/\"((v0"\/"v1)"\/"v0) by A203;
hence thesis by A122;
end;
A210: for v1,v0 holds ((v0"/\"v1)"/\"v0)"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
v0"/\"(v0"\/"(v0"/\"v1)) = v0 by A206;
hence thesis by A154;
end;
A212: for v1,v0 holds (v0"/\"v1)"/\"v0 = v0"/\"v1
proof let v1,v0;
((v0"/\"v1)"/\"v0)"\/"((v0"/\"v1)"/\"v0) = (v0"/\"v1)"/\"v0 by A98;
hence thesis by A210;
end;
A214: for v1,v0 holds (v0"/\"(v0"\/"v1))"\/"(v0"/\"(v0"\/"v1)) = v0
proof let v1,v0;
(v0"\/"v1)"/\"((v0"\/"v1)"\/"v0) = v0"\/"v1 by A208;
hence thesis by A135;
end;
A216: for v1,v0 holds v0"/\"(v0"\/"v1) = v0
proof let v1,v0;
(v0"/\"(v0"\/"v1))"\/"(v0"/\"(v0"\/"v1)) = v0"/\"(v0"\/"v1) by A98;
hence thesis by A214;
end;
A219: for v101,v102,v1 holds
((v1"\/"v102)"/\"(v101"\/"v102))"/\"(v102"/\"(v1"\/"v102)) =
v102"/\"(v1"\/"v102)
proof let v101,v102,v1;
v102"/\"(v1"\/"v102) = v102 by A196;
hence thesis by A27;
end;
A222: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1"/\"(v0"\/"v1)
proof let v2,v1,v0;
v1"/\"(v0"\/"v1) = v1 by A196;
hence thesis by A219;
end;
A224: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1
proof let v2,v1,v0;
v1"/\"(v0"\/"v1) = v1 by A196;
hence thesis by A222;
end;
A227: for v1,v101 holds (v101"\/"v1)"\/"v101 = v101"\/"v1
proof let v1,v101;
v101"/\"(v101"\/"v1) = v101 by A216;
hence thesis by A101;
end;
A231: for v1,v100 holds v100"\/"(v100"/\"v1) = v100
proof let v1,v100;
(v100"/\"v1)"/\"v100 = v100"/\"v1 by A212;
hence thesis by A101;
end;
A239: for v1,v101,v100 holds ((v100"\/"v101)"/\"(v101"\/"v1))"/\"v101 = v101
proof let v1,v101,v100;
(v101"\/"v1)"\/"v101 = v101"\/"v1 by A227;
hence thesis by A224;
end;
A249: for v1,v0 holds v0"/\"v1 = v1"/\"v0 by A1,A2,A3,A4,A5,Lemma3;
A251: for v2,v1,v0 holds v1"/\"((v0"\/"v1)"/\"(v1"\/"v2)) = v1
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))"/\"v1 = v1"/\"((v0"\/"v1)"/\"(v1"\/"v2)) by A249;
hence thesis by A239;
end;
A255: for v103,v100 holds
(v100"\/"v103)"\/"((v100"\/"v103)"/\"(v103"\/"v100)) =
(v100"\/"v103)"/\"(v103"\/"v100)
proof let v103,v100;
v103"/\"((v100"\/"v103)"/\"(v103"\/"v100)) = v103 by A251;
hence thesis by A35;
end;
A258: for v1,v0 holds v0"\/"v1 = (v0"\/"v1)"/\"(v1"\/"v0)
proof let v1,v0;
(v0"\/"v1)"\/"((v0"\/"v1)"/\"(v1"\/"v0)) = v0"\/"v1 by A231;
hence thesis by A255;
end;
A262: for v0,v1 holds (v1"\/"v0)"\/"(v0"\/"v1) = v1"\/"v0
proof let v0,v1;
(v0"\/"v1)"/\"(v1"\/"v0) = v0"\/"v1 by A258;
hence thesis by A101;
end;
A266: for v1,v0 holds (v0"\/"v1)"\/"(v1"\/"v0) = v1"\/"v0
proof let v1,v0;
(v0"\/"v1)"/\"(v1"\/"v0) = v0"\/"v1 by A258;
hence thesis by A141;
end;
for v1,v0 holds v0"\/"v1 = v1"\/"v0
proof let v1,v0;
(v0"\/"v1)"\/"(v1"\/"v0) = v0"\/"v1 by A262;
hence thesis by A266;
end;
hence thesis by A6;
end;
definition let L be non empty LattStr;
attr L is satisfying_WAL31 means
for v1,v0 being Element of L holds
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0;
attr L is satisfying_WAL32 means
for v0,v1 being Element of L holds
(v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0;
attr L is satisfying_WAL33 means
for v1,v0 being Element of L holds
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1;
attr L is satisfying_WAL34 means
for v2,v1,v0 being Element of L holds
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0;
attr L is satisfying_WAL35 means
for v2,v1,v0 being Element of L holds
((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0;
end;
registration
cluster trivial -> satisfying_WAL31 satisfying_WAL32 satisfying_WAL33
satisfying_WAL34 satisfying_WAL35 for non empty LattStr;
coherence by STRUCT_0:def 10;
end;
registration
cluster satisfying_WAL31 satisfying_WAL32 satisfying_WAL33 satisfying_WAL34
satisfying_WAL35 -> join-idempotent meet-idempotent
join-commutative meet-commutative for non empty LattStr;
coherence
proof
let L be non empty LattStr;
assume
a1: L is satisfying_WAL31 satisfying_WAL32 satisfying_WAL33
satisfying_WAL34 satisfying_WAL35; then
A2: for v0,v1 being Element of L holds v0 "/\" v1 = v1 "/\" v0 by Lemma3;
for v0,v1 being Element of L holds v0 "\/" v1 = v1 "\/" v0 by a1,Lemma4;
hence thesis by A2,a1,Lemma2,LATTICES:def 4,def 6,Lemma1;
end;
end;
begin :: Short Single Axiom for WAL: WAL-4
definition let L be non empty LattStr;
attr L is satisfying_WAL4 means
for v2,v0,v5,v4,v3,v1 being Element of L holds
(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"
(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"v2)) = v1;
end;
reserve v108,v107,v106,v101,v10,v9,v8,v7,v6,v105,v102,v100,
v104,v103,v5,v4,v3,v2,v1,v0 for Element of L;
theorem LemmaW1:
(for v2,v0,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"v2)))=v1) implies
for v0 holds v0"/\"v0 = v0
proof
assume A1: for v2,v0,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"v2)))=v1;
assume not thesis; then
consider C being Element of L such that
A2: not (C"/\"C)=C;
A5: for v102,v100,v104,v103,v1,v0 holds
((((v100"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))"\/"(((v0"/\"v1)"\/"(v1"/\"(v0
"\/"v1)))"/\"
(v100"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))))"/\"v102)"\/"(((v100"/\"(((((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"/\"v103)"\/"(v104"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))
"\/"(
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"\/"(v1"/\"(v100"\/"(((((v0"/\"v1)"\/"(v1
"/\"
(v0"\/"v1)))"/\"v103)"\/"(v104"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"\/"((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))))))"/\"(((v100"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))"\/"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(v100"\/"((v0"/\"v1)"\/"(v1"/\"
(v0"\/"v1))))))"\/"v102)))=(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))
proof
now let v100,v102,v103,v104,v0,v5,v4,v3,v1;
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))
"\/"v103)"/\"
(v104"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))))"\/"((
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"(((((v0"/\"v1)
"\/"(v1"/\"
(v0"\/"v1)))"\/"v103)"/\"(v104"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"/\"((v0
"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))))=v1 by A1;
hence
((((v100"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))"\/"(((v0"/\"v1)"\/"(v1"/\"(v0
"\/"v1)))"/\"
(v100"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))))"/\"v102)"\/"(((v100"/\"(((((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"/\"v103)"\/"(v104"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))
"\/"(
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"\/"(v1"/\"(v100"\/"(((((v0"/\"v1)"\/"(v1
"/\"
(v0"\/"v1)))"/\"v103)"\/"(v104"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"\/"((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))))))"/\"(((v100"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))"\/"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(v100"\/"((v0"/\"v1)"\/"(v1"/\"
(v0"\/"v1))))))"\/"v102)))=((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))) by A1;
end;
hence thesis;
end;
A9: for v103,v100,v105,v104,v0,v5,v4,v3,v1 holds
((((v100"/\"v1)"\/"(((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"
v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))"\/"((
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))))"/\"
(v100"\/"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))"\/"((
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"/\"v103)"\/"(((v100"/\"(((((((v0"/\"v1)"\/"(v1"/\"
(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))"/\"v104)"\/"(v105"/\"((((v0"/\"
v1)"\/"
(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"((((v0"/\"v1)"\/"(v1"/\"
(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"
(v100"\/"(((((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))"\/"((
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"v104)"\/"(v105"/\"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1
)))"/\"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))"\/"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))))"/\"(((v100"/\"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))
"/\"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))"\/"(((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"(v100"\/"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((
v0"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"\/"v103)))=((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"
((v0"/\"(
((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"
v1))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))
proof let v103,v100,v105,v104,v0,v5,v4,v3,v1;
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A5;
end;
A12: for v6,v0,v8,v7,v2,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"/\"v6)"\/"(((v0"/\"(((((((v2"/\"v1)"\/"(v1"/\"(v2
"\/"v1)))"/\"
((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"(((v2"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"(v0"\/"
(((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"((v2"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"((v2"/\"(
((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"
v1))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))"\/"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"\/"v6)))=((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((
v2"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))
proof let v6,v0,v8,v7,v2,v5,v4,v3,v1;
((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A9;
end;
A14: for v6,v0,v8,v7,v2,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v6)"\/"(((v0"/\"(((((((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"(((v2"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"(v0"\/"
(((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"((v2"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"((v2"/\"(
((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"
v1))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))"\/"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"\/"v6)))=((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((
v2"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))
proof let v6,v0,v8,v7,v2,v5,v4,v3,v1;
((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A12;
end;
A17: for v2,v0,v7,v8,v3,v6,v5,v4,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v7)"\/"(v8
"/\"(((
(v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(
v1"\/"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1
))))"/\"((
(v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))))))"\/"((((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v4)"/\"
(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(
v3"\/"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"
(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3
"/\"v1)"\/"
(v1"/\"(v3"\/"v1)))"\/"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))))))"\/"(((v3"/\"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(
v1"\/"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1
))))"/\"(v0"\/"
(((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"
(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))"\/"(((v3
"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"((v3"/\"(((v1
"/\"v4)"\/"
(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(
v1"\/"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"((v3"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))))"\/"((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(
(
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"((v3"/\"(
((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"
v1))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))))))))"\/"(((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(
(
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3
"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((
v3"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))
proof let v2,v0,v7,v8,v3,v6,v5,v4,v1;
((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"
(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))"\/"(((v3
"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"((v3"/\"(((v1
"/\"v4)"\/"
(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(
v1"\/"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A14;
end;
A20: for v2,v0,v3,v4,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4
"/\"v1))"\/"(((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"(v0"\/"
(((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))"/\"v3)"\/"(v4"/\"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"((v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))))"\/"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(
(
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"((v5"/\"(
((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"
v1))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(
(
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((
v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))
proof let v2,v0,v3,v4,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A17;
end;
A22: for v2,v0,v4,v3,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((((((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))"/\"v3)"\/"(v4"/\"((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))"\/"((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v0,v4,v3,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A20;
end;
A24: for v2,v0,v3,v4,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"(
((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))"\/"((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v0,v3,v4,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A22;
end;
A26: for v2,v0,v3,v4,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"
v1))"\/"(((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v0,v3,v4,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A24;
end;
A28: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(
(
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((
v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A26;
end;
A30: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"((v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((
v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A28;
end;
A32: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A30;
end;
A34: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"v2)))=((((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A32;
end;
A36: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"v2)))=v1
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A34;
end;
A39: for v102,v101,v105 holds
((((((v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"v101)"\/"(v101"/\"((
(v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"\/"v101)))"/\"v102)"\/"(v101"/\"(((
(
(v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"v101)"\/"(v101"/\"(((v105"/\"
v101)"\/"
(v101"/\"(v105"\/"v101)))"\/"v101)))"\/"v102)))=v101
proof
now let v102,v103,v104,v105,v108,v107,v106,v101;
((((v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"(((v101"/\"v103)"\/"
(v104"/\"v101))"\/"v101))"\/"(((v105"/\"(((v101"/\"v106)"\/"
(v107"/\"v101))"\/"v101))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v105"\/"(((v101"/\"v106)"\/"
(v107"/\"v101))"\/"v101))))"/\"(((v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))
"\/"((
(v101"/\"v103)"\/"(v104"/\"v101))"\/"v101))))=v101 by A1;
hence
((((((v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"v101)"\/"(v101"/\"((
(v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"\/"v101)))"/\"v102)"\/"(v101"/\"(((
(
(v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"v101)"\/"(v101"/\"(((v105"/\"
v101)"\/"(v101"/\"(v105"\/"v101)))"\/"v101)))"\/"v102)))=v101 by A36;
end;
hence thesis;
end;
A43: for v103,v100,v105,v104,v102,v0 holds
((((v100"/\"v102)"\/"(((((((v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"/\"v102)
"\/"
(v102"/\"(((v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102
"/\"((((
(v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"
(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))"/\"(v100"\/"((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102))))))"/\"v103)"\/"(((v100"/\"((((((((
(v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"
(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))"/\"v104)"\/"(v105"/\"((((((v0"/\"v102)"\/"
(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))))"\/"((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))))"\/"(v102"/\"(v100"\/"(((((((((v0"/\"v102
)"\/"
(v102"/\"(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))"/\"v104)"\/"(v105"/\"((((((v0"/\"v102)"\/"
(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))))"\/"((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))))))"/\"(((v100"/\"((((((v0"/\"v102)"\/"(
v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102))))"\/"(((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))"/\"(v100"\/"((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102))))))"\/"v103)))=((((((v0"/\"v102)"\/"(v102
"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))
proof let v103,v100,v105,v104,v102,v0;
((((((v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102
)"\/"
(v102"/\"(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(
v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))=v102 by A39;
hence thesis by A5;
end;
A46: for v3,v0,v5,v4,v1,v2 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)
"\/"(v1"/\"((
(v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(
v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1))))))"/\"v3)"\/"(((v0"/\"(((((((((v2"/\"v1)"\/"(v1
"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"((((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"
v1)))))"\/"
(v1"/\"(v0"\/"(((((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"/\"v1)"\/"
(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"(
((((
(v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))))))"/\"(((v0"/\"((((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"
v1)))"/\"(v0"\/"
((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v3)))=((((((v2"/\"
v1)"\/"
(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(
v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))
proof let v3,v0,v5,v4,v1,v2;
((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A43;
end;
A48: for v3,v0,v5,v4,v1,v2 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v3)"\/"(((v0"/\"(((((((((v2"/\"v1)"\/"
(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"((((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"
v1)))))"\/"
(v1"/\"(v0"\/"(((((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"/\"v1)"\/"
(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"(
((((
(v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))))))"/\"(((v0"/\"((((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"
v1)))"/\"(v0"\/"
((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v3)))=((((((v2"/\"
v1)"\/"
(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))
proof let v3,v0,v5,v4,v1,v2;
((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A46;
end;
A51: for v2,v0,v4,v5,v1,v3 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v4)"\/"(v5
"/\"(((((
(v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v3"/\"v1)"\/"(
v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))))"\/"(v1"/\"(v0"\/"(((((((((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"((((((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3"/\"v1)
"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"\/"
v1)))))))"/\"(
((v0"/\"((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)
"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v3"/\"v1)"\/"(
v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3
"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v4,v5,v1,v3;
((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A48;
end;
A54: for v2,v0,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4
"/\"v1))"\/"((((
((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))))"\/"(v1"/\"(v0"\/"((((((
((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"v3)"\/"(v4"/\"((((((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))))))"/\"(
((v0"/\"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v5,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A51;
end;
A56: for v2,v0,v4,v3,v1,v5 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))"/\"v3)"\/"
(v4"/\"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"
(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))))))"/\"(((v0"/\"((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))"/\"(v0"\/"
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"
v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v4,v3,v1,v5;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A54;
end;
A58: for v2,v0,v3,v4,v1,v5 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"((((((v5"/\"v1)"\/"
(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))))))"/\"(
((v0"/\"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v3,v4,v1,v5;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A56;
end;
A60: for v2,v0,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"((((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))))))"/\"(((v0"/\"((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))"/\"(v0"\/"
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"
v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(
v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v5,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A58;
end;
A62: for v5,v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"(((((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A60;
end;
A64: for v5,v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A62;
end;
A66: for v5,v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"
v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"
v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(
v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))
"\/"v1)))=v1 by A39;
hence thesis by A64;
end;
A68: for v5,v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(
v1"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))
proof let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A66;
end;
A70: for v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"v2)))=v1
proof
now let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"v2)))=v1 by A68;
end;
hence thesis;
end;
A73: for v102,v103,v104,v100,v108,v107,v106,v101 holds
((((v100"/\"v101)"\/"(v101"/\"(v100"\/"v101)))"/\"v102)"\/"(((v100"/\"((
(v101"/\"v103)"\/"(v104"/\"v101))"\/"v101))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v100"\/"(((v101"/\"v103)"\/"
(v104"/\"v101))"\/"v101))))"/\"(((v100"/\"v101)"\/"(v101"/\"
(v100"\/"v101)))"\/"v102)))=v101
proof
now let v0,v102,v103,v104,v100,v108,v107,v106,v101;
((((((v0"/\"((v101"/\"(((v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108
"/\"
(v101"\/"(((v101"\/"v106)"/\"(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"((
(v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"
v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v0"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"/\"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(((v0"/\"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v0"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"/\"(((v101"/\"v106)"\/"(v107"/\"v101))"\/"v101))
"\/"((
(v101"/\"(((v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"((
(v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))))"/\"(((((v0"/\"((v101"/\"((
(v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"
v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v0"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"/\"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(((v0"/\"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v0"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"\/"(((v101"/\"v106)"\/"(v107"/\"v101))"\/"v101))
))=(
(v101"/\"(((v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"((
(v101"\/"v106)"/\"(v107"\/"v101))"/\"v101)))) by A39;
hence
((((v100"/\"v101)"\/"(v101"/\"(v100"\/"v101)))"/\"v102)"\/"(((v100"/\"((
(v101"/\"v103)"\/"(v104"/\"v101))"\/"v101))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v100"\/"(((v101"/\"v103)"\/"
(v104"/\"v101))"\/"v101))))"/\"(((v100"/\"v101)"\/"(v101"/\"
(v100"\/"v101)))"\/"v102)))=v101 by A36;
end;
hence thesis;
end;
A77: for v102,v101,v0 holds
((v101"/\"v102)"\/"(v101"/\"(((((((v0"/\"v101)"\/"(v101"/\"(v0"\/"v101)))"/\"
v101)"\/"
(v101"/\"(((v0"/\"v101)"\/"(v101"/\"(v0"\/"v101)))"\/"v101)))"/\"v101)"\/"(v101
"/\"((((
(v0"/\"v101)"\/"(v101"/\"(v0"\/"v101)))"/\"v101)"\/"(v101"/\"(((v0"/\"v101)"\/"
(v101"/\"
(v0"\/"v101)))"\/"v101)))"\/"v101)))"\/"v102)))=v101
proof let v102,v101,v0;
((((((v0"/\"v101)"\/"(v101"/\"(v0"\/"v101)))"/\"v101)"\/"(v101"/\"(((v0"/\"v101
)"\/"
(v101"/\"(v0"\/"v101)))"\/"v101)))"/\"v101)"\/"(v101"/\"(((((v0"/\"v101)"\/"(
v101"/\"
(v0"\/"v101)))"/\"v101)"\/"(v101"/\"(((v0"/\"v101)"\/"(v101"/\"
(v0"\/"v101)))"\/"v101)))"\/"v101)))=v101 by A39;
hence thesis by A39;
end;
A80: for v1,v0 holds ((v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)))=v0
proof
now let v1,v0,v2;
((((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"v0)"\/"(v0"/\"(((v2"/\"v0)"\/"(v0"/\"
(v2"\/"v0)))"\/"v0)))"/\"v0)"\/"(v0"/\"(((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))
"/\"v0)"\/"(v0"/\"
(((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"\/"v0)))"\/"v0)))=v0 by A39;
hence ((v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)))=v0 by A77;
end;
hence thesis;
end;
A83: for v103,v102,v101 holds
((((v102"/\"((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102))))"\/"(((v101"/\"v102)
"\/"
(v102"/\"(v101"\/"v102)))"/\"(v102"\/"((v101"/\"v102)"\/"(v102"/\"
(v101"\/"v102))))))"/\"v103)"\/"(v102"/\"(((v102"/\"((v101"/\"v102)"\/"(v102
"/\"
(v101"\/"v102))))"\/"(((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))"/\"(v102"\/"
(
(v101"/\"v102)"\/"(v102"/\"(v101"\/"v102))))))"\/"v103)))=((v101"/\"v102)"\/"(
v102"/\"
(v101"\/"v102)))
proof
now let v103,v105,v104,v102,v101;
((v102"/\"(((((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))"/\"v104)"\/"(v105"/\"
(
(v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))))"\/"((v101"/\"v102)"\/"(v102"/\"
(v101"\/"v102)))))"\/"(v102"/\"(v102"\/"(((((v101"/\"v102)"\/"(v102"/\"
(v101"\/"v102)))"/\"v104)"\/"(v105"/\"((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102
)))))"\/"
((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))))))=v102 by A80;
hence
((((v102"/\"((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102))))"\/"(((v101"/\"v102)
"\/"
(v102"/\"(v101"\/"v102)))"/\"(v102"\/"((v101"/\"v102)"\/"(v102"/\"
(v101"\/"v102))))))"/\"v103)"\/"(v102"/\"(((v102"/\"((v101"/\"v102)"\/"(v102
"/\"
(v101"\/"v102))))"\/"(((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))"/\"(v102"\/"
(
(v101"/\"v102)"\/"(v102"/\"(v101"\/"v102))))))"\/"v103)))=((v101"/\"v102)"\/"(
v102"/\"(v101"\/"v102))) by A5;
end;
hence thesis;
end;
A87: for v102,v104,v103,v0,v4,v3,v1 holds
((v1"/\"v102)"\/"(((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(((((v0"/\"(((v1"/\"
v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"
v103)"\/"
(v104"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"
v3)"\/"
(v4"/\"v1))"\/"v1))))))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1
"/\"(v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"
(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(
v0"\/"v1)))"\/"
(((((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)
"\/"
(v4"/\"v1))"\/"v1))))"/\"v103)"\/"(v104"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"
(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))"\/"((v0"/\"(((v1"/\"v3)
"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))))
"/\"((((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)
)"\/"(v1"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))"\/"v102)))=((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))
proof let v102,v104,v103,v0,v4,v3,v1;
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"(v1"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))=v1 by A70;
hence thesis by A70;
end;
A90: for v1,v2,v4,v3,v0 holds
((v0"/\"v1)"\/"(v0"/\"(((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"((v2"/\"(((v0
"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))"\/"
(((v2"/\"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))
"\/"v0))))"/\"((
(v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"\/"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)
)"\/"(v0"/\"
(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))))"\/"v1)))=((v2"/\"(((v0"/\"v3)
"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))
proof
now let v1,v6,v5,v2,v4,v3,v0;
((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"(((((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))
"\/"v0))"\/"
(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))"/\"v5)"\/"(v6"/\"((v2"/\"((
(v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))))
"\/"((v2"/\"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))
"\/"v0))))))"\/"
(((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))))"/\"(((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"\/"(((((v2"/\"(((
v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))"/\"
v5)"\/"(v6"/\"(
(v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))))))"\/"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0
"/\"(v2"\/"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))))))=v0 by A70;
hence
((v0"/\"v1)"\/"(v0"/\"(((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"((v2"/\"(((v0
"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))"\/"
(((v2"/\"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))
"\/"v0))))"/\"((
(v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"\/"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)
)"\/"(v0"/\"
(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))))"\/"v1)))=((v2"/\"(((v0"/\"v3)
"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))) by
A87;
end;
hence thesis;
end;
A92: for v1,v2,v4,v3,v0 holds
((v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)))=((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))
"\/"(v0"/\"
(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))
proof let v1,v2,v4,v3,v0;
((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"
v0))"\/"(v0"/\"
(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))"\/"(((v2"/\"(((v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))"/\"(
((v2"/\"v0)"\/"
(v0"/\"(v2"\/"v0)))"\/"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(
v2"\/"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))))=v0 by A70;
hence thesis by A90;
end;
A94: for v2,v4,v3,v0 holds
v0=((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"
(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))
proof
now let v1,v2,v4,v3,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1))=v0 by A80;
hence
v0=((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)
"\/"(v4"/\"v0))"\/"v0)))) by A92;
end;
hence thesis;
end;
A100: for v3,v4,v0,v7,v6,v5,v1 holds
v1=((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"
(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(
v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))
proof
now let v103,v102,v3,v4,v0,v7,v6,v5,v1;
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(((((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"
(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"v102)
"\/"(v103"/\"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"(v6"\/"
v1))"/\"v1))"\/"
(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(
v1"\/"((
(v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"(((((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"
(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"v102)
"\/"(v103"/\"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"(v6"\/"
v1))"/\"v1))"\/"
(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))))=v1 by A73;
hence
v1=((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"
(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))) by A94;
end;
hence thesis;
end;
A106: for v6,v5,v4,v1 holds
v1=((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)
"/\"(v5"\/"v1))"/\"v1))))
proof
now let v2,v3,v6,v5,v4,v1;
((((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"
(v5"\/"v1))"/\"v1))))"/\"(((v1"/\"v2)"\/"(v3"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v4)"/\"
(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(
((v1"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"\/"(((v1"/\"v2)"\/"(v3"/\"v1))"\/"v1))))=v1 by A100;
hence
v1=((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)
"/\"(v5"\/"v1))"/\"v1)))) by A80;
end;
hence thesis;
end;
A111: for v101,v1 holds (v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))=v101
proof
now let v1,v103,v102,v101;
((((v101"/\"((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))))"\/"(((v1"/\"v101)"\/"(
v101"/\"
(v1"\/"v101)))"/\"(v101"\/"((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))))))"/\"((
(v101"/\"v102)"\/"(v103"/\"v101))"\/"v101))"\/"(v101"/\"(((v101"/\"((v1"/\"v101
)"\/"
(v101"/\"(v1"\/"v101))))"\/"(((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101)))"/\"(v101
"\/"(
(v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))))))"\/"(((v101"/\"v102)"\/"
(v103"/\"v101))"\/"v101))))=((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))) by A83;
hence ((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101)))=v101 by A94;
end;
hence thesis;
end;
A115: for v2,v1,v100 holds v100=((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100
proof let v2,v1,v100;
((v100"/\"(((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100))"\/"((((v100"\/"v1)"/\"
(v2"\/"v100))"/\"v100)"/\"(v100"\/"(((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100))))=
v100 by A106;
hence thesis by A111;
end;
A119: for v3,v2,v1,v0 holds
((v0"/\"v0)"\/"(v3"/\"(v0"\/"(((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0))))=v0
proof let v3,v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0=v0 by A115;
hence thesis by A106;
end;
A122: for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0))=v0
proof
now let v1,v3,v2,v0;
((v0"\/"v2)"/\"(v3"\/"v0))"/\"v0=v0 by A115;
hence (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0))=v0 by A119;
end;
hence thesis;
end;
A125: for v103,v102,v101 holds
((v101"/\"v102)"\/"(v103"/\"v101))"\/"v101=v101
proof let v103,v102,v101;
(((((v101"/\"v102)"\/"(v103"/\"v101))"\/"v101)"/\"(((v101"/\"v102)"\/"
(v103"/\"v101))"\/"v101))"\/"(v101"/\"((((v101"/\"v102)"\/"(v103"/\"v101))"\/"
v101)"\/"(
((v101"/\"v102)"\/"(v103"/\"v101))"\/"v101))))=(((v101"/\"v102)"\/"
(v103"/\"v101))"\/"v101) by A122;
hence thesis by A94;
end;
A129: for v101,v100 holds ((v100"\/"v101)"/\"v100)"/\"v100=v100
proof
now let v101,v2,v1,v100;
((v100"/\"v1)"\/"(v2"/\"v100))"\/"v100=v100 by A125;
hence ((v100"\/"v101)"/\"v100)"/\"v100=v100 by A115;
end;
hence thesis;
end;
A133: for v1,v0 holds (v0"/\"(v0"/\"v1))"/\"(v0"/\"v1)=v0"/\"v1
proof let v1,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1))=v0 by A80;
hence thesis by A129;
end;
A136: for v2,v1,v101 holds
((((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101)"/\"(((v101"\/"v1)"/\"(v2"\/"v101))
"/\"v101))=((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101
proof let v2,v1,v101;
((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101=v101 by A115;
hence thesis by A133;
end;
A139: for v2,v1,v0 holds
v0"/\"(((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0)=((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0=v0 by A115;
hence thesis by A136;
end;
A141: for v2,v1,v0 holds v0"/\"v0=((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0=v0 by A115;
hence thesis by A139;
end;
for v0 holds v0"/\"v0 = v0
proof
now let v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0=v0 by A115;
hence v0"/\"v0=v0 by A141;
end;
hence thesis;
end;
hence thesis by A2;
end;
theorem Lemma2:
(for v2,v0,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"v2)))=v1) implies
for v0 holds v0"\/"v0 = v0
proof
assume A1: for v2,v0,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"v2)))=v1;
assume not thesis; then
consider C being Element of L such that
A2: not (C"\/"C)=C;
A5: for v102,v100,v104,v103,v1,v0 holds
((((v100"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))"\/"(((v0"/\"v1)"\/"(v1"/\"(v0
"\/"v1)))"/\"
(v100"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))))"/\"v102)"\/"(((v100"/\"(((((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"/\"v103)"\/"(v104"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))
"\/"(
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"\/"(v1"/\"(v100"\/"(((((v0"/\"v1)"\/"(v1
"/\"
(v0"\/"v1)))"/\"v103)"\/"(v104"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"\/"((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))))))"/\"(((v100"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))"\/"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(v100"\/"((v0"/\"v1)"\/"(v1"/\"
(v0"\/"v1))))))"\/"v102)))=(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))
proof
now let v100,v102,v103,v104,v0,v5,v4,v3,v1;
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))
"\/"v103)"/\"
(v104"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))))"\/"((
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"(((((v0"/\"v1)
"\/"(v1"/\"
(v0"\/"v1)))"\/"v103)"/\"(v104"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"/\"((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))))))=v1 by A1;
hence
((((v100"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))"\/"(((v0"/\"v1)"\/"(v1"/\"(v0
"\/"v1)))"/\"
(v100"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))))"/\"v102)"\/"(((v100"/\"(((((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"/\"v103)"\/"(v104"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))
"\/"(
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"\/"(v1"/\"(v100"\/"(((((v0"/\"v1)"\/"(v1
"/\"
(v0"\/"v1)))"/\"v103)"\/"(v104"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))))"\/"((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))))))"/\"(((v100"/\"((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))))"\/"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(v100"\/"((v0"/\"v1)"\/"(v1"/\"
(v0"\/"v1))))))"\/"v102)))=((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1))) by A1;
end;
hence thesis;
end;
A9: for v103,v100,v105,v104,v0,v5,v4,v3,v1 holds
((((v100"/\"v1)"\/"(((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"
v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))"\/"((
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))))"/\"
(v100"\/"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))"\/"((
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"/\"v103)"\/"(((v100"/\"(((((((v0"/\"v1)"\/"(v1"/\"
(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))"/\"v104)"\/"(v105"/\"((((v0"/\"
v1)"\/"
(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"((((v0"/\"v1)"\/"(v1"/\"
(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0
"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"
(v100"\/"(((((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))"\/"((
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"v104)"\/"(v105"/\"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1
)))"/\"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))"\/"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))))"/\"(((v100"/\"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))
"/\"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))"\/"(((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"(v100"\/"((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((
v0"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"\/"v103)))=((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"
((v0"/\"(
((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"
v1))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"
v1)))"\/"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))
proof let v103,v100,v105,v104,v0,v5,v4,v3,v1;
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))))=v1
by A1;
hence thesis by A5;
end;
A12: for v6,v0,v8,v7,v2,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"/\"v6)"\/"(((v0"/\"(((((((v2"/\"v1)"\/"(v1"/\"(v2
"\/"v1)))"/\"
((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"(((v2"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"(v0"\/"
(((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"((v2"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"((v2"/\"(
((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"
v1))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))"\/"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"\/"v6)))=((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((
v2"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))
proof let v6,v0,v8,v7,v2,v5,v4,v3,v1;
((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A9;
end;
A14: for v6,v0,v8,v7,v2,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v6)"\/"(((v0"/\"(((((((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v3)"/\"
(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(
v2"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))))"\/"(((v2"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"(v0"\/"
(((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"((v2"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"((v2"/\"(
((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"
v1))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))"\/"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(
(
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))))))"\/"v6)))=((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((
v2"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))"\/"(((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))
"/\"v1))))"/\"
(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"\/"(
(v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"
v1))"/\"v1))"\/"
(v5"/\"(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1)))))))
proof let v6,v0,v8,v7,v2,v5,v4,v3,v1;
((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"((v2"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(v1"\/"(((v1"\/"v3)"/\"
(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v2
"/\"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1
))"\/"(v5"/\"
(v1"\/"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"((v2"/\"(((v1
"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))"\/"(v5"/\"(
v1"\/"((
(v1"\/"v3)"/\"(v4"\/"v1))"/\"v1))))"/\"(v2"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
)))))))=v1
by A1;
hence thesis by A12;
end;
A17: for v2,v0,v7,v8,v3,v6,v5,v4,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v7)"\/"(v8
"/\"(((
(v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(
v1"\/"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1
))))"/\"((
(v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))))))"\/"((((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v4)"/\"
(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(
v3"\/"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"
(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3
"/\"v1)"\/"
(v1"/\"(v3"\/"v1)))"\/"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))))))"\/"(((v3"/\"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(
v1"\/"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1
))))"/\"(v0"\/"
(((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"
(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))"\/"(((v3
"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"((v3"/\"(((v1
"/\"v4)"\/"
(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(
v1"\/"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))"/\"v7)"\/"(v8"/\"((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"((v3"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))))"\/"((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(
(
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"((v3"/\"(
((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"
v1))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))))))))"\/"(((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(
(
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3
"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((
v3"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))"\/"(((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"/\"
(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"
v1)))"\/"(
(v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"
v1))"/\"v1))"\/"
(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1)))))))
proof let v2,v0,v7,v8,v3,v6,v5,v4,v1;
((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"((v3"/\"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"
(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1)))))"\/"(((v3
"/\"((
(v1"/\"v4)"\/"(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1
))"\/"(v6"/\"
(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"
(v5"/\"v1))"\/"v1))))"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"((v3"/\"(((v1
"/\"v4)"\/"
(v5"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(
v1"\/"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(v3"\/"(((v1"/\"v4)"\/"(v5"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A14;
end;
A20: for v2,v0,v3,v4,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4
"/\"v1))"\/"(((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"(v0"\/"
(((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))"/\"v3)"\/"(v4"/\"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"((v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))))"\/"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(
(
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"((v5"/\"(
((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"
v1))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(
(
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((
v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))
proof let v2,v0,v3,v4,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A17;
end;
A22: for v2,v0,v4,v3,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((((((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))"/\"v3)"\/"(v4"/\"((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))"\/"((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v0,v4,v3,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A20;
end;
A24: for v2,v0,v3,v4,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"(
((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))"\/"((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v0,v3,v4,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A22;
end;
A26: for v2,v0,v3,v4,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"
v1))"\/"(((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))))))"/\"(((v0"/\"((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v0,v3,v4,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A24;
end;
A28: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))"\/"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(
(
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((
v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A26;
end;
A30: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"((v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))"/\"(v0"\/"((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((
v5"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"
v1)))"\/"(
(v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"
v1))"/\"v1))"\/"
(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1)))))))
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A28;
end;
A32: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))))))))"\/"v2)))=((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v6)"/\"
(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(
v5"\/"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A30;
end;
A34: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"v2)))=((((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"
((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5"/\"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
))))"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)
)"\/"(((v1"/\"(
((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))))
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A32;
end;
A36: for v2,v3,v4,v0,v5,v8,v7,v6,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))
"/\"v1))))"/\"
(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"v2)))=v1
proof let v2,v3,v4,v0,v5,v8,v7,v6,v1;
((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"((v5"/\"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(v1"\/"(((v1"\/"v6)"/\"
(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1)))))"\/"(((v5
"/\"((
(v1"/\"v6)"\/"(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1
))"\/"(v8"/\"
(v1"\/"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"
(v7"/\"v1))"\/"v1))))"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"((v5"/\"(((v1
"/\"v6)"\/"
(v7"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))"\/"(v8"/\"(
v1"\/"((
(v1"\/"v6)"/\"(v7"\/"v1))"/\"v1))))"/\"(v5"\/"(((v1"/\"v6)"\/"(v7"/\"v1))"\/"v1
)))))))=v1 by A1;
hence thesis by A34;
end;
A39: for v102,v101,v105 holds
((((((v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"v101)"\/"(v101"/\"((
(v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"\/"v101)))"/\"v102)"\/"(v101"/\"(((
(
(v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"v101)"\/"(v101"/\"(((v105"/\"
v101)"\/"
(v101"/\"(v105"\/"v101)))"\/"v101)))"\/"v102)))=v101
proof
now let v102,v103,v104,v105,v108,v107,v106,v101;
((((v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"(((v101"/\"v103)"\/"
(v104"/\"v101))"\/"v101))"\/"(((v105"/\"(((v101"/\"v106)"\/"
(v107"/\"v101))"\/"v101))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v105"\/"(((v101"/\"v106)"\/"
(v107"/\"v101))"\/"v101))))"/\"(((v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))
"\/"(((v101"/\"v103)"\/"(v104"/\"v101))"\/"v101))))=v101 by A1;
hence
((((((v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"v101)"\/"(v101"/\"((
(v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"\/"v101)))"/\"v102)"\/"(v101"/\"(((
(
(v105"/\"v101)"\/"(v101"/\"(v105"\/"v101)))"/\"v101)"\/"(v101"/\"(((v105"/\"
v101)"\/"(v101"/\"(v105"\/"v101)))"\/"v101)))"\/"v102)))=v101 by A36;
end;
hence thesis;
end;
A43: for v103,v100,v105,v104,v102,v0 holds
((((v100"/\"v102)"\/"(((((((v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"/\"v102)
"\/"
(v102"/\"(((v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102
"/\"((((
(v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"
(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))"/\"(v100"\/"((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102))))))"/\"v103)"\/"(((v100"/\"((((((((
(v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"
(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))"/\"v104)"\/"(v105"/\"((((((v0"/\"v102)"\/"
(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))))"\/"((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))))"\/"(v102"/\"(v100"\/"(((((((((v0"/\"v102
)"\/"
(v102"/\"(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))"/\"v104)"\/"(v105"/\"((((((v0"/\"v102)"\/"
(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))))"\/"((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))))))"/\"(((v100"/\"((((((v0"/\"v102)"\/"(
v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102))))"\/"(((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))"/\"(v100"\/"((((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102))))))"\/"v103)))=((((((v0"/\"v102)"\/"(v102
"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))
proof let v103,v100,v105,v104,v102,v0;
((((((v0"/\"v102)"\/"(v102"/\"(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102
)"\/"
(v102"/\"(v0"\/"v102)))"\/"v102)))"/\"v102)"\/"(v102"/\"(((((v0"/\"v102)"\/"(
v102"/\"
(v0"\/"v102)))"/\"v102)"\/"(v102"/\"(((v0"/\"v102)"\/"(v102"/\"
(v0"\/"v102)))"\/"v102)))"\/"v102)))=v102 by A39;
hence thesis by A5;
end;
A46: for v3,v0,v5,v4,v1,v2 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)
"\/"(v1"/\"((
(v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1))))))"/\"v3)"\/"(((v0"/\"(((((((((v2"/\"v1)"\/"(v1
"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"((((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"
v1)))))"\/"
(v1"/\"(v0"\/"(((((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"/\"v1)"\/"
(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"(
((((
(v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))))))"/\"(((v0"/\"((((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"
v1)))"/\"(v0"\/"
((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v3)))=((((((v2"/\"
v1)"\/"
(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))
proof let v3,v0,v5,v4,v1,v2;
((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A43;
end;
A48: for v3,v0,v5,v4,v1,v2 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v3)"\/"(((v0"/\"(((((((((v2"/\"v1)"\/"
(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"((((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"
v1)))))"\/"
(v1"/\"(v0"\/"(((((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2
"/\"v1)"\/"
(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"
v1)))"/\"v1)"\/"
(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"(
((((
(v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))))))"/\"(((v0"/\"((((((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)
"\/"(v1"/\"
(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"
v1)))"/\"(v0"\/"
((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v3)))=((((((v2"/\"
v1)"\/"
(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(
v1"/\"
(v2"\/"v1)))"\/"v1)))"\/"v1)))
proof let v3,v0,v5,v4,v1,v2;
((((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"/\"v1)"\/"(v1"/\"(((v2"/\"v1)"\/"(v1"/\"
(v2"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v2"/\"v1)"\/"(v1"/\"(v2"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A46;
end;
A51: for v2,v0,v4,v5,v1,v3 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v4)"\/"(v5
"/\"(((((
(v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v3"/\"v1)"\/"(
v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))))"\/"(v1"/\"(v0"\/"(((((((((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))"/\"v4)"\/"(v5"/\"((((((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3"/\"v1)
"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"\/"
v1)))))))"/\"(
((v0"/\"((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)
"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v3"/\"v1)"\/"(
v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3
"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v4,v5,v1,v3;
((((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"/\"v1)"\/"(v1"/\"(((v3"/\"v1)"\/"(v1"/\"
(v3"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v3"/\"v1)"\/"(v1"/\"(v3"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A48;
end;
A54: for v2,v0,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4
"/\"v1))"\/"((((
((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))))"\/"(v1"/\"(v0"\/"((((((
((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"v3)"\/"(v4"/\"((((((v5
"/\"v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))))))"/\"(
((v0"/\"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v5,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A51;
end;
A56: for v2,v0,v4,v3,v1,v5 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))"/\"v3)"\/"
(v4"/\"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"
(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))))))"/\"(((v0"/\"((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))"/\"(v0"\/"
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"
v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v4,v3,v1,v5;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A54;
end;
A58: for v2,v0,v3,v4,v1,v5 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"((((((v5"/\"v1)"\/"
(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))))"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))))))"/\"(
((v0"/\"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v3,v4,v1,v5;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A56;
end;
A60: for v2,v0,v5,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"((((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))))))"/\"(((v0"/\"((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"
v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))"/\"(v0"\/"
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"
v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v2,v0,v5,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A58;
end;
A62: for v5,v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"(((((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))"\/"(((((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"
(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5
"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A60;
end;
A64: for v5,v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1
"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))"/\"(v0"\/"((((((v5"/\"v1)
"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"
v1)"\/"(v1"/\"((
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A62;
end;
A66: for v5,v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"
v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1))))))"\/"v2)))=((((((v5"/\"
v1)"\/"
(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)
))"/\"v1)"\/"
(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"\/"v1)))"\/"v1)))
proof let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A64;
end;
A68: for v5,v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"v2)))=((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(
v1"/\"((
(v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(
v1"/\"
(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"
v1)))
proof let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence thesis by A66;
end;
A70: for v2,v0,v4,v3,v1 holds
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"v2)))=v1
proof
now let v5,v2,v0,v4,v3,v1;
((((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"/\"v1)"\/"(v1"/\"(((v5"/\"v1)"\/"(v1"/\"
(v5"\/"v1)))"\/"v1)))"/\"v1)"\/"(v1"/\"(((((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))
"/\"v1)"\/"(v1"/\"
(((v5"/\"v1)"\/"(v1"/\"(v5"\/"v1)))"\/"v1)))"\/"v1)))=v1 by A39;
hence
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"v2)"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"v2)))=v1 by A68;
end;
hence thesis;
end;
A73: for v102,v103,v104,v100,v108,v107,v106,v101 holds
((((v100"/\"v101)"\/"(v101"/\"(v100"\/"v101)))"/\"v102)"\/"(((v100"/\"((
(v101"/\"v103)"\/"(v104"/\"v101))"\/"v101))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v100"\/"(((v101"/\"v103)"\/"
(v104"/\"v101))"\/"v101))))"/\"(((v100"/\"v101)"\/"(v101"/\"
(v100"\/"v101)))"\/"v102)))=v101
proof
now let v0,v102,v103,v104,v100,v108,v107,v106,v101;
((((((v0"/\"((v101"/\"(((v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108
"/\"
(v101"\/"(((v101"\/"v106)"/\"(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"((
(v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"
v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v0"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"/\"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(((v0"/\"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v0"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"/\"(((v101"/\"v106)"\/"(v107"/\"v101))"\/"v101))
"\/"((
(v101"/\"(((v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"((
(v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))))"/\"(((((v0"/\"((v101"/\"((
(v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"
v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v0"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"/\"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(((v0"/\"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v0"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"\/"((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101)))))))"\/"(((v101"/\"v106)"\/"(v107"/\"v101))"\/"v101))
))=(
(v101"/\"(((v101"\/"v106)"/\"(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"((
(v101"\/"v106)"/\"(v107"\/"v101))"/\"v101)))) by A39;
hence
((((v100"/\"v101)"\/"(v101"/\"(v100"\/"v101)))"/\"v102)"\/"(((v100"/\"((
(v101"/\"v103)"\/"(v104"/\"v101))"\/"v101))"\/"(((v101"/\"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))"\/"(v108"/\"(v101"\/"(((v101"\/"v106)"/\"
(v107"\/"v101))"/\"v101))))"/\"(v100"\/"(((v101"/\"v103)"\/"
(v104"/\"v101))"\/"v101))))"/\"(((v100"/\"v101)"\/"(v101"/\"
(v100"\/"v101)))"\/"v102)))=v101 by A36;
end;
hence thesis;
end;
A77: for v102,v101,v0 holds
((v101"/\"v102)"\/"(v101"/\"(((((((v0"/\"v101)"\/"(v101"/\"(v0"\/"v101)))"/\"
v101)"\/"
(v101"/\"(((v0"/\"v101)"\/"(v101"/\"(v0"\/"v101)))"\/"v101)))"/\"v101)"\/"(v101
"/\"((((
(v0"/\"v101)"\/"(v101"/\"(v0"\/"v101)))"/\"v101)"\/"(v101"/\"(((v0"/\"v101)"\/"
(v101"/\"
(v0"\/"v101)))"\/"v101)))"\/"v101)))"\/"v102)))=v101
proof let v102,v101,v0;
((((((v0"/\"v101)"\/"(v101"/\"(v0"\/"v101)))"/\"v101)"\/"(v101"/\"(((v0"/\"v101
)"\/"
(v101"/\"(v0"\/"v101)))"\/"v101)))"/\"v101)"\/"(v101"/\"(((((v0"/\"v101)"\/"(
v101"/\"
(v0"\/"v101)))"/\"v101)"\/"(v101"/\"(((v0"/\"v101)"\/"(v101"/\"
(v0"\/"v101)))"\/"v101)))"\/"v101)))=v101 by A39;
hence thesis by A39;
end;
A80: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1))=v0
proof
now let v1,v0,v2;
((((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"v0)"\/"(v0"/\"(((v2"/\"v0)"\/"(v0"/\"
(v2"\/"v0)))"\/"v0)))"/\"v0)"\/"(v0"/\"(((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))
"/\"v0)"\/"(v0"/\"
(((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"\/"v0)))"\/"v0)))=v0 by A39;
hence ((v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)))=v0 by A77;
end;
hence thesis;
end;
A83: for v103,v102,v101 holds
((((v102"/\"((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102))))"\/"(((v101"/\"v102)
"\/"
(v102"/\"(v101"\/"v102)))"/\"(v102"\/"((v101"/\"v102)"\/"(v102"/\"
(v101"\/"v102))))))"/\"v103)"\/"(v102"/\"(((v102"/\"((v101"/\"v102)"\/"(v102
"/\"
(v101"\/"v102))))"\/"(((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))"/\"(v102"\/"
(
(v101"/\"v102)"\/"(v102"/\"(v101"\/"v102))))))"\/"v103)))=((v101"/\"v102)"\/"(
v102"/\"(v101"\/"v102)))
proof
now let v103,v105,v104,v102,v101;
((v102"/\"(((((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))"/\"v104)"\/"(v105"/\"
(
(v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))))"\/"((v101"/\"v102)"\/"(v102"/\"
(v101"\/"v102)))))"\/"(v102"/\"(v102"\/"(((((v101"/\"v102)"\/"(v102"/\"
(v101"\/"v102)))"/\"v104)"\/"(v105"/\"((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102
)))))"\/"
((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))))))=v102 by A80;
hence
((((v102"/\"((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102))))"\/"(((v101"/\"v102)
"\/"
(v102"/\"(v101"\/"v102)))"/\"(v102"\/"((v101"/\"v102)"\/"(v102"/\"
(v101"\/"v102))))))"/\"v103)"\/"(v102"/\"(((v102"/\"((v101"/\"v102)"\/"(v102
"/\"
(v101"\/"v102))))"\/"(((v101"/\"v102)"\/"(v102"/\"(v101"\/"v102)))"/\"(v102"\/"
(
(v101"/\"v102)"\/"(v102"/\"(v101"\/"v102))))))"\/"v103)))=((v101"/\"v102)"\/"(
v102"/\"(v101"\/"v102))) by A5;
end;
hence thesis;
end;
A87: for v102,v104,v103,v0,v4,v3,v1 holds
((v1"/\"v102)"\/"(((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(((((v0"/\"(((v1"/\"
v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"
v103)"\/"
(v104"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"
v3)"\/"
(v4"/\"v1))"\/"v1))))))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1
"/\"(v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))"\/"(((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"
(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(((v0"/\"v1)"\/"(v1"/\"(
v0"\/"v1)))"\/"
(((((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)
"\/"
(v4"/\"v1))"\/"v1))))"/\"v103)"\/"(v104"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"
(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))"\/"((v0"/\"(((v1"/\"v3)
"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))))
"/\"((((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)
)"\/"(v1"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))"\/"v102)))=((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))
proof let v102,v104,v103,v0,v4,v3,v1;
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"(v1"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(v1"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"(
((v0"/\"v1)"\/"
(v1"/\"(v0"\/"v1)))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(v1"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))))))=v1 by A70;
hence thesis by A70;
end;
A90: for v1,v2,v4,v3,v0 holds
((v0"/\"v1)"\/"(v0"/\"(((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"((v2"/\"(((v0
"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))"\/"
(((v2"/\"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))
"\/"v0))))"/\"((
(v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"\/"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)
)"\/"(v0"/\"
(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))))"\/"v1)))=((v2"/\"(((v0"/\"v3)
"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))
proof
now let v1,v6,v5,v2,v4,v3,v0;
((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"(((((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))
"\/"v0))"\/"
(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))"/\"v5)"\/"(v6"/\"((v2"/\"((
(v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))))
"\/"((v2"/\"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))
"\/"v0))))))"\/"
(((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))))"/\"(((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"\/"(((((v2"/\"(((
v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))"/\"
v5)"\/"(v6"/\"(
(v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))))))"\/"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0
"/\"(v2"\/"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))))))=v0 by A70;
hence
((v0"/\"v1)"\/"(v0"/\"(((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"((v2"/\"(((v0
"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))"\/"
(((v2"/\"((
(v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))
"\/"v0))))"/\"((
(v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"\/"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)
)"\/"(v0"/\"
(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))))"\/"v1)))=((v2"/\"(((v0"/\"v3)
"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))) by
A87;
end;
hence thesis;
end;
A92: for v1,v2,v4,v3,v0 holds
((v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)))=((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))
"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))
proof let v1,v2,v4,v3,v0;
((((v2"/\"v0)"\/"(v0"/\"(v2"\/"v0)))"/\"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"
v0))"\/"(v0"/\"
(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))"\/"(((v2"/\"(((v0"/\"v3)"\/"
(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))))"/\"(
((v2"/\"v0)"\/"
(v0"/\"(v2"\/"v0)))"\/"((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(
v2"\/"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0)))))))=v0 by A70;
hence thesis by A90;
end;
A94: for v2,v4,v3,v0 holds
v0=((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)
"\/"(v4"/\"v0))"\/"v0))))
proof
now let v1,v2,v4,v3,v0;
(v0"/\"v1)"\/"(v0"/\"(v0"\/"v1))=v0 by A80;
hence
v0=((v2"/\"(((v0"/\"v3)"\/"(v4"/\"v0))"\/"v0))"\/"(v0"/\"(v2"\/"(((v0"/\"v3)
"\/"(v4"/\"v0))"\/"v0)))) by A92;
end;
hence thesis;
end;
A100: for v3,v4,v0,v7,v6,v5,v1 holds
v1=((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"
(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(
v0"\/"((
(v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))
proof
now let v103,v102,v3,v4,v0,v7,v6,v5,v1;
((((v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"/\"(((((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))
"\/"v1))"\/"((
(v1"/\"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"
(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"v102)
"\/"(v103"/\"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"(v6"\/"
v1))"/\"v1))"\/"
(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))"\/"(((v0"/\"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(
v1"\/"((
(v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1
))))"/\"((
(v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)))"\/"(((((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"
v1))"\/"((
(v1"/\"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"
(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))"/\"v102)
"\/"(v103"/\"(
(v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"(v6"\/"
v1))"/\"v1))"\/"
(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(v0"\/"(((v1"/\"v3)"\/"
(v4"/\"v1))"\/"v1))))))"\/"((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1
"/\"((
(v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))
"/\"v1))))"/\"
(v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))))))))=v1 by A73;
hence
v1=((v0"/\"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1"\/"v5)"/\"
(v6"\/"v1))"/\"v1))"\/"(v7"/\"(v1"\/"(((v1"\/"v5)"/\"(v6"\/"v1))"/\"v1))))"/\"(
v0"\/"(((v1"/\"v3)"\/"(v4"/\"v1))"\/"v1)))) by A94;
end;
hence thesis;
end;
A106: for v6,v5,v4,v1 holds
v1=((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)
"/\"(v5"\/"v1))"/\"v1))))
proof
now let v2,v3,v6,v5,v4,v1;
((((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"
(v5"\/"v1))"/\"v1))))"/\"(((v1"/\"v2)"\/"(v3"/\"v1))"\/"v1))"\/"(((v1"/\"(((v1
"\/"v4)"/\"
(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))))"/\"(
((v1"/\"((
(v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)"/\"(v5"\/"v1))
"/\"v1))))"\/"((
(v1"/\"v2)"\/"(v3"/\"v1))"\/"v1))))=v1 by A100;
hence
v1=((v1"/\"(((v1"\/"v4)"/\"(v5"\/"v1))"/\"v1))"\/"(v6"/\"(v1"\/"(((v1"\/"v4)
"/\"(v5"\/"v1))"/\"v1)))) by A80;
end;
hence thesis;
end;
A111: for v101,v1 holds (v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))=v101
proof
now let v1,v103,v102,v101;
((((v101"/\"((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))))"\/"(((v1"/\"v101)"\/"(
v101"/\"
(v1"\/"v101)))"/\"(v101"\/"((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))))))"/\"((
(v101"/\"v102)"\/"(v103"/\"v101))"\/"v101))"\/"(v101"/\"(((v101"/\"((v1"/\"v101
)"\/"
(v101"/\"(v1"\/"v101))))"\/"(((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101)))"/\"(v101
"\/"(
(v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))))))"\/"(((v101"/\"v102)"\/"
(v103"/\"v101))"\/"v101))))=((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101))) by A83;
hence ((v1"/\"v101)"\/"(v101"/\"(v1"\/"v101)))=v101 by A94;
end;
hence thesis;
end;
A115: for v2,v1,v100 holds v100=((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100
proof let v2,v1,v100;
((v100"/\"(((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100))"\/"((((v100"\/"v1)"/\"
(v2"\/"v100))"/\"v100)"/\"(v100"\/"(((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100))))=
v100 by A106;
hence thesis by A111;
end;
A119: for v3,v2,v1,v0 holds
(v0"/\"v0)"\/"(v3"/\"(v0"\/"(((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0)))=v0
proof let v3,v2,v1,v0;
((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0=v0 by A115;
hence thesis by A106;
end;
A122: for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0))=v0
proof
now let v1,v3,v2,v0;
((v0"\/"v2)"/\"(v3"\/"v0))"/\"v0=v0 by A115;
hence (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0))=v0 by A119;
end;
hence thesis;
end;
A129: for v100 holds (v100"/\"v100)"\/"(v100"\/"v100)=v100
proof
now let v2,v1,v100;
((((v100"\/"v100)"\/"v1)"/\"(v2"\/"(v100"\/"v100)))"/\"(v100"\/"v100))=(v100
"\/"v100) by A115;
hence (v100"/\"v100)"\/"(v100"\/"v100)=v100 by A122;
end;
hence thesis;
end;
A133: for v0 holds ((v0"/\"v0)"/\"(v0"\/"v0))"\/"((v0"/\"v0)"/\"v0)=v0"/\"v0
proof let v0;
(v0"/\"v0)"\/"(v0"\/"v0)=v0 by A129;
hence thesis by A80;
end;
A136: for v0 holds ((v0"/\"v0)"/\"(v0"\/"v0))"\/"((v0"\/"v0)"/\"v0)=v0"\/"v0
proof let v0;
(v0"/\"v0)"\/"(v0"\/"v0)=v0 by A129;
hence thesis by A111;
end;
A155: for v0 holds (v0"/\"(v0"\/"v0))"\/"((v0"\/"v0)"/\"v0)=v0"\/"v0
proof let v0;
v0"/\"v0=v0 by A1,LemmaW1;
hence thesis by A136;
end;
A157: for v0 holds (v0"/\"(v0"\/"v0))"\/"((v0"/\"v0)"/\"v0)=v0"/\"v0
proof let v0;
v0"/\"v0=v0 by A1,LemmaW1;
hence thesis by A133;
end;
A159: for v0 holds (v0"/\"(v0"\/"v0))"\/"(v0"/\"v0)=v0"/\"v0
proof let v0;
v0"/\"v0=v0 by A1,LemmaW1;
hence thesis by A157;
end;
A161: for v0 holds (v0"/\"(v0"\/"v0))"\/"v0=v0"/\"v0
proof let v0;
v0"/\"v0=v0 by A1,LemmaW1;
hence thesis by A159;
end;
A163: for v0 holds (v0"/\"(v0"\/"v0))"\/"v0=v0
proof let v0;
v0"/\"v0=v0 by A1,LemmaW1;
hence thesis by A161;
end;
A166: for v102 holds (v102"\/"v102)"/\"v102=v102
proof let v102;
(v102"\/"v102)"/\"(v102"\/"v102)=v102"\/"v102 by A1,LemmaW1;
hence thesis by A115;
end;
A169: for v0 holds (v0"/\"(v0"\/"v0))"\/"v0=v0"\/"v0
proof let v0;
(v0"\/"v0)"/\"v0=v0 by A166;
hence thesis by A155;
end;
for v0 holds v0=v0"\/"v0
proof let v0;
(v0"/\"(v0"\/"v0))"\/"v0=v0 by A163;
hence thesis by A169;
end;
hence thesis by A2;
end;
registration
cluster trivial -> satisfying_WAL4 for non empty LattStr;
coherence by STRUCT_0:def 10;
end;
registration
cluster satisfying_WAL4 -> join-idempotent meet-idempotent
for non empty LattStr;
coherence by Lemma2,LemmaW1;
end;