 reserve L for non empty LattStr;
 reserve v64,v65,v66,v67,v103,v3,v102,v101,v100,v2,v1,v0 for Element of L;
 reserve L for distributive join-commutative meet-commutative
   non empty LattStr;
 reserve v0,v1,v2 for Element of L;
 reserve L for non empty LattStr;
 reserve v103,v3,v102,v101,v100,v2,v1,v0 for Element of L;

theorem MainMcKenzie:
(L is satisfying_McKenzie_1 satisfying_McKenzie_2 &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v1"/\"v2))"\/"v1 = v1) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v1"\/"v2))"/\"v1 = v1))
implies
((for v1,v0 holds (v0"/\"(v0"\/"v1))=v0) &
(for v1,v0 holds (v0"\/"(v0"/\"v1))=v0) &
L is join-commutative meet-commutative meet-associative join-associative)
proof
assume A2: L is satisfying_McKenzie_1;
assume A3: L is satisfying_McKenzie_2;
assume A4: for v2,v1,v0 holds (((v0"/\"v1)"\/"(v1"/\"v2))"\/"v1)=v1;
assume A5: for v2,v1,v0 holds (((v0"\/"v1)"/\"(v1"\/"v2))"/\"v1)=v1;
A9: for v100,v101 holds (v100"\/"(v101"/\"v100))=v100
proof
 now let v101,v1,v2,v100;
(v100"/\"(v1"\/"(v100"\/"v2)))=v100 by A3;
hence (v100"\/"(v101"/\"v100))=v100 by A2;
end;
hence thesis;
end;

A13: for v100,v101 holds (v100"/\"(v101"\/"v100))=v100
proof
 now let v101,v1,v2,v100;
(v100"\/"(v1"/\"(v100"/\"v2)))=v100 by A2;
hence (v100"/\"(v101"\/"v100))=v100 by A3;
end;
hence thesis;
end;

A17: for v101,v100 holds ((v100"/\"v101)"\/"v101)=v101
proof
 now let v2,v101,v100;
((v100"/\"v101)"\/"(v101"/\"((v100"/\"v101)"/\"v2)))=(v100"/\"v101) by A2;
hence ((v100"/\"v101)"\/"v101)=v101 by A4;
end;
hence thesis;
end;

A21: for v102,v100 holds (v100"/\"(v100"\/"v102))=v100
proof
 now let v2,v0,v102,v100;
(((v0"/\"(v100"\/"v102))"\/"((v100"\/"v102)"/\"v2))"\/"(v100"\/"v102))
=(v100"\/"v102)
 by A4;
hence (v100"/\"(v100"\/"v102))=v100 by A3;
end;
hence thesis;
end;

A25: for v102,v1,v2,v100 holds
 ((v100"\/"((v1"\/"(v100"\/"v2))"/\"v102))"\/"(v1"\/"(v100"\/"v2)))=
 (v1"\/"(v100"\/"v2))
proof let v102,v1,v2,v100;
(v100"/\"(v1"\/"(v100"\/"v2)))=v100 by A3;
hence thesis by A4;
end;

A33: for v102,v100 holds (v100"\/"(v100"/\"v102))=v100
proof
 now let v2,v0,v102,v100;
(((v0"\/"(v100"/\"v102))"/\"((v100"/\"v102)"\/"v2))"/\"(v100"/\"v102))=
(v100"/\"v102)
 by A5;
hence (v100"\/"(v100"/\"v102))=v100 by A2;
end;
hence thesis;
end;

A37: for v102,v1,v2,v100 holds
 ((v100"/\"((v1"/\"(v100"/\"v2))"\/"v102))"/\"(v1"/\"(v100"/\"v2)))=
 (v1"/\"(v100"/\"v2))
proof let v102,v1,v2,v100;
(v100"\/"(v1"/\"(v100"/\"v2)))=v100 by A2;
hence thesis by A5;
end;

A41: for v101,v100 holds ((v100"\/"v101)"/\"v101)=v101
proof
 now let v2,v101,v100;
((v100"\/"v101)"/\"(v101"\/"((v100"\/"v101)"\/"v2)))=(v100"\/"v101) by A3;
hence ((v100"\/"v101)"/\"v101)=v101 by A5;
end;
hence thesis;
end;

A49: for v102,v100,v1 holds
 ((v100"/\"((v1"/\"v100)"\/"v102))"/\"(v1"/\"v100))=(v1"/\"v100)
proof let v102,v100,v1;
(v100"\/"(v1"/\"v100))=v100 by A9;
hence thesis by A5;
end;

A53: for v102,v100,v1 holds
 ((v100"\/"((v1"\/"v100)"/\"v102))"\/"(v1"\/"v100))=(v1"\/"v100)
proof let v102,v100,v1;
(v100"/\"(v1"\/"v100))=v100 by A13;
hence thesis by A4;
end;

A57: for v1,v2,v100 holds (v100"\/"(v1"\/"(v100"\/"v2)))=(v1"\/"(v100"\/"v2))
proof let v1,v2,v100;
(v100"/\"(v1"\/"(v100"\/"v2)))=v100 by A3;
hence thesis by A17;
end;

A61: for v100,v1 holds (v100"\/"(v1"\/"v100))=(v1"\/"v100)
proof let v100,v1;
(v100"/\"(v1"\/"v100))=v100 by A13;
hence thesis by A17;
end;

A65: for v1,v101 holds ((v101"\/"v1)"\/"v101)=(v101"\/"v1)
proof let v1,v101;
(v101"/\"(v101"\/"v1))=v101 by A21;
hence thesis by A9;
end;

A69: for v1,v100 holds (v100"\/"(v100"\/"v1))=(v100"\/"v1)
proof let v1,v100;
(v100"/\"(v100"\/"v1))=v100 by A21;
hence thesis by A17;
end;

A73: for v1,v101 holds ((v101"/\"v1)"/\"v101)=(v101"/\"v1)
proof let v1,v101;
(v101"\/"(v101"/\"v1))=v101 by A33;
hence thesis by A13;
end;

A77: for v1,v2,v100 holds (v100"/\"(v1"/\"(v100"/\"v2)))=(v1"/\"(v100"/\"v2))
proof let v1,v2,v100;
(v100"\/"(v1"/\"(v100"/\"v2)))=v100 by A2;
hence thesis by A41;
end;

A81: for v100,v1 holds (v100"/\"(v1"/\"v100))=(v1"/\"v100)
proof let v100,v1;
(v100"\/"(v1"/\"v100))=v100 by A9;
hence thesis by A41;
end;

A85: for v1,v2,v101 holds
 ((v1"/\"(v101"/\"v2))"\/"v101)=(v101"\/"(v1"/\"(v101"/\"v2)))
proof let v1,v2,v101;
(v101"\/"(v1"/\"(v101"/\"v2)))=v101 by A2;
hence thesis by A61;
end;

A88: for v0,v2,v1 holds ((v0"/\"(v1"/\"v2))"\/"v1)=v1
proof let v0,v2,v1;
(v1"\/"(v0"/\"(v1"/\"v2)))=v1 by A2;
hence thesis by A85;
end;

A91: for v1,v101 holds ((v101"/\"v1)"\/"v101)=(v101"\/"(v101"/\"v1))
proof let v1,v101;
(v101"\/"(v101"/\"v1))=v101 by A33;
hence thesis by A61;
end;

A94: for v1,v0 holds ((v0"/\"v1)"\/"v0)=v0
proof let v1,v0;
(v0"\/"(v0"/\"v1))=v0 by A33;
hence thesis by A91;
end;

A97: for v1,v102,v100 holds (v100"/\"((v100"\/"v102)"\/"v1))=v100
proof let v1,v102,v100;
(((v100"\/"v102)"\/"v1)"\/"(v100"\/"v102))=((v100"\/"v102)"\/"v1) by A65;
hence thesis by A3;
end;

A101: for v1,v101 holds ((v101"\/"v1)"/\"v101)=v101
proof let v1,v101;
((v101"\/"v1)"\/"v101)=(v101"\/"v1) by A65;
hence thesis by A41;
end;

A105: for v103,v102,v100 holds
 ((v100"\/"v103)"\/"(v103"\/"(v100"\/"v102)))=(v103"\/"(v100"\/"v102))
proof let v103,v102,v100;
((v103"\/"(v100"\/"v102))"/\"v103)=v103 by A101;
hence thesis by A25;
end;

A109: for v101,v100,v1 holds (v100"\/"(v101"/\"(v1"/\"v100)))=v100
proof let v101,v100,v1;
(v100"/\"(v1"/\"v100))=(v1"/\"v100) by A81;
hence thesis by A2;
end;

A113: for v103,v102,v100 holds
 ((v100"/\"v103)"/\"(v103"/\"(v100"/\"v102)))=(v103"/\"(v100"/\"v102))
proof let v103,v102,v100;
((v103"/\"(v100"/\"v102))"\/"v103)=v103 by A94;
hence thesis by A37;
end;

A117: for v1,v102,v101 holds (((v101"/\"v102)"/\"v1)"\/"v101)=v101
proof let v1,v102,v101;
(((v101"/\"v102)"/\"v1)"/\"(v101"/\"v102))=((v101"/\"v102)"/\"v1) by A73;
hence thesis by A88;
end;

A121: for v2,v1,v101 holds
 (((v101"\/"v1)"\/"v2)"/\"v101)=(v101"/\"((v101"\/"v1)"\/"v2))
proof let v2,v1,v101;
(v101"/\"((v101"\/"v1)"\/"v2))=v101 by A97;
hence thesis by A81;
end;

A124: for v2,v1,v0 holds (((v0"\/"v1)"\/"v2)"/\"v0)=v0
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"\/"v2))=v0 by A97;
hence thesis by A121;
end;

A127: for v1,v100,v2 holds (v100"/\"(v1"/\"(v2"/\"v100)))=(v1"/\"(v2"/\"v100))
proof let v1,v100,v2;
(v100"\/"(v1"/\"(v2"/\"v100)))=v100 by A109;
hence thesis by A41;
end;

A131: for v0,v102,v101 holds ((v101"/\"v102)"\/"(v0"\/"v101))=(v0"\/"v101)
proof let v0,v102,v101;
((v0"\/"v101)"/\"v101)=v101 by A41;
hence thesis by A117;
end;

A135: for v1,v102,v101 holds ((v101"/\"v102)"\/"(v101"\/"v1))=(v101"\/"v1)
proof let v1,v102,v101;
((v101"\/"v1)"/\"v101)=v101 by A101;
hence thesis by A117;
end;

A139: for v0,v102,v101 holds ((v101"\/"v102)"/\"(v0"/\"v101))=(v0"/\"v101)
proof let v0,v102,v101;
((v0"/\"v101)"\/"v101)=v101 by A17;
hence thesis by A124;
end;

A143: for v102,v100 holds ((v100"/\"v102)"/\"(v102"/\"v100))=(v102"/\"v100)
proof let v102,v100;
((v102"/\"v100)"\/"v102)=v102 by A94;
hence thesis by A49;
end;

A147: for v100,v1,v102 holds
 ((v100"/\"v102)"/\"((v102"/\"v1)"/\"v100))=((v102"/\"v1)"/\"v100)
proof let v100,v1,v102;
(((v102"/\"v1)"/\"v100)"\/"v102)=v102 by A117;
hence thesis by A49;
end;

A151: for v102,v100 holds ((v100"\/"v102)"\/"(v102"\/"v100))=(v102"\/"v100)
proof let v102,v100;
((v102"\/"v100)"/\"v102)=v102 by A101;
hence thesis by A53;
end;

A155: for v100,v101,v2 holds
 ((v100"/\"(v2"\/"v101))"/\"(v101"/\"v100))=(v101"/\"v100)
proof let v100,v101,v2;
((v101"/\"v100)"\/"(v2"\/"v101))=(v2"\/"v101) by A131;
hence thesis by A49;
end;

A159: for v100,v2,v101 holds
 ((v100"/\"(v101"\/"v2))"/\"(v101"/\"v100))=(v101"/\"v100)
proof let v100,v2,v101;
((v101"/\"v100)"\/"(v101"\/"v2))=(v101"\/"v2) by A135;
hence thesis by A49;
end;

A163: for v100,v101,v2 holds
 ((v100"\/"(v2"/\"v101))"\/"(v101"\/"v100))=(v101"\/"v100)
proof let v100,v101,v2;
((v101"\/"v100)"/\"(v2"/\"v101))=(v2"/\"v101) by A139;
hence thesis by A53;
end;

A167: for v1,v0 holds ((v0"/\"v1)"\/"(v1"/\"v0))=(v0"/\"v1)
proof let v1,v0;
((v0"/\"v1)"/\"(v1"/\"v0))=(v1"/\"v0) by A143;
hence thesis by A33;
end;

A170: for v0,v1 holds ((v1"/\"v0)"\/"(v0"/\"v1))=(v0"/\"v1)
proof let v0,v1;
((v0"/\"v1)"/\"(v1"/\"v0))=(v1"/\"v0) by A143;
hence thesis by A94;
end;

A173: for v1,v0 holds (v0"/\"v1)=(v1"/\"v0)
proof let v1,v0;
((v0"/\"v1)"\/"(v1"/\"v0))=(v0"/\"v1) by A167;
hence thesis by A170;
end;

A182: for v1,v0 holds ((v0"\/"v1)"/\"(v1"\/"v0))=(v0"\/"v1)
proof let v1,v0;
((v0"\/"v1)"\/"(v1"\/"v0))=(v1"\/"v0) by A151;
hence thesis by A21;
end;

A185: for v0,v1 holds ((v1"\/"v0)"\/"(v0"\/"v1))=((v0"\/"v1)"\/"(v1"\/"v0))
proof let v0,v1;
((v0"\/"v1)"\/"(v1"\/"v0))=(v1"\/"v0) by A151;
hence thesis by A65;
end;

A188: for v0,v1 holds (v1"\/"v0)=((v1"\/"v0)"\/"(v0"\/"v1))
proof let v0,v1;
((v0"\/"v1)"\/"(v1"\/"v0))=(v1"\/"v0) by A151;
hence thesis by A185;
end;

A191: for v1,v0 holds (v0"\/"v1)=(v1"\/"v0)
proof let v1,v0;
((v0"\/"v1)"\/"(v1"\/"v0))=(v1"\/"v0) by A151;
hence thesis by A188;
end;

A200: for v100,v2,v101 holds
 ((v100"\/"v101)"\/"(v100"\/"(v101"\/"v2)))=(v101"\/"(v100"\/"(v101"\/"v2)))
proof let v100,v2,v101;
(v101"\/"(v100"\/"(v101"\/"v2)))=(v100"\/"(v101"\/"v2)) by A57;
hence thesis by A105;
end;

A203: for v0,v2,v1 holds ((v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)))=(v0"\/"(v1"\/"v2))
proof let v0,v2,v1;
(v1"\/"(v0"\/"(v1"\/"v2)))=(v0"\/"(v1"\/"v2)) by A57;
hence thesis by A200;
end;

A205: for v1,v2,v0 holds ((v0"\/"v1)"\/"((v0"\/"v2)"\/"v1))=(v1"\/"(v0"\/"v2))
proof let v1,v2,v0;
(v1"\/"(v0"\/"v2))=((v0"\/"v2)"\/"v1) by A191;
hence thesis by A105;
end;

A208: for v102,v100,v1 holds
 ((v100"\/"(v102"\/"(v1"/\"v100)))"\/"(v100"\/"v102))=
 ((v102"\/"(v1"/\"v100))"\/"(v100"\/"v102))
proof let v102,v100,v1;
((v102"\/"(v1"/\"v100))"\/"(v100"\/"v102))=(v100"\/"v102) by A163;
hence thesis by A105;
end;

A211: for v1,v0,v2 holds
 ((v0"\/"v1)"\/"(v0"\/"(v1"\/"(v2"/\"v0))))=((v1"\/"(v2"/\"v0))"\/"(v0"\/"v1))
proof let v1,v0,v2;
((v0"\/"(v1"\/"(v2"/\"v0)))"\/"(v0"\/"v1))=
((v0"\/"v1)"\/"(v0"\/"(v1"\/"(v2"/\"v0)))) by A191;
hence thesis by A208;
end;

A213: for v1,v0,v2 holds
 (v0"\/"(v1"\/"(v2"/\"v0)))=((v1"\/"(v2"/\"v0))"\/"(v0"\/"v1))
proof let v1,v0,v2;
((v0"\/"v1)"\/"(v0"\/"(v1"\/"(v2"/\"v0))))=(v0"\/"(v1"\/"(v2"/\"v0))) by A203;
hence thesis by A211;
end;

A215: for v1,v0,v2 holds (v0"\/"(v1"\/"(v2"/\"v0)))=(v0"\/"v1)
proof let v1,v0,v2;
((v1"\/"(v2"/\"v0))"\/"(v0"\/"v1))=(v0"\/"v1) by A163;
hence thesis by A213;
end;

A218: for v101,v102,v1 holds
 ((v1"\/"v102)"\/"(v101"\/"v102))=((v1"\/"v102)"\/"v101)
proof let v101,v102,v1;
(v102"/\"(v1"\/"v102))=v102 by A13;
hence thesis by A215;
end;

A221: for v1,v0,v2 holds (v0"\/"((v2"/\"v0)"\/"v1))=(v0"\/"v1)
proof let v1,v0,v2;
(v1"\/"(v2"/\"v0))=((v2"/\"v0)"\/"v1) by A191;
hence thesis by A215;
end;

A224: for v2,v1,v0 holds ((v0"\/"v1)"\/"(v0"\/"v2))=(v1"\/"(v0"\/"v2))
proof let v2,v1,v0;
((v0"\/"v1)"\/"((v0"\/"v2)"\/"v1))=((v0"\/"v1)"\/"(v0"\/"v2)) by A218;
hence thesis by A205;
end;

A227: for v102,v1,v101 holds
 ((v101"\/"v1)"\/"(v101"\/"v102))=((v101"\/"v1)"\/"v102)
proof let v102,v1,v101;
(v101"/\"(v101"\/"v1))=v101 by A21;
hence thesis by A221;
end;

A230: for v1,v2,v0 holds (v1"\/"(v0"\/"v2))=((v0"\/"v1)"\/"v2)
proof let v1,v2,v0;
((v0"\/"v1)"\/"(v0"\/"v2))=(v1"\/"(v0"\/"v2)) by A224;
hence thesis by A227;
end;

A236: for v102,v1,v0 holds
 ((v1"\/"v0)"\/"((v0"\/"v1)"\/"v102))=((v1"\/"v0)"\/"v102)
proof let v102,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v0))=(v0"\/"v1) by A182;
hence thesis by A221;
end;

A239: for v0,v2,v1 holds ((v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)))=((v0"\/"v1)"\/"v2)
proof let v0,v2,v1;
((v1"\/"v0)"\/"v2)=(v0"\/"(v1"\/"v2)) by A230;
hence thesis by A236;
end;

A241: for v0,v2,v1 holds (v1"\/"(v0"\/"(v0"\/"(v1"\/"v2))))=((v0"\/"v1)"\/"v2)
proof let v0,v2,v1;
((v0"\/"v1)"\/"(v0"\/"(v1"\/"v2)))=(v1"\/"(v0"\/"(v0"\/"(v1"\/"v2)))) by A230;
hence thesis by A239;
end;

A244: for v1,v2,v0 holds (v0"\/"(v1"\/"(v0"\/"v2)))=((v1"\/"v0)"\/"v2)
proof let v1,v2,v0;
(v1"\/"(v1"\/"(v0"\/"v2)))=(v1"\/"(v0"\/"v2)) by A69;
hence thesis by A241;
end;

A246: for v1,v2,v0 holds (v1"\/"(v0"\/"v2))=((v1"\/"v0)"\/"v2)
proof let v1,v2,v0;
(v0"\/"(v1"\/"(v0"\/"v2)))=(v1"\/"(v0"\/"v2)) by A57;
hence thesis by A244;
end;

A257: for v1,v2,v0 holds ((v1"/\"v0)"/\"(v1"/\"(v0"/\"v2)))=(v1"/\"(v0"/\"v2))
proof let v1,v2,v0;
(v0"/\"v1)=(v1"/\"v0) by A173;
hence thesis by A113;
end;

A261: for v102,v100,v1 holds
 ((v100"/\"(v102"/\"(v1"\/"v100)))"/\"(v100"/\"v102))=
 ((v102"/\"(v1"\/"v100))"/\"(v100"/\"v102))
proof let v102,v100,v1;
((v102"/\"(v1"\/"v100))"/\"(v100"/\"v102))=(v100"/\"v102) by A155;
hence thesis by A113;
end;

A264: for v1,v0,v2 holds
 ((v0"/\"v1)"/\"(v0"/\"(v1"/\"(v2"\/"v0))))=((v1"/\"(v2"\/"v0))"/\"(v0"/\"v1))
proof let v1,v0,v2;
((v0"/\"(v1"/\"(v2"\/"v0)))"/\"(v0"/\"v1))=
((v0"/\"v1)"/\"(v0"/\"(v1"/\"(v2"\/"v0)))) by A173;
hence thesis by A261;
end;

A266: for v1,v0,v2 holds
 (v0"/\"(v1"/\"(v2"\/"v0)))=((v1"/\"(v2"\/"v0))"/\"(v0"/\"v1))
proof let v1,v0,v2;
((v0"/\"v1)"/\"(v0"/\"(v1"/\"(v2"\/"v0))))=(v0"/\"(v1"/\"(v2"\/"v0))) by A257;
hence thesis by A264;
end;

A268: for v1,v0,v2 holds (v0"/\"(v1"/\"(v2"\/"v0)))=(v0"/\"v1)
proof let v1,v0,v2;
((v1"/\"(v2"\/"v0))"/\"(v0"/\"v1))=(v0"/\"v1) by A155;
hence thesis by A266;
end;

A271: for v101,v0,v2,v1 holds
 (((v0"/\"(v1"\/"v2))"/\"v101)"/\"(v101"/\"(v1"/\"v0)))=
 (v101"/\"((v0"/\"(v1"\/"v2))"/\"(v1"/\"v0)))
proof let v101,v0,v2,v1;
((v0"/\"(v1"\/"v2))"/\"(v1"/\"v0))=(v1"/\"v0) by A159;
hence thesis by A113;
end;

A274: for v3,v0,v2,v1 holds
 (((v0"/\"(v1"\/"v2))"/\"v3)"/\"(v3"/\"(v1"/\"v0)))=(v3"/\"(v1"/\"v0))
proof let v3,v0,v2,v1;
((v0"/\"(v1"\/"v2))"/\"(v1"/\"v0))=(v1"/\"v0) by A159;
hence thesis by A271;
end;

A277: for v102,v2,v100 holds
 ((v100"/\"(v102"/\"(v100"\/"v2)))"/\"(v100"/\"v102))=
 ((v102"/\"(v100"\/"v2))"/\"(v100"/\"v102))
proof let v102,v2,v100;
((v102"/\"(v100"\/"v2))"/\"(v100"/\"v102))=(v100"/\"v102) by A159;
hence thesis by A113;
end;

A280: for v1,v2,v0 holds
 ((v0"/\"v1)"/\"(v0"/\"(v1"/\"(v0"\/"v2))))=((v1"/\"(v0"\/"v2))"/\"(v0"/\"v1))
proof let v1,v2,v0;
((v0"/\"(v1"/\"(v0"\/"v2)))"/\"(v0"/\"v1))=
((v0"/\"v1)"/\"(v0"/\"(v1"/\"(v0"\/"v2)))) by A173;
hence thesis by A277;
end;

A282: for v1,v2,v0 holds
 (v0"/\"(v1"/\"(v0"\/"v2)))=((v1"/\"(v0"\/"v2))"/\"(v0"/\"v1))
proof let v1,v2,v0;
((v0"/\"v1)"/\"(v0"/\"(v1"/\"(v0"\/"v2))))=(v0"/\"(v1"/\"(v0"\/"v2))) by A257;
hence thesis by A280;
end;

A284: for v1,v2,v0 holds (v0"/\"(v1"/\"(v0"\/"v2)))=(v0"/\"v1)
proof let v1,v2,v0;
((v1"/\"(v0"\/"v2))"/\"(v0"/\"v1))=(v0"/\"v1) by A159;
hence thesis by A282;
end;

A287: for v101,v1,v102 holds
 ((v102"/\"v1)"/\"(v101"/\"v102))=((v102"/\"v1)"/\"v101)
proof let v101,v1,v102;
(v102"\/"(v102"/\"v1))=v102 by A33;
hence thesis by A268;
end;

A290: for v1,v0,v2 holds (v0"/\"((v2"\/"v0)"/\"v1))=(v0"/\"v1)
proof let v1,v0,v2;
(v1"/\"(v2"\/"v0))=((v2"\/"v0)"/\"v1) by A173;
hence thesis by A268;
end;

A293: for v2,v1,v0 holds ((v0"/\"v1)"/\"(v1"/\"v2))=((v1"/\"v2)"/\"v0)
proof let v2,v1,v0;
((v0"/\"v1)"/\"((v1"/\"v2)"/\"v0))=((v0"/\"v1)"/\"(v1"/\"v2)) by A287;
hence thesis by A147;
end;

A295: for v1,v2,v0 holds (v0"/\"((v0"\/"v2)"/\"v1))=(v0"/\"v1)
proof let v1,v2,v0;
(v1"/\"(v0"\/"v2))=((v0"\/"v2)"/\"v1) by A173;
hence thesis by A284;
end;

A299: for v102,v101,v1 holds
 ((v1"/\"v101)"/\"(v101"/\"v102))=((v1"/\"v101)"/\"v102)
proof let v102,v101,v1;
(v101"\/"(v1"/\"v101))=v101 by A9;
hence thesis by A290;
end;

A303: for v102,v1,v101 holds
 ((v101"/\"v1)"/\"(v101"/\"v102))=((v101"/\"v1)"/\"v102)
proof let v102,v1,v101;
(v101"\/"(v101"/\"v1))=v101 by A33;
hence thesis by A290;
end;

A307: for v101,v2,v100,v1 holds
 ((v100"/\"v101)"/\"(v101"/\"(v100"/\"v2)))=
 (v101"/\"(v100"/\"((v1"\/"v100)"/\"v2)))
proof let v101,v2,v100,v1;
(v100"/\"((v1"\/"v100)"/\"v2))=(v100"/\"v2) by A290;
hence thesis by A113;
end;

A310: for v1,v2,v0,v3 holds
 ((v0"/\"v1)"/\"(v0"/\"v2))=(v1"/\"(v0"/\"((v3"\/"v0)"/\"v2)))
proof let v1,v2,v0,v3;
((v0"/\"v1)"/\"(v1"/\"(v0"/\"v2)))=((v0"/\"v1)"/\"(v0"/\"v2)) by A299;
hence thesis by A307;
end;

A312: for v1,v2,v0,v3 holds
((v0"/\"v1)"/\"v2)=(v1"/\"(v0"/\"((v3"\/"v0)"/\"v2)))
proof let v1,v2,v0,v3;
((v0"/\"v1)"/\"(v0"/\"v2))=((v0"/\"v1)"/\"v2) by A303;
hence thesis by A310;
end;

A314: for v2,v1,v0 holds ((v0"/\"v1)"/\"v2)=(v1"/\"(v0"/\"v2))
proof
 now let v1,v2,v0,v3;
(v0"/\"((v3"\/"v0)"/\"v2))=(v0"/\"v2) by A290;
hence ((v0"/\"v1)"/\"v2)=(v1"/\"(v0"/\"v2)) by A312;
end;
hence thesis;
end;

A316: for v0,v2,v1 holds (v1"/\"(v0"/\"(v1"/\"v2)))=((v1"/\"v2)"/\"v0)
proof let v0,v2,v1;
((v0"/\"v1)"/\"(v1"/\"v2))=(v1"/\"(v0"/\"(v1"/\"v2))) by A314;
hence thesis by A293;
end;

A319: for v1,v2,v0 holds (v1"/\"(v0"/\"v2))=((v0"/\"v2)"/\"v1)
proof let v1,v2,v0;
(v0"/\"(v1"/\"(v0"/\"v2)))=(v1"/\"(v0"/\"v2)) by A77;
hence thesis by A316;
end;

A322: for v0,v2,v1 holds (v0"/\"(v1"/\"v2))=(v2"/\"(v1"/\"v0))
proof let v0,v2,v1;
((v1"/\"v2)"/\"v0)=(v2"/\"(v1"/\"v0)) by A314;
hence thesis by A319;
end;

A324: for v0,v3,v2,v1 holds
 (((v1"\/"v2)"/\"(v0"/\"v3))"/\"(v3"/\"(v1"/\"v0)))=(v3"/\"(v1"/\"v0))
proof let v0,v3,v2,v1;
((v0"/\"(v1"\/"v2))"/\"v3)=((v1"\/"v2)"/\"(v0"/\"v3)) by A314;
hence thesis by A274;
end;

A327: for v2,v3,v1,v0 holds
 ((v0"/\"v2)"/\"(v3"/\"((v0"\/"v1)"/\"(v2"/\"v3))))=(v3"/\"(v0"/\"v2))
proof let v2,v3,v1,v0;
(((v0"\/"v1)"/\"(v2"/\"v3))"/\"(v3"/\"(v0"/\"v2)))=
((v0"/\"v2)"/\"(v3"/\"((v0"\/"v1)"/\"(v2"/\"v3)))) by A322;
hence thesis by A324;
end;

A330: for v1,v2,v3,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"v3)"/\"(v1"/\"v2)))=(v2"/\"(v0"/\"v1))
proof let v1,v2,v3,v0;
(v2"/\"((v0"\/"v3)"/\"(v1"/\"v2)))=((v0"\/"v3)"/\"(v1"/\"v2)) by A127;
hence thesis by A327;
end;

A333: for v1,v3,v2,v0 holds
 (v1"/\"(v0"/\"((v0"\/"v2)"/\"(v1"/\"v3))))=(v3"/\"(v0"/\"v1))
proof let v1,v3,v2,v0;
((v0"/\"v1)"/\"((v0"\/"v2)"/\"(v1"/\"v3)))=
(v1"/\"(v0"/\"((v0"\/"v2)"/\"(v1"/\"v3)))) by A314;
hence thesis by A330;
end;

A336: for v1,v3,v0 holds (v0"/\"(v1"/\"(v0"/\"v3)))=(v3"/\"(v1"/\"v0))
proof
 now let v0,v3,v2,v1;
(v1"/\"((v1"\/"v2)"/\"(v0"/\"v3)))=(v1"/\"(v0"/\"v3)) by A295;
hence (v0"/\"(v1"/\"(v0"/\"v3)))=(v3"/\"(v1"/\"v0)) by A333;
end;
hence thesis;
end;

A339: for v1,v2,v0 holds (v1"/\"(v0"/\"v2))=(v2"/\"(v1"/\"v0))
proof let v1,v2,v0;
(v0"/\"(v1"/\"(v0"/\"v2)))=(v1"/\"(v0"/\"v2)) by A77;
hence thesis by A336;
end;

for v0,v2,v1 holds (v0"/\"(v1"/\"v2))=((v0"/\"v1)"/\"v2)
proof
let v0,v2,v1;
(v0"/\"(v1"/\"v2))=(v2"/\"(v0"/\"v1)) by A339 .= ((v0"/\"v1)"/\"v2) by A173;
hence thesis;
end;

hence thesis by A173,A191,A21,A33,A246;
end;
