 reserve T for Ternary_Boolean_Algebra;
 reserve a,b,c,d,e for Element of T;
 reserve x,y,z for Element of T;
reserve T for Ternary_Boolean_Algebra;
reserve x for Element of T;
reserve B for Boolean Lattice;
reserve v0,v1,v2,v3,v4,v5,v6,v103,v100,v102,v104,v105,v101 for
  Element of BA2TBAA B;

theorem TBA2:
(for v2,v1,v0 holds Tern(v0,v1,v2)=(((v0"\/"v1)"/\"(v1"\/"v2))"/\"(v0"\/"v2)))
&
(for v0,v2,v1 holds v0"\/"(v1"/\"v2) = (v0"\/"v1)"/\"(v0"\/"v2)) &
(for v0,v2,v1 holds v0"/\"(v1"\/"v2) = (v0"/\"v1)"\/"(v0"/\"v2)) &
(for v2,v1,v0 holds (v0"\/"v1)"\/"v2 = v0"\/"(v1"\/"v2)) &
(for v2,v1,v0 holds (v0"/\"v1)"/\"v2 = v0"/\"(v1"/\"v2)) implies
  for v1,v2,v3,v4 holds
    Tern(Tern(v1,v2,v3),v2,v4)=Tern(v1,v2,Tern(v3,v2,v4))
proof
assume A1: for v2,v1,v0 holds
 Tern(v0,v1,v2)=(((v0"\/"v1)"/\"(v1"\/"v2))"/\"(v0"\/"v2));
assume A4: for v0,v2,v1 holds (v0"\/"(v1"/\"v2))=((v0"\/"v1)"/\"(v0"\/"v2));
assume A6: for v0,v2,v1 holds (v0"/\"(v1"\/"v2))=((v0"/\"v1)"\/"(v0"/\"v2));
assume A8: for v2,v1,v0 holds ((v0"\/"v1)"\/"v2)=(v0"\/"(v1"\/"v2));

assume A14: for v2,v1,v0 holds ((v0"/\"v1)"/\"v2)=(v0"/\"(v1"/\"v2));

assume not thesis; then
consider c1,c2,c3,c4 being Element of BA2TBAA B such that
A20:  not Tern(Tern(c1,c2,c3),c2,c4)=Tern(c1,c2,Tern(c3,c2,c4));

not
 Tern((((c1"\/"c2)"/\"(c2"\/"c3))"/\"(c1"\/"c3)),c2,c4)=Tern(c1,c2,Tern(c3,c2,
c4)) by
 A1,A20; then

not
 Tern(((c1"\/"c2)"/\"((c2"\/"c3)"/\"(c1"\/"c3))),c2,c4)=Tern(c1,c2,Tern(c3,c2,
c4)) by A14; then

AA:
not
 (((((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3)))"\/"c2)"/\"(c2"\/"c4))"/\"(((c1
"\/"c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3)))"\/"c4))=Tern(c1,c2,Tern(c3,c2,c4)) by A1;

A38:  not
 ((c2"\/"(c4"/\"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3)))))"/\"(c4"\/"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3)))))=Tern(c1,c2,Tern(c3,c2,c4)) by A4,AA;

A42:  not
 ((c4"\/"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3))))))=Tern(c1,c2,(((c3"\/"c2)"/\"(c2"\/"c4))"/\"(c3"\/"
c4))) by
 A1,A38;

A48:  not
 ((c4"\/"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3))))))=Tern(c1,c2,((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))) by
 A4,A42;

A52:  not
 ((c4"\/"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3))))))=((c1"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))"/\"((
c1"\/"c2)"/\"
(c2"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A1,A48;

A56:  not
 ((c4"\/"((c1"\/"c2)"/\"((c1"\/"c3)"/\"(c2"\/"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"
c2)"/\"(
(c1"\/"c3)"/\"(c2"\/"c3))))))=((c1"\/"c2)"/\"((c1"\/"((c3"\/"c4)"/\"(c2"\/"(c3
"/\"c4))))"/\"
(c2"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A52,A14;

A63: for v2,v1,v0 holds Tern(v0,v1,v2)=((v0"\/"v2)"/\"(v1"\/"(v0"/\"v2)))
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A1;
end;

A69: for v2,v101,v1,v0 holds
 (((v0"/\"v1)"\/"v101)"/\"(v0"/\"(v1"\/"v2)))=((v0"/\"v1)"\/"(v101"/\"(v0"/\"v2
)))
proof let v2,v101,v1,v0;
((v0"/\"v1)"\/"(v0"/\"v2))=(v0"/\"(v1"\/"v2)) by A6;
hence thesis by A4;
end;

A75: for v3,v0,v2,v1 holds
 (v1"/\"((v2"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=((v1"/\"v2)"\/"(v0"/\"(v1"/\"v3)))
proof let v3,v0,v2,v1;
(v1"/\"((v2"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=((v0"\/"(v1"/\"v2))"/\"(v1"/\"(v2
"\/"v3))) by A14;
hence thesis by A69;
end;

A78: for v2,v3,v1,v0 holds
 (v0"/\"((v1"\/"v2)"/\"(v3"\/"(v0"/\"v1))))=((v0"/\"v1)"\/"(v0"/\"(v2"/\"v3)))
proof let v2,v3,v1,v0;
(v0"/\"(v2"/\"v3))=(v3"/\"(v0"/\"v2)) by A14;
hence thesis by A75;
end;

A82: for v2,v3,v1,v0 holds
 (v0"/\"((v1"\/"v2)"/\"(v3"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v3"/\"v2)))
proof let v2,v3,v1,v0;
((v0"/\"v1)"\/"(v0"/\"(v3"/\"v2)))=(v0"/\"(v1"\/"(v3"/\"v2))) by A6;
hence thesis by A78;
end;

A85: for v102,v1,v101 holds
 (((v101"/\"v1)"\/"v101)"/\"((v101"/\"v1)"\/"v102))=(v101"/\"(v1"\/"v102))
proof let v102,v1,v101;
((v101"/\"v1)"\/"(v101"/\"v102))=(v101"/\"(v1"\/"v102)) by A6;
hence thesis by A4;
end;

A93: for v2,v101,v1,v0 holds
 ((v0"\/"v1)"/\"v101)"\/"(v0"\/"(v1"/\"v2)) =
  (v0"\/"v1)"/\"(v101"\/"(v0"\/"v2))
proof let v2,v101,v1,v0;
  (v0"\/"v1)"/\"(v0"\/"v2) = v0"\/"(v1"/\"v2) by A4;
  hence thesis by A6;
end;

A99: for v3,v0,v2,v1 holds
 (v1"\/"((v2"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=((v1"\/"v2)"/\"(v0"\/"(v1"\/"v3)))
proof let v3,v0,v2,v1;
(v1"\/"((v2"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=
((v0"/\"(v1"\/"v2))"\/"(v1"\/"(v2"/\"v3))) by A8;
hence thesis by A93;
end;

A102: for v2,v3,v1,v0 holds
 (v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v1))))=((v0"\/"v1)"/\"(v0"\/"(v2"\/"v3)))
proof let v2,v3,v1,v0;
(v0"\/"(v2"\/"v3))=(v3"\/"(v0"\/"v2)) by A8;
hence thesis by A99;
end;

A106: for v2,v3,v1,v0 holds
 v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v1))) = v0"\/"(v1"/\"(v3"\/"v2))
proof let v2,v3,v1,v0;
  (v0"\/"v1)"/\"(v0"\/"(v3"\/"v2)) = v0"\/"(v1"/\"(v3"\/"v2)) by A4;
  hence thesis by A102;
end;

A109: for v102,v2,v1,v100 holds
 (v2"\/"(v100"\/"v1))"/\"(v100"\/"v102) = v100"\/"((v1"\/"v2)"/\"v102)
proof let v102,v2,v1,v100;
  v100"\/"(v1"\/"v2) = v2"\/"(v100"\/"v1) by A8;
  hence thesis by A4;
end;

A117: for v102,v0,v100,v1 holds
 (v0"\/"(v1"\/"v100))"/\"(v100"\/"v102) = v100"\/"((v0"\/"v1)"/\"v102)
proof let v102,v0,v100,v1;
  v0"\/"(v1"\/"v100) = v100"\/"(v0"\/"v1) by A8;
  hence thesis by A4;
end;

A123: for v102,v2,v1,v100 holds
 (v2"/\"(v100"/\"v1))"\/"(v100"/\"v102) = v100"/\"((v1"/\"v2)"\/"v102)
proof let v102,v2,v1,v100;
  v100"/\"(v1"/\"v2) = v2"/\"(v100"/\"v1) by A14;
  hence thesis by A6;
end;

A131: for v102,v0,v100,v1 holds
 ((v0"/\"(v1"/\"v100))"\/"(v100"/\"v102))=(v100"/\"((v0"/\"v1)"\/"v102))
proof let v102,v0,v100,v1;
(v0"/\"(v1"/\"v100))=(v100"/\"(v0"/\"v1)) by A14;
hence thesis by A6;
end;

A137: for v2,v101,v1,v0 holds
 (((v0"\/"v1)"/\"v101)"\/"(v1"\/"(v0"/\"v2)))=((v0"\/"v1)"/\"(v101"\/"(v1"\/"v2
)))
proof let v2,v101,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A6;
end;

A143: for v3,v0,v2,v1 holds
 (v2"\/"((v1"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=((v1"\/"v2)"/\"(v0"\/"(v2"\/"v3)))
proof let v3,v0,v2,v1;
(v2"\/"((v1"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=
((v0"/\"(v1"\/"v2))"\/"(v2"\/"(v1"/\"v3))) by A8;
hence thesis by A137;
end;

A146: for v2,v3,v0,v1 holds
 (v0"\/"((v1"/\"v2)"\/"(v3"/\"(v1"\/"v0))))=((v1"\/"v0)"/\"(v0"\/"(v2"\/"v3)))
proof let v2,v3,v0,v1;
(v0"\/"(v2"\/"v3))=(v3"\/"(v0"\/"v2)) by A8;
hence thesis by A143;
end;

A150: for v2,v3,v0,v1 holds
 (v0"\/"((v1"/\"v2)"\/"(v3"/\"(v1"\/"v0))))=(v0"\/"(v1"/\"(v3"\/"v2)))
proof let v2,v3,v0,v1;
((v1"\/"v0)"/\"(v0"\/"(v3"\/"v2)))=(v0"\/"(v1"/\"(v3"\/"v2))) by A4;
hence thesis by A146;
end;

A153: for v2,v100,v1,v0 holds
 ((v100"\/"(v0"/\"v1))"/\"(v0"/\"(v1"\/"v2)))=
((v0"/\"v1)"\/"(v100"/\"(v0"/\"v2)))
proof let v2,v100,v1,v0;
((v0"/\"v1)"\/"(v0"/\"v2))=(v0"/\"(v1"\/"v2)) by A6;
hence thesis by A4;
end;

A156: for v3,v0,v2,v1 holds
 (v1"/\"((v2"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=((v1"/\"v2)"\/"(v0"/\"(v1"/\"v3)))
proof let v3,v0,v2,v1;
(v1"/\"((v2"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=
((v0"\/"(v1"/\"v2))"/\"(v1"/\"(v2"\/"v3))) by A14;
hence thesis by A153;
end;

A159: for v0,v1,v2,v3 holds
 (v0"/\"(v1"\/"(v3"/\"v2)))=((v0"/\"v1)"\/"(v3"/\"(v0"/\"v2)))
proof let v0,v1,v2,v3;
(v0"/\"((v1"\/"v2)"/\"(v3"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v3"/\"v2))) by A82;
hence thesis by A156;
end;

A164: for v102,v2,v1,v100 holds
 ((v2"\/"(v100"\/"v1))"/\"((v1"\/"v2)"\/"v102))=((v1"\/"v2)"\/"(v100"/\"v102))
proof let v102,v2,v1,v100;
(v100"\/"(v1"\/"v2))=(v2"\/"(v100"\/"v1)) by A8;
hence thesis by A4;
end;

A171: for v3,v0,v2,v1 holds
 ((v0"\/"(v1"\/"v2))"/\"(v2"\/"(v3"\/"v0)))=((v2"\/"v0)"\/"(v1"/\"v3))
proof let v3,v0,v2,v1;
(v3"\/"(v0"\/"v2))=(v2"\/"(v3"\/"v0)) by A8;
hence thesis by A164;
end;

A175: for v3,v0,v2,v1 holds
 ((v0"\/"(v1"\/"v2))"/\"(v0"\/"(v3"\/"v2)))=((v2"\/"v0)"\/"(v1"/\"v3))
proof let v3,v0,v2,v1;
(v0"\/"(v3"\/"v2))=(v2"\/"(v0"\/"v3)) by A8;
hence thesis by A171;
end;

A179: for v0,v3,v2,v1 holds
 (v0"\/"((v1"\/"v2)"/\"(v2"\/"v3)))=((v2"\/"v0)"\/"(v1"/\"v3))
proof let v0,v3,v2,v1;
((v0"\/"(v1"\/"v2))"/\"(v0"\/"(v2"\/"v3)))=
(v0"\/"((v1"\/"v2)"/\"(v2"\/"v3))) by A4;
hence thesis by A175;
end;

A181: for v0,v2,v3,v1 holds (v0"\/"(v2"\/"(v1"/\"v3)))=((v2"\/"v0)"\/"(v1"/\"v3
))
proof let v0,v2,v3,v1;
((v1"\/"v2)"/\"(v2"\/"v3))=(v2"\/"(v1"/\"v3)) by A4;
hence thesis by A179;
end;

A188: for v0,v102,v2,v1 holds
 ((v0"\/"v1)"/\"((v1"\/"v2)"/\"v102))=(v102"/\"(v1"\/"(v0"/\"v2)))
proof let v0,v102,v2,v1;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A14;
end;

A194: for v2,v0,v3,v1 holds
 (v2"/\"((v1"\/"v3)"/\"(v0"\/"v1)))=(v2"/\"(v1"\/"(v0"/\"v3)))
proof let v2,v0,v3,v1;
(v2"/\"((v1"\/"v3)"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v2"/\"(v1"\/"v3))) by A14;
hence thesis by A188;
end;

A198: for v2,v101,v1,v0 holds
 (((v0"\/"v1)"\/"v101)"/\"(v101"\/"(v1"\/"v2)))=(v101"\/"(v1"\/"(v0"/\"v2)))
proof let v2,v101,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A4;
end;

A204: for v3,v2,v1,v0 holds
 ((v2"\/"(v0"\/"v1))"/\"(v0"\/"(v2"\/"v3)))=(v0"\/"(v2"\/"(v1"/\"v3)))
proof let v3,v2,v1,v0;
(v0"\/"(v1"\/"v2))=(v2"\/"(v0"\/"v1)) by A8;
hence thesis by A198;
end;

A210: for v3,v1,v0,v2 holds
 ((v1"\/"(v2"\/"v0))"/\"(v2"\/"(v0"\/"v3)))=(v2"\/"(v0"\/"(v1"/\"v3)))
proof let v3,v1,v0,v2;
  v1"\/"(v2"\/"v0) = v0"\/"(v1"\/"v2) by A8;
  hence thesis by A204;
end;

A216: for v3,v0,v2,v1 holds
 ((v0"\/"(v1"\/"v2))"/\"(v1"\/"(v3"\/"v2)))=(v2"\/"(v1"\/"(v0"/\"v3)))
proof let v3,v0,v2,v1;
  v1"\/"(v3"\/"v2) = v2"\/"(v1"\/"v3) by A8;
  hence thesis by A210;
end;

A220: for v1,v0,v3,v2 holds
 (v1"\/"((v2"\/"v3)"/\"(v0"\/"v2)))=(v2"\/"(v1"\/"(v0"/\"v3)))
proof let v1,v0,v3,v2;
((v0"\/"(v1"\/"v2))"/\"(v1"\/"(v2"\/"v3)))=
(v1"\/"((v2"\/"v3)"/\"(v0"\/"v2))) by A109;
hence thesis by A216;
end;

A223: for v0,v3,v2,v1 holds
 (v0"\/"((v1"\/"v2)"/\"(v3"\/"v1)))=(v0"\/"((v3"/\"v2)"\/"v1))
proof let v0,v3,v2,v1;
(v0"\/"((v3"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v3"/\"v2))) by A8;
hence thesis by A220;
end;

A228: for v2,v101,v1,v0 holds
 (((v0"/\"v1)"\/"v101)"/\"(v1"/\"(v0"\/"v2)))=((v0"/\"v1)"\/"(v101"/\"(v1"/\"v2
)))
proof let v2,v101,v1,v0;
((v0"/\"v1)"\/"(v1"/\"v2))=(v1"/\"(v0"\/"v2)) by A6;
hence thesis by A4;
end;

A234: for v3,v0,v2,v1 holds
 (v2"/\"((v1"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=((v1"/\"v2)"\/"(v0"/\"(v2"/\"v3)))
proof let v3,v0,v2,v1;
(v2"/\"((v1"\/"v3)"/\"(v0"\/"(v1"/\"v2))))=
((v0"\/"(v1"/\"v2))"/\"(v2"/\"(v1"\/"v3))) by A14;
hence thesis by A228;
end;

A237: for v2,v3,v0,v1 holds
 (v0"/\"((v1"\/"v2)"/\"(v3"\/"(v1"/\"v0))))=((v1"/\"v0)"\/"(v0"/\"(v2"/\"v3)))
proof let v2,v3,v0,v1;
(v0"/\"(v2"/\"v3))=(v3"/\"(v0"/\"v2)) by A14;
hence thesis by A234;
end;

A241: for v2,v3,v0,v1 holds
 (v0"/\"((v1"\/"v2)"/\"(v3"\/"(v1"/\"v0))))=(v0"/\"(v1"\/"(v3"/\"v2)))
proof let v2,v3,v0,v1;
((v1"/\"v0)"\/"(v0"/\"(v3"/\"v2)))=(v0"/\"(v1"\/"(v3"/\"v2))) by A6;
hence thesis by A237;
end;

A244: for v102,v0,v2,v1 holds
 ((v0"\/"(v1"/\"v2))"\/"((v0"\/"v2)"/\"v102))=
((v0"\/"v2)"/\"((v0"\/"v1)"\/"v102))
proof let v102,v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A6;
end;

A249: for v1,v3,v2,v0 holds
 (v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2))))=((v0"\/"v2)"/\"((v0"\/"v1)"\/"v3))
proof let v1,v3,v2,v0;
((v0"\/"(v1"/\"v2))"\/"(v3"/\"(v0"\/"v2)))=
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2)))) by A181;
hence thesis by A244;
end;

A253: for v1,v3,v2,v0 holds
 (v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2))))=((v0"\/"v2)"/\"(v1"\/"(v3"\/"v0)))
proof let v1,v3,v2,v0;
(v3"\/"(v0"\/"v1))=(v1"\/"(v3"\/"v0)) by A8;
hence thesis by A249;
end;

A257: for v1,v3,v2,v0 holds
 v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2))) = (v0"\/"v2)"/\"(v0"\/"(v3"\/"v1))
proof let v1,v3,v2,v0;
  v0"\/"(v3"\/"v1) = v1"\/"(v0"\/"v3) by A8;
  hence thesis by A253;
end;

A261: for v1,v3,v2,v0 holds
 v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v2))) = v0"\/"(v2"/\"(v1"\/"v3))
proof let v1,v3,v2,v0;
  (v0"\/"v2)"/\"(v0"\/"(v1"\/"v3)) = v0"\/"(v2"/\"(v1"\/"v3)) by A4;
  hence thesis by A257;
end;

A264: for v2,v100,v1,v0 holds
 (v100"/\"(v0"\/"v1))"\/"(v0"\/"(v1"/\"v2)) =
  (v0"\/"v1)"/\"(v100"\/"(v0"\/"v2))
proof let v2,v100,v1,v0;
  (v0"\/"v1)"/\"(v0"\/"v2) = v0"\/"(v1"/\"v2) by A4;
  hence thesis by A6;
end;

A267: for v3,v0,v2,v1 holds
 v1"\/"((v2"/\"v3)"\/"(v0"/\"(v1"\/"v2))) = (v1"\/"v2)"/\"(v0"\/"(v1"\/"v3))
proof let v3,v0,v2,v1;
  v1"\/"((v2"/\"v3)"\/"(v0"/\"(v1"\/"v2))) =
   (v0"/\"(v1"\/"v2))"\/"(v1"\/"(v2"/\"v3)) by A8;
  hence thesis by A264;
end;

A270: for v0,v1,v2,v3 holds
 v0"\/"(v1"/\"(v3"\/"v2)) = (v0"\/"v1)"/\"(v3"\/"(v0"\/"v2))
proof let v0,v1,v2,v3;
  v0"\/"((v1"/\"v2)"\/"(v3"/\"(v0"\/"v1))) = v0"\/"(v1"/\"(v3"\/"v2)) by A106;
  hence thesis by A267;
end;

A275: for v102,v2,v1,v100 holds
 (v2"/\"(v100"/\"v1))"\/"((v1"/\"v2)"/\"v102) = (v1"/\"v2)"/\"(v100"\/"v102)
proof let v102,v2,v1,v100;
  v100"/\"(v1"/\"v2) = v2"/\"(v100"/\"v1) by A14;
  hence thesis by A6;
end;

A282: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"/\"v2))"\/"(v2"/\"(v3"/\"v0)))=((v2"/\"v0)"/\"(v1"\/"v3))
proof let v3,v0,v2,v1;
(v3"/\"(v0"/\"v2))=(v2"/\"(v3"/\"v0)) by A14;
hence thesis by A275;
end;

A286: for v3,v0,v2,v1 holds
 (v0"/\"(v1"/\"v2))"\/"(v0"/\"(v3"/\"v2)) = (v2"/\"v0)"/\"(v1"\/"v3)
proof let v3,v0,v2,v1;
  v0"/\"(v3"/\"v2) = v2"/\"(v0"/\"v3) by A14;
  hence thesis by A282;
end;

A290: for v0,v3,v2,v1 holds
 (v0"/\"((v1"/\"v2)"\/"(v2"/\"v3)))=((v2"/\"v0)"/\"(v1"\/"v3))
proof let v0,v3,v2,v1;
((v0"/\"(v1"/\"v2))"\/"(v0"/\"(v2"/\"v3)))=(v0"/\"((v1"/\"v2)"\/"(v2"/\"v3)))
by A6;
hence thesis by A286;
end;

A292: for v0,v2,v3,v1 holds (v0"/\"(v2"/\"(v1"\/"v3)))=((v2"/\"v0)"/\"(v1"\/"v3
))
proof let v0,v2,v3,v1;
  (v1"/\"v2)"\/"(v2"/\"v3) = v2"/\"(v1"\/"v3) by A6;
  hence thesis by A290;
end;

A299: for v2,v100,v1,v0 holds
 ((v100"/\"(v0"\/"v1))"\/"(v1"\/"(v0"/\"v2)))=((v0"\/"v1)"/\"(v100"\/"(v1"\/"v2
)))
proof let v2,v100,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A6;
end;

A302: for v3,v0,v2,v1 holds
 (v2"\/"((v1"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=((v1"\/"v2)"/\"(v0"\/"(v2"\/"v3)))
proof let v3,v0,v2,v1;
(v2"\/"((v1"/\"v3)"\/"(v0"/\"(v1"\/"v2))))=((v0"/\"(v1"\/"v2))"\/"(v2"\/"(v1
"/\"v3))) by
 A8;
hence thesis by A299;
end;

A305: for v0,v1,v2,v3 holds
 (v0"\/"(v1"/\"(v3"\/"v2)))=((v1"\/"v0)"/\"(v3"\/"(v0"\/"v2)))
proof let v0,v1,v2,v3;
(v0"\/"((v1"/\"v2)"\/"(v3"/\"(v1"\/"v0))))=(v0"\/"(v1"/\"(v3"\/"v2))) by A150;
hence thesis by A302;
end;

A311: for v2,v101,v1,v0 holds
 ((v0"/\"v1)"/\"v101)"\/"(v101"/\"(v1"/\"v2)) = v101"/\"(v1"/\"(v0"\/"v2))
proof let v2,v101,v1,v0;
  (v0"/\"v1)"\/"(v1"/\"v2) = v1"/\"(v0"\/"v2) by A6;
  hence thesis by A6;
end;

A317: for v3,v2,v1,v0 holds
 ((v2"/\"(v0"/\"v1))"\/"(v0"/\"(v2"/\"v3)))=(v0"/\"(v2"/\"(v1"\/"v3)))
proof let v3,v2,v1,v0;
(v0"/\"(v1"/\"v2))=(v2"/\"(v0"/\"v1)) by A14;
hence thesis by A311;
end;

A323: for v3,v1,v0,v2 holds
 (v1"/\"(v2"/\"v0))"\/"(v2"/\"(v0"/\"v3)) = v2"/\"(v0"/\"(v1"\/"v3))
proof let v3,v1,v0,v2;
  v1"/\"(v2"/\"v0) = v0"/\"(v1"/\"v2) by A14;
  hence thesis by A317;
end;

A329: for v3,v0,v2,v1 holds
 (v0"/\"(v1"/\"v2))"\/"(v1"/\"(v3"/\"v2)) = v2"/\"(v1"/\"(v0"\/"v3))
proof let v3,v0,v2,v1;
  v1"/\"(v3"/\"v2) = v2"/\"(v1"/\"v3) by A14;
  hence thesis by A323;
end;

A333: for v1,v0,v3,v2 holds
 (v1"/\"((v2"/\"v3)"\/"(v0"/\"v2)))=(v2"/\"(v1"/\"(v0"\/"v3)))
proof let v1,v0,v3,v2;
((v0"/\"(v1"/\"v2))"\/"(v1"/\"(v2"/\"v3)))=
(v1"/\"((v2"/\"v3)"\/"(v0"/\"v2))) by A123;
hence thesis by A329;
end;

A336: for v0,v3,v2,v1 holds
 v0"/\"((v1"/\"v2)"\/"(v3"/\"v1)) = v0"/\"((v3"\/"v2)"/\"v1)
proof let v0,v3,v2,v1;
  v0"/\"((v3"\/"v2)"/\"v1) = v1"/\"(v0"/\"(v3"\/"v2)) by A14;
  hence thesis by A333;
end;

A341: for v102,v103,v0,v2,v1 holds
 ((v0"/\"(v1"\/"v2))"\/"(v102"/\"v103))=
((v0"/\"v1)"\/"((v0"/\"v2)"\/"(v102"/\"v103)))
proof let v102,v103,v0,v2,v1;
((v0"/\"v1)"\/"(v0"/\"v2))=(v0"/\"(v1"\/"v2)) by A6;
hence thesis by A181;
end;

A346: for v102,v0,v1,v3,v2 holds
 ((v0"\/"(v1"\/"(v2"/\"v3)))"/\"((v2"/\"v3)"\/"v102))=
((v2"/\"v3)"\/"((v0"\/"v1)"/\"v102))
proof let v102,v0,v1,v3,v2;
((v0"\/"v1)"\/"(v2"/\"v3))=(v0"\/"(v1"\/"(v2"/\"v3))) by A181;
hence thesis by A4;
end;

A354: for v102,v103,v0,v2,v1 holds
 ((v0"\/"(v1"/\"v2))"/\"(v102"\/"v103))=
((v0"\/"v1)"/\"((v0"\/"v2)"/\"(v102"\/"v103)))
proof let v102,v103,v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A292;
end;

A360:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"((c1"\/"c2)"/\"((
c1"\/"c3)"/\"
(c2"\/"c3))))))=((c1"\/"c2)"/\"((c1"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))"/\"(
c2"\/"(
(c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A354,A56;

A362:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"
((c1"\/"(c2"/\"c3))"/\"(c2"\/"c3)))))=
((c1"\/"c2)"/\"((c1"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))"/\"(c2"\/"
((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A354,A360;

A368:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"
(c2"\/"(c4"/\"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))))=
((c2"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))"/\"
(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A362,A354;

A371: for v102,v103,v100 holds
 (v100"/\"(v103"\/"(v102"/\"(v100"/\"v103))))=(v100"/\"(v103"\/"(v103"/\"v102))
)
proof let v102,v103,v100;
((v103"\/"v102)"/\"(v103"\/"(v100"/\"v103)))=(v103"\/"(v102"/\"(v100"/\"v103)))
by
 A4;
hence thesis by A82;
end;

A374: for v1,v0,v2 holds
 v0"/\"(v1"\/"(v1"/\"(v2"/\"v0))) = v0"/\"(v1"\/"(v1"/\"v2))
proof let v1,v0,v2;
  v2"/\"(v0"/\"v1) = v1"/\"(v2"/\"v0) by A14;
  hence thesis by A371;
end;

A378: for v0,v1,v2 holds
 v0"/\"(v1"\/"(v0"/\"(v2"/\"v1))) = v0"/\"(v1"\/"(v1"/\"v2))
proof let v0,v1,v2;
  v0"/\"(v2"/\"v1) = v1"/\"(v0"/\"v2) by A14;
  hence thesis by A374;
end;

A383: for v102,v100,v101,v1 holds
 (v100"/\"((v101"\/"v102)"/\"(v100"/\"(v1"\/"v101))))=(v100"/\"(v101"\/"(
(v100"/\"v1)"/\"v102)))
proof let v102,v100,v101,v1;
((v100"/\"v1)"\/"(v100"/\"v101))=(v100"/\"(v1"\/"v101)) by A6;
hence thesis by A82;
end;

A388: for v0,v2,v3,v1 holds
 (v0"/\"(v0"/\"((v1"\/"v3)"/\"(v1"\/"v2))))=(v0"/\"(v1"\/"((v0"/\"v3)"/\"v2)))
proof let v0,v2,v3,v1;
(v0"/\"((v1"\/"v3)"/\"(v1"\/"v2)))=((v1"\/"v2)"/\"(v0"/\"(v1"\/"v3))) by A14;
hence thesis by A383;
end;

A391: for v0,v1,v3,v2 holds
 (v0"/\"(v0"/\"(v1"\/"(v2"/\"v3))))=(v0"/\"(v1"\/"((v0"/\"v2)"/\"v3)))
proof let v0,v1,v3,v2;
((v1"\/"v2)"/\"(v1"\/"v3))=(v1"\/"(v2"/\"v3)) by A4;
hence thesis by A388;
end;

A398: for v0,v1,v3,v2 holds
 (v0"/\"(v0"/\"(v1"\/"(v2"/\"v3))))=(v0"/\"(v1"\/"(v0"/\"(v3"/\"v2))))
proof let v0,v1,v3,v2;
(v0"/\"(v3"/\"v2))=(v2"/\"(v0"/\"v3)) by A14;
hence thesis by A391;
end;

A408: for v100,v1 holds
 (v100"/\"(v1"\/"v100))=(v100"\/"((v100"/\"v1)"/\"(v100"/\"v1)))
proof let v100,v1;
((v100"\/"(v100"/\"v1))"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v1"\/"v100)) by
A85;
hence thesis;
end;

A413: for v1,v0 holds (v0"/\"(v0"\/"v1))=(v0"\/"(v1"/\"((v0"/\"v1)"/\"v0)))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"/\"v1))=(v1"/\"((v0"/\"v1)"/\"v0)) by A14;
hence thesis by A408;
end;

A417: for v1,v0 holds (v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"((v0"/\"v1)"/\"v1)))
proof let v1,v0;
(v0"/\"((v0"/\"v1)"/\"v1))=(v1"/\"(v0"/\"(v0"/\"v1))) by A14;
hence thesis by A413;
end;

A421: for v1,v0 holds (v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"(v0"/\"(v1"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A417;
end;

A425: for v102,v0,v2,v1 holds
 ((v0"/\"(v1"\/"v2))"\/"((v0"\/"(v0"/\"v1))"/\"v102))=
((v0"\/"(v0"/\"v1))"/\"((v2"\/"(v0"/\"v1))"\/"v102))
proof let v102,v0,v2,v1;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v2)) by A85;
hence thesis by A6;
end;

A432: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=
((v0"\/"(v0"/\"v1))"/\"(v2"\/"((v0"/\"v1)"\/"v3)))
proof let v3,v0,v2,v1;
(v2"\/"((v0"/\"v1)"\/"v3))=(v3"\/"(v2"\/"(v0"/\"v1))) by A8;
hence thesis by A425;
end;

A438: for v2,v101,v1,v0 holds
 (((v0"\/"(v0"/\"v1))"/\"v101)"\/"(v0"/\"(v1"\/"v2)))=
((v0"\/"(v0"/\"v1))"/\"(v101"\/"(v2"\/"(v0"/\"v1))))
proof let v2,v101,v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v2)) by A85;
hence thesis by A6;
end;

A444: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"\/"(v1"/\"v2)))"\/"(v1"/\"(v2"\/"v3)))=
((v1"/\"(v2"\/"v0))"\/"(v3"/\"(v1"\/"(v1"/\"v2))))
proof let v3,v0,v2,v1;
((v1"\/"(v1"/\"v2))"/\"(v0"\/"(v3"\/"(v1"/\"v2))))=
((v1"/\"(v2"\/"v0))"\/"(v3"/\"(v1"\/"(v1"/\"v2)))) by A432;
hence thesis by A438;
end;

A447: for v100,v101,v2,v1 holds
 ((v100"\/"(v100"/\"v101))"/\"((v1"\/"v2)"\/"(v100"/\"v101)))=
(v100"/\"(v2"\/"(v101"\/"v1)))
proof let v100,v101,v2,v1;
(v101"\/"(v1"\/"v2))=(v2"\/"(v101"\/"v1)) by A8;
hence thesis by A85;
end;

A450: for v2,v3,v1,v0 holds
 ((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v3"\/"(v0"/\"v1))))=(v0"/\"(v3"\/"(v1"\/"v2)))
proof let v2,v3,v1,v0;
((v2"\/"v3)"\/"(v0"/\"v1))=(v2"\/"(v3"\/"(v0"/\"v1))) by A181;
hence thesis by A447;
end;

A452: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v3"\/"(v1"\/"v2)))
proof let v3,v0,v2,v1;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v3"\/"(v0"/\"v1))))=
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1)))) by A432;
hence thesis by A450;
end;

A454: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v2"\/"(v3"\/"v1)))
proof let v3,v0,v2,v1;
(v3"\/"(v1"\/"v2))=(v2"\/"(v3"\/"v1)) by A8;
hence thesis by A452;
end;

A458: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v3"\/"v2)))
proof let v3,v0,v2,v1;
(v1"\/"(v3"\/"v2))=(v2"\/"(v1"\/"v3)) by A8;
hence thesis by A454;
end;

A504: for v102,v2,v1,v0 holds
 ((v0"/\"(v1"\/"v2))"\/"((v2"\/"(v0"/\"v1))"/\"v102))=((v2"\/"(v0"/\"v1))"/\"((
v0"\/"
(v0"/\"v1))"\/"v102))
proof let v102,v2,v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v2)) by A85;
hence thesis by A6;
end;

A511: for v3,v2,v1,v0 holds
 ((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v2"\/"(v0"/\"v1))))=((v2"\/"(v0"/\"v1))"/\"(v0
"\/"(
(v0"/\"v1)"\/"v3)))
proof let v3,v2,v1,v0;
(v0"\/"((v0"/\"v1)"\/"v3))=(v3"\/"(v0"\/"(v0"/\"v1))) by A8;
hence thesis by A504;
end;

A516: for v102,v101,v1,v0 holds
 ((v0"\/"(v1"\/"((v0"\/"v1)"/\"v101)))"/\"(v102"\/"((v0"\/"v1)"/\"v101)))=((v0
"\/"v1)"/\"
(v101"\/"v102))
proof let v102,v101,v1,v0;
((v0"\/"v1)"\/"((v0"\/"v1)"/\"v101))=(v0"\/"(v1"\/"((v0"\/"v1)"/\"v101))) by
A181;
hence thesis by A85;
end;

A523: for v3,v2,v1,v0 holds
 ((v2"/\"(v0"\/"v1))"\/"(v3"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v2"\/"v3))
proof let v3,v2,v1,v0;
((v0"\/"(v1"\/"(v2"/\"(v0"\/"v1))))"/\"(v3"\/"(v2"/\"(v0"\/"v1))))=((v2"/\"(v0
"\/"v1))"\/"
(v3"/\"(v0"\/"v1))) by A346;
hence thesis by A516;
end;

A527: for v103,v100 holds
 (v100"/\"(v100"/\"(v100"\/"v103)))=(v100"/\"(v100"\/"(v103"/\"(v100"/\"v100)))
)
proof let v103,v100;
((v100"\/"(v100"/\"v100))"/\"(v103"\/"(v100"/\"v100)))=(v100"/\"(v100"\/"v103))
;
hence thesis by A82;
end;

A530: for v1,v0 holds (v0"/\"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"(v0"/\"(v1"/\"v0
))))
proof let v1,v0;
(v1"/\"(v0"/\"v0))=(v0"/\"(v1"/\"v0)) by A14;
hence thesis by A527;
end;

A534: for v1,v0 holds (v0"/\"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"(v0"/\"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"/\"(v0"/\"v1))))=(v0"/\"(v0"\/"(v0"/\"v1))) by A378;
hence thesis by A530;
end;

A539: for v102,v1,v100 holds
 ((v100"/\"(v100"\/"v1))"/\"(v100"\/"v102))=(v100"\/"((v100"/\"(v100"/\"
(v1"/\"v1)))"/\"v102))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v100"/\"(v1"/\"v1))))=(v100"/\"(v100"\/"v1)) by A421;
hence thesis by A4;
end;

A542: for v2,v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"(v0"\/"v2)))=(v0"\/"((v0"/\"(v0"/\"(v1"/\"v1)))"/\"v2))
proof let v2,v1,v0;
((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2))) by A292;
hence thesis by A539;
end;

A544: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v1"/\"v2)))=(v0"\/"((v0"/\"(v0"/\"(v1"/\"v1)))"/\"v2))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A542;
end;

A548: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v1"/\"v2)))=(v0"\/"(v0"/\"((v0"/\"(v1"/\"v1))"/\"v2)))
proof let v0,v2,v1;
(v0"/\"((v0"/\"(v1"/\"v1))"/\"v2))=(v2"/\"(v0"/\"(v0"/\"(v1"/\"v1)))) by A14;
hence thesis by A544;
end;

A552: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v1"/\"v2)))=(v0"\/"(v0"/\"(v0"/\"((v1"/\"v1)"/\"v2))))
proof let v0,v2,v1;
(v0"/\"((v1"/\"v1)"/\"v2))=(v2"/\"(v0"/\"(v1"/\"v1))) by A14;
hence thesis by A548;
end;

A556: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v1"/\"v2)))=(v0"\/"(v0"/\"(v0"/\"(v1"/\"(v2"/\"v1)))))
proof let v0,v2,v1;
(v2"/\"(v1"/\"v1))=(v1"/\"(v2"/\"v1)) by A14;
hence thesis by A552;
end;

A576: for v1,v101,v100 holds
 ((v100"\/"v101)"/\"(v101"/\"(v101"\/"v1)))=(v101"\/"(v100"/\"(v101"/\"(v101
"/\"
(v1"/\"v1)))))
proof let v1,v101,v100;
(v101"\/"(v101"/\"(v101"/\"(v1"/\"v1))))=(v101"/\"(v101"\/"v1)) by A421;
hence thesis by A4;
end;

A579: for v0,v2,v1 holds
 (v1"/\"((v1"\/"v2)"/\"(v0"\/"v1)))=(v1"\/"(v0"/\"(v1"/\"(v1"/\"(v2"/\"v2)))))
proof let v0,v2,v1;
(v1"/\"((v1"\/"v2)"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v1"/\"(v1"\/"v2))) by A14;
hence thesis by A576;
end;

A582: for v0,v1,v2 holds
 (v0"/\"(v0"\/"(v2"/\"v1)))=(v0"\/"(v2"/\"(v0"/\"(v0"/\"(v1"/\"v1)))))
proof let v0,v1,v2;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"v0)))=(v0"/\"(v0"\/"(v2"/\"v1))) by A194;
hence thesis by A579;
end;

A590: for v1,v0 holds
 (v0"\/"(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"(v0"\/"(v1"\/"v1)))
proof let v1,v0;
(v0"/\"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1)))) by A398;
hence thesis by A421;
end;

A592: for v1,v0 holds (v0"\/"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"
v1)))
proof let v1,v0;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v1"\/"(v1"/\"v1))) by A378;
hence thesis by A590;
end;

A693: for v102,v1,v100 holds
 (v100"/\"(((v100"/\"(v1"/\"v1))"\/"v102)"/\"(v100"/\"(v100"\/"v1))))=(v100"/\"
(
(v100"/\"(v1"/\"v1))"\/"(v100"/\"v102)))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v100"/\"(v1"/\"v1))))=(v100"/\"(v100"\/"v1)) by A421;
hence thesis by A82;
end;

A699: for v1,v2,v0 holds
 (v0"/\"((v0"\/"v2)"/\"((v1"\/"(v0"/\"(v2"/\"v2)))"/\"v0)))=(v0"/\"((v0"/\"(v2
"/\"v2))"\/"
(v0"/\"v1)))
proof let v1,v2,v0;
((v1"\/"(v0"/\"(v2"/\"v2)))"/\"(v0"/\"(v0"\/"v2)))=((v0"\/"v2)"/\"((v1"\/"(v0
"/\"
(v2"/\"v2)))"/\"v0)) by A14;
hence thesis by A693;
end;

A704: for v2,v1,v0 holds
 (v0"/\"(v0"/\"((v2"\/"(v0"/\"(v1"/\"v1)))"/\"(v0"\/"v1))))=(v0"/\"((v0"/\"(v1
"/\"v1))"\/"
(v0"/\"v2)))
proof let v2,v1,v0;
(v0"/\"((v2"\/"(v0"/\"(v1"/\"v1)))"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v0"/\"(v2
"\/"(v0"/\"
(v1"/\"v1))))) by A14;
hence thesis by A699;
end;

A710: for v2,v1,v0 holds
 (v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1))))))=(v0"/\"(v0"/\"(
(v1"/\"v1)"\/"v2)))
proof let v2,v1,v0;
((v0"/\"(v1"/\"v1))"\/"(v0"/\"v2))=(v0"/\"((v1"/\"v1)"\/"v2)) by A6;
hence thesis by A704;
end;

A714: for v2,v1,v0 holds
 (v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1))))))=(v0"/\"(v2"\/"(v0
"/\"
(v1"/\"v1))))
proof let v2,v1,v0;
(v0"/\"(v0"/\"(v2"\/"(v1"/\"v1))))=(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1)))) by A398;
hence thesis by A710;
end;

A717: for v100,v1,v103 holds
 (v100"/\"((v103"\/"(v103"/\"(v1"/\"v1)))"/\"(v103"\/"(v100"/\"v103))))=(v100
"/\"
(v103"/\"(v103"\/"v1)))
proof let v100,v1,v103;
(v103"\/"(v103"/\"(v103"/\"(v1"/\"v1))))=(v103"/\"(v103"\/"v1)) by A421;
hence thesis by A82;
end;

A720: for v0,v2,v1 holds
 (v0"/\"(v1"\/"((v1"/\"(v2"/\"v2))"/\"(v0"/\"v1))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v2,v1;
((v1"\/"(v1"/\"(v2"/\"v2)))"/\"(v1"\/"(v0"/\"v1)))=(v1"\/"((v1"/\"(v2"/\"v2))
"/\"
(v0"/\"v1))) by A4;
hence thesis by A717;
end;

A722: for v0,v2,v1 holds
 (v0"/\"(v1"\/"(v1"/\"((v1"/\"(v2"/\"v2))"/\"v0))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v2,v1;
((v1"/\"(v2"/\"v2))"/\"(v0"/\"v1))=(v1"/\"((v1"/\"(v2"/\"v2))"/\"v0)) by A14;
hence thesis by A720;
end;

A726: for v0,v2,v1 holds
 (v0"/\"(v1"\/"(v0"/\"((v1"/\"(v2"/\"v2))"/\"v1))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v2,v1;
(v0"/\"((v1"/\"(v2"/\"v2))"/\"v1))=(v1"/\"(v0"/\"(v1"/\"(v2"/\"v2)))) by A14;
hence thesis by A722;
end;

A730: for v1,v2,v0 holds
 (v0"/\"(v1"/\"(v1"\/"(v0"/\"v2))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v1"\/"(v0"/\"(v1"/\"(v1"/\"(v2"/\"v2)))))=(v1"/\"(v1"\/"(v0"/\"v2))) by A582;
hence thesis by A726;
end;

A733: for v1,v100 holds
 (v100"\/"(v100"/\"(v100"/\"(v1"\/"(v1"/\"(v100"/\"v1))))))=(v100"/\"(v100"\/"(
v1"\/"
(v100"/\"v1))))
proof let v1,v100;
(v100"/\"((v1"\/"(v100"/\"v1))"/\"(v1"\/"(v100"/\"v1))))=(v100"/\"(v1"\/"(v1
"/\"
(v100"/\"v1)))) by A82;
hence thesis by A421;
end;

A736: for v1,v0 holds
 (v0"\/"(v0"/\"(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1))))))=(v0"/\"(v0"\/"(v1"\/"(v0
"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A733;
end;

A738: for v1,v0 holds
 (v0"\/"(v0"/\"(v0"/\"(v1"\/"(v1"/\"v1)))))=(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v1"\/"(v1"/\"v1))) by A378;
hence thesis by A736;
end;

A740: for v1,v0 holds
 (v0"\/"(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1)))) by A398;
hence thesis by A738;
end;

A742: for v1,v0 holds
 (v0"\/"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v1"\/"(v1"/\"v1))) by A378;
hence thesis by A740;
end;

A744: for v1,v0 holds (v0"/\"(v0"\/"(v1"\/"v1)))=(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1
))))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"v1))) by A592;
hence thesis by A742;
end;

A754: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"/\"((v0"/\"
v1)"/\"
(v0"/\"v1)))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"(v0
"\/"
(v0"/\"v1)))) by A85;
hence thesis by A421;
end;

A756: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"/\"(v1"/\"(
(v0"/\"v1)"/\"v0)))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"/\"v1))=(v1"/\"((v0"/\"v1)"/\"v0)) by A14;
hence thesis by A754;
end;

A760: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(
(v0"/\"v1)"/\"v1)))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v0"/\"v1)"/\"v1))=(v1"/\"(v0"/\"(v0"/\"v1))) by A14;
hence thesis by A756;
end;

A764: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(
v0"/\"
(v1"/\"v1))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A760;
end;

A766: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"((v0"/\"(v1"/\"v1))"/\"(
v0"\/"
(v0"/\"v1))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v0"/\"(v1"/\"v1))"/\"(v0"\/"(v0"/\"v1))))=((v0"\/"(v0"/\"v1))"/\"(v0
"/\"(v0"/\"
(v1"/\"v1)))) by A14;
hence thesis by A764;
end;

A768: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(v0"/\"((v1"/\"v1)"/\"(v0
"\/"
(v0"/\"v1)))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v0"/\"(v1"/\"v1))"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"((v1"/\"v1)"/\"(v0"\/"(v0"/\"
v1)))) by
 A292;
hence thesis by A766;
end;

A770: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(v0"/\"(v1"/\"(v1"/\"(v0
"\/"
(v0"/\"v1))))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v1"/\"v1)"/\"(v0"\/"(v0"/\"v1)))=(v1"/\"(v1"/\"(v0"\/"(v0"/\"v1)))) by A292;
hence thesis by A768;
end;

A772: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v1
"/\"
(v0"/\"v1))))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v1"/\"(v1"/\"(v0"\/"(v0"/\"v1))))=(v1"/\"(v0"\/"(v1"/\"(v0"/\"v1)))) by A398;
hence thesis by A770;
end;

A774: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"((v0"\/"(v0"/\"v1))"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v0
"/\"
(v1"/\"v1))))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A772;
end;

A776: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"((v0"/\"(v1"/\"(v0"\/"(v0"/\"(v1"/\"v1)))))"/\"(
v0"\/"
(v0"/\"v1)))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v0"/\"(v1"/\"(v0"\/"(v0"/\"(v1"/\"v1)))))"/\"(v0"\/"(v0"/\"v1))))=((v0
"\/"
(v0"/\"v1))"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v0"/\"(v1"/\"v1))))))) by A14;
hence thesis by A774;
end;

A780: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"((v1"/\"(v0"\/"(v0"/\"(v1"/\"v1))))"/\"(
v0"\/"
(v0"/\"v1))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v1"/\"(v0"\/"(v0"/\"(v1"/\"v1))))"/\"(v0"\/"(v0"/\"v1))))=((v0"\/"(v0
"/\"v1))"/\"
(v0"/\"(v1"/\"(v0"\/"(v0"/\"(v1"/\"v1)))))) by A14;
hence thesis by A776;
end;

A784: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"((v0"\/"(v0"/\"(v1"/\"v1)))"/\"(v0
"\/"
(v0"/\"v1)))))))=(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v1"/\"((v0"\/"(v0"/\"(v1"/\"v1)))"/\"(v0"\/"(v0"/\"v1))))=((v0"\/"(v0"/\"v1))
"/\"(v1"/\"
(v0"\/"(v0"/\"(v1"/\"v1))))) by A14;
hence thesis by A780;
end;

A788: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"((v0"/\"v1)"/\"(v0"/\"(v1
"/\"v1))))))))=
(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v0"\/"(v0"/\"(v1"/\"v1))))=(v0"\/"((v0"/\"v1)"/\"(v0
"/\"
(v1"/\"v1))));
hence thesis by A784;
end;

A790: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v0"/\"((v1"/\"v1)"/\"(v0
"/\"v1))))))))=
(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v1"/\"v1)"/\"(v0"/\"v1)))=((v0"/\"v1)"/\"(v0"/\"(v1"/\"v1))) by A14;
hence thesis by A788;
end;

A796: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"(v0"/\"(v0"/\"((v1"/\"v1)
"/\"v1))))))))=
(v0"/\"(v1"\/"(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v1"/\"v1)"/\"v1))=(v1"/\"(v0"/\"(v1"/\"v1))) by A14;
hence thesis by A790;
end;

A800: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"/\"(v0"\/"(v1"/\"v1)))))))=(v0
"/\"(v1"\/"
(v0"\/"(v0"/\"v1))))
proof let v1,v0;
(v0"\/"(v0"/\"(v0"/\"(v1"/\"(v1"/\"v1)))))=(v0"/\"(v0"\/"(v1"/\"v1))) by A556;
hence thesis by A796;
end;

A802: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v1"/\"(v0"/\"(v0"\/"v1))))))=(v0"/\"(v1
"\/"(v0"\/"
(v0"/\"v1))))
proof let v1,v0;
(v1"/\"(v0"/\"(v0"\/"(v1"/\"v1))))=(v1"/\"(v0"/\"(v0"\/"v1)));
hence thesis by A800;
end;

A804: for v1,v0 holds
 ((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v0"/\"((v0"\/"v1)"/\"v1)))))=(v0"/\"(v1
"\/"(v0"\/"
(v0"/\"v1))))
proof let v1,v0;
(v0"/\"((v0"\/"v1)"/\"v1))=(v1"/\"(v0"/\"(v0"\/"v1))) by A14;
hence thesis by A802;
end;

A808: for v1,v0 holds
 (v0"\/"((v0"/\"v1)"\/"(v0"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1)))))))=(v0"/\"(v1
"\/"(v0"\/"
(v0"/\"v1))))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1))))))=(v0"\/"((v0
"/\"v1)"\/"
(v0"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1))))))) by A181;
hence thesis by A804;
end;

A810: for v1,v0 holds
 (v0"\/"(v0"/\"(v1"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1)))))))=(v0"/\"(v1"\/"(v0
"\/"
(v0"/\"v1))))
proof let v1,v0;
((v0"/\"v1)"\/"(v0"/\"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1))))))=(v0"/\"(v1"\/"(v0
"/\"(v0"/\"(v1"/\"
(v0"\/"v1)))))) by A6;
hence thesis by A808;
end;

A812: for v1,v0 holds
 (v0"\/"(v0"/\"(v1"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1)))))))=(v0"/\"(v0"\/"(
(v0"/\"v1)"\/"v1)))
proof let v1,v0;
(v0"\/"((v0"/\"v1)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v1))) by A8;
hence thesis by A810;
end;

A816: for v1,v0 holds
 (v0"\/"(v0"/\"(v1"\/"(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1)))))))=(v0"/\"(v0"\/"(v1
"\/"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"\/"(v0"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"v1))) by A744;
hence thesis by A812;
end;

A821: for v102,v1,v100 holds
 (v100"/\"((v100"/\"(v100"\/"v1))"/\"v102))=(v102"/\"(v100"/\"(v100"\/"(v100
"/\"v1))))
proof let v102,v1,v100;
(v100"/\"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"(v100"/\"v1))) by A534;
hence thesis by A14;
end;

A827: for v1,v2,v0 holds
 (v0"/\"(v0"/\"((v0"\/"v2)"/\"v1)))=(v1"/\"(v0"/\"(v0"\/"(v0"/\"v2))))
proof let v1,v2,v0;
(v0"/\"((v0"\/"v2)"/\"v1))=(v1"/\"(v0"/\"(v0"\/"v2))) by A14;
hence thesis by A821;
end;

A833: for v1,v2,v0 holds
 (v0"/\"(v0"/\"(v1"/\"(v0"\/"v2))))=(v0"/\"((v0"\/"(v0"/\"v2))"/\"v1))
proof let v1,v2,v0;
(v0"/\"((v0"\/"(v0"/\"v2))"/\"v1))=(v1"/\"(v0"/\"(v0"\/"(v0"/\"v2)))) by A14;
hence thesis by A827;
end;

A839: for v2,v1,v0 holds
 ((v0"\/"v1)"/\"((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1"\/"v2))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A534;
end;

A841: for v2,v1,v0 holds
 ((v0"\/"v1)"/\"((v0"\/"v1)"/\"(v2"\/"((v0"\/"v1)"\/"v1))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v2,v1,v0;
((v0"\/"v1)"\/"(v1"\/"v2))=(v2"\/"((v0"\/"v1)"\/"v1)) by A8;
hence thesis by A839;
end;

A845: for v2,v1,v0 holds
 ((v0"\/"v1)"/\"((v0"\/"v1)"/\"(v2"\/"(v0"\/"(v1"\/"v1)))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v2,v1,v0;
(v0"\/"(v1"\/"v1))=(v1"\/"(v0"\/"v1)) by A8;
hence thesis by A841;
end;

A847: for v0,v2,v1 holds
 ((v0"\/"v1)"/\"((v0"\/"v1)"/\"(v0"\/"((v1"\/"v1)"\/"v2))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v0,v2,v1;
(v0"\/"((v1"\/"v1)"\/"v2))=(v2"\/"(v0"\/"(v1"\/"v1))) by A8;
hence thesis by A845;
end;

A851: for v0,v1,v2 holds
 ((v0"\/"v1)"/\"((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v2"\/"v1)))))=((v0"\/"v1)"/\"((v0
"\/"v1)"\/"
(v1"\/"(v0"/\"v2))))
proof let v0,v1,v2;
(v2"\/"(v1"\/"v1))=(v1"\/"(v2"\/"v1)) by A8;
hence thesis by A847;
end;

A855: for v0,v2,v1 holds
 ((v0"\/"v1)"/\"(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2)))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"(v1"\/"
(v0"/\"v2))))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v1"\/"v2))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2))))
by A4;
hence thesis by A851;
end;

A857: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"/\"(v1"\/"(v1"\/"v2)))))=((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1
"\/"
(v0"/\"v2))))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2)))))=(v0"\/"(v1"/\"(v1"/\"(v1"\/"
(v1"\/"v2))))) by A4;
hence thesis by A855;
end;

A859: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1
"\/"
(v0"/\"v2))))
proof let v0,v2,v1;
(v1"/\"(v1"/\"(v1"\/"(v1"\/"v2))))=(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))) by A534;
hence thesis by A857;
end;

A861: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"(v1"\/"((v0"/\"v2)
"\/"
(v0"\/"v1))))
proof let v0,v2,v1;
(v1"\/"((v0"/\"v2)"\/"(v0"\/"v1)))=((v0"\/"v1)"\/"(v1"\/"(v0"/\"v2))) by A8;
hence thesis by A859;
end;

A863: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"(v1"\/"(v1"\/"(
(v0"/\"v2)"\/"v0))))
proof let v0,v2,v1;
((v0"/\"v2)"\/"(v0"\/"v1))=(v1"\/"((v0"/\"v2)"\/"v0)) by A8;
hence thesis by A861;
end;

A867: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"(v1"\/"(v0"\/"(
(v0"/\"v2)"\/"v1))))
proof let v0,v2,v1;
(v0"\/"((v0"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v2))) by A8;
hence thesis by A863;
end;

A871: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=((v0"\/"v1)"/\"(v0"\/"((v1"\/"
(v0"/\"v2))"\/"v1)))
proof let v0,v2,v1;
(v0"\/"((v1"\/"(v0"/\"v2))"\/"v1))=(v1"\/"(v0"\/"(v1"\/"(v0"/\"v2)))) by A8;
hence thesis by A867;
end;

A875: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"
v2)))))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"
(v0"/\"v2))))) by A4;
hence thesis by A871;
end;

A879: for v102,v1,v100 holds
 ((v100"/\"(v100"\/"(v100"/\"v1)))"\/"((v100"/\"(v100"\/"v1))"/\"v102))=((v100
"/\"
(v100"\/"v1))"/\"(v100"\/"v102))
proof let v102,v1,v100;
(v100"/\"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"(v100"/\"v1))) by A534;
hence thesis by A6;
end;

A884: for v2,v1,v0 holds
 ((v0"/\"(v0"\/"(v0"/\"v1)))"\/"(v0"/\"((v0"\/"v1)"/\"v2)))=((v0"/\"(v0"\/"v1))
"/\"
(v0"\/"v2))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"v2))=(v2"/\"(v0"/\"(v0"\/"v1))) by A14;
hence thesis by A879;
end;

A888: for v2,v1,v0 holds
 (v0"/\"((v0"\/"(v0"/\"v1))"\/"(v2"/\"(v0"\/"v1))))=((v0"/\"(v0"\/"v1))"/\"(v0
"\/"v2))
proof let v2,v1,v0;
((v0"/\"(v0"\/"(v0"/\"v1)))"\/"(v0"/\"(v2"/\"(v0"\/"v1))))=(v0"/\"((v0"\/"(v0
"/\"v1))"\/"
(v2"/\"(v0"\/"v1)))) by A6;
hence thesis by A884;
end;

A890: for v2,v1,v0 holds
 (v0"/\"(v0"\/"((v0"/\"v1)"\/"(v2"/\"(v0"\/"v1)))))=((v0"/\"(v0"\/"v1))"/\"(v0
"\/"v2))
proof let v2,v1,v0;
((v0"\/"(v0"/\"v1))"\/"(v2"/\"(v0"\/"v1)))=(v0"\/"((v0"/\"v1)"\/"(v2"/\"(v0"\/"
v1)))) by
 A181;
hence thesis by A888;
end;

A892: for v1,v2,v0 holds
 (v0"/\"(v0"\/"(v1"/\"(v0"\/"v2))))=((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))
proof let v1,v2,v0;
(v0"\/"((v0"/\"v1)"\/"(v2"/\"(v0"\/"v1))))=(v0"\/"(v1"/\"(v0"\/"v2))) by A261;
hence thesis by A890;
end;

A894: for v1,v2,v0 holds
 (v0"/\"(v0"\/"(v1"/\"(v0"\/"v2))))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2)))
proof let v1,v2,v0;
((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2))) by A292;
hence thesis by A892;
end;

A896: for v1,v2,v0 holds
 (v0"/\"(v0"\/"(v1"/\"(v0"\/"v2))))=(v0"/\"(v0"\/"(v1"/\"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A894;
end;

A907: for v102,v103,v1,v100 holds
 ((v100"/\"(v100"\/"(v100"/\"v1)))"/\"(v102"\/"v103))=(v100"/\"((v100"/\"
(v100"\/"v1))"/\"(v102"\/"v103)))
proof let v102,v103,v1,v100;
(v100"/\"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"(v100"/\"v1))) by A534;
hence thesis by A292;
end;

A910: for v2,v3,v1,v0 holds
 (v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2"\/"v3)))=(v0"/\"((v0"/\"(v0"\/"v1))"/\"(v2
"\/"v3)))
proof let v2,v3,v1,v0;
((v0"/\"(v0"\/"(v0"/\"v1)))"/\"(v2"\/"v3))=(v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2
"\/"v3))) by
 A292;
hence thesis by A907;
end;

A912: for v2,v3,v1,v0 holds
 (v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2"\/"v3)))=(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2
"\/"v3))))
proof let v2,v3,v1,v0;
((v0"/\"(v0"\/"v1))"/\"(v2"\/"v3))=(v0"/\"((v0"\/"v1)"/\"(v2"\/"v3))) by A292;
hence thesis by A910;
end;

A932: for v1,v2,v0 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v1"/\"v2))))
proof let v1,v2,v0;
(v1"/\"(v1"\/"(v1"/\"(v1"\/"v2))))=(v1"/\"(v1"\/"(v1"/\"v2))) by A896;
hence thesis by A875;
end;

A941: for v102,v100,v101,v1 holds
 (v100"\/"((v101"/\"v102)"\/"(v100"\/"(v1"/\"v101))))=(v100"\/"(v101"/\"(
(v100"\/"v1)"\/"v102)))
proof let v102,v100,v101,v1;
((v100"\/"v1)"/\"(v100"\/"v101))=(v100"\/"(v1"/\"v101)) by A4;
hence thesis by A106;
end;

A946: for v0,v2,v3,v1 holds
 (v0"\/"(v0"\/"((v1"/\"v3)"\/"(v1"/\"v2))))=(v0"\/"(v1"/\"((v0"\/"v3)"\/"v2)))
proof let v0,v2,v3,v1;
(v0"\/"((v1"/\"v3)"\/"(v1"/\"v2)))=((v1"/\"v2)"\/"(v0"\/"(v1"/\"v3))) by A8;
hence thesis by A941;
end;

A949: for v0,v1,v3,v2 holds
 (v0"\/"(v0"\/"(v1"/\"(v2"\/"v3))))=(v0"\/"(v1"/\"((v0"\/"v2)"\/"v3)))
proof let v0,v1,v3,v2;
((v1"/\"v2)"\/"(v1"/\"v3))=(v1"/\"(v2"\/"v3)) by A6;
hence thesis by A946;
end;

A956: for v0,v1,v3,v2 holds
 (v0"\/"(v0"\/"(v1"/\"(v2"\/"v3))))=(v0"\/"(v1"/\"(v0"\/"(v3"\/"v2))))
proof let v0,v1,v3,v2;
(v0"\/"(v3"\/"v2))=(v2"\/"(v0"\/"v3)) by A8;
hence thesis by A949;
end;

A982: for v103,v100,v1,v101 holds
 ((v100"/\"(v101"/\"(v101"\/"(v101"/\"v1))))"\/"((v101"/\"(v101"\/"v1))"/\"v103
))=(
(v101"/\"(v101"\/"v1))"/\"(v103"\/"(v100"/\"v101)))
proof let v103,v100,v1,v101;
(v101"/\"(v101"/\"(v101"\/"v1)))=(v101"/\"(v101"\/"(v101"/\"v1))) by A534;
hence thesis by A131;
end;

A987: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"/\"(v1"\/"(v1"/\"v2))))"\/"(v1"/\"((v1"\/"v2)"/\"v3)))=((v1"/\"(v1
"\/"v2))"/\"
(v3"\/"(v0"/\"v1)))
proof let v3,v0,v2,v1;
(v1"/\"((v1"\/"v2)"/\"v3))=(v3"/\"(v1"/\"(v1"\/"v2))) by A14;
hence thesis by A982;
end;

A991: for v0,v3,v2,v1 holds
 (v1"/\"((v3"/\"(v1"\/"v2))"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=((v1"/\"(v1"\/"v2))
"/\"(v3"\/"
(v0"/\"v1)))
proof let v0,v3,v2,v1;
((v0"/\"(v1"/\"(v1"\/"(v1"/\"v2))))"\/"(v1"/\"(v3"/\"(v1"\/"v2))))=(v1"/\"((v3
"/\"
(v1"\/"v2))"\/"(v0"/\"(v1"\/"(v1"/\"v2))))) by A123;
hence thesis by A987;
end;

A994: for v3,v1,v2,v0 holds
 (v0"/\"((v1"/\"(v0"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v2)))))=(v0"/\"((v0"\/"v2)
"/\"(v1"\/"
(v3"/\"v0))))
proof let v3,v1,v2,v0;
((v0"/\"(v0"\/"v2))"/\"(v1"\/"(v3"/\"v0)))=(v0"/\"((v0"\/"v2)"/\"(v1"\/"(v3"/\"
v0)))) by
 A292;
hence thesis by A991;
end;

A1005: for v100,v3,v101 holds
 (v100"/\"(v101"\/"(v101"/\"v3)))=(v101"/\"(v100"\/"(v100"/\"v3)))
proof let v100,v3,v101;
((v100"/\"v101)"\/"(v101"/\"(v100"/\"v3)))=(v100"/\"(v101"\/"(v101"/\"v3))) by
 A159;
hence thesis by A6;
end;

A1020: for v2,v101,v100 holds
 (v100"/\"((v100"\/"v101)"\/"((v100"\/"v101)"/\"v2)))=(v100"\/"(v101"/\"(v100
"/\"v2)))
proof let v2,v101,v100;
((v100"\/"v101)"/\"(v100"\/"(v100"/\"v2)))=(v100"/\"((v100"\/"v101)"\/"(
(v100"\/"v101)"/\"v2))) by A1005;
hence thesis by A4;
end;

A1025: for v2,v1,v0 holds
 (v0"/\"(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))))=(v0"\/"(v1"/\"(v0"/\"v2)))
proof let v2,v1,v0;
((v0"\/"v1)"\/"(v2"/\"(v0"\/"v1)))=(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))) by A181;
hence thesis by A1020;
end;

A1027: for v2,v1,v0 holds
 (v0"/\"(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))))=(v0"\/"(v0"/\"(v2"/\"v1)))
proof let v2,v1,v0;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1025;
end;

A1032: for v100,v102,v101 holds
 (v100"/\"(v100"/\"((v101"\/"v102)"\/"((v101"\/"v102)"/\"v101))))=(v100"/\"(
v101"\/"
(v100"/\"v102)))
proof let v100,v102,v101;
((v101"\/"v102)"/\"(v100"\/"(v100"/\"v101)))=(v100"/\"((v101"\/"v102)"\/"(
(v101"\/"v102)"/\"v101))) by A1005;
hence thesis by A82;
end;

A1037: for v0,v2,v1 holds
 (v0"/\"(v0"/\"(v1"\/"(v2"\/"(v1"/\"(v1"\/"v2))))))=(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v0,v2,v1;
((v1"\/"v2)"\/"(v1"/\"(v1"\/"v2)))=(v1"\/"(v2"\/"(v1"/\"(v1"\/"v2)))) by A181;
hence thesis by A1032;
end;

A1040: for v101,v100 holds
 (v100"/\"((v100"\/"(v100"/\"v101))"\/"((v100"\/"(v100"/\"v101))"/\"v101)))=(
v100"/\"
(v101"\/"v100))
proof let v101,v100;
((v100"\/"(v100"/\"v101))"/\"(v100"\/"(v100"/\"v101)))=(v100"/\"((v100"\/"
(v100"/\"v101))"\/"((v100"\/"(v100"/\"v101))"/\"v101))) by A1005;
hence thesis by A85;
end;

A1045: for v1,v0 holds
 (v0"/\"(v0"\/"((v0"/\"v1)"\/"(v1"/\"(v0"\/"(v0"/\"v1))))))=(v0"/\"(v1"\/"v0))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"\/"(v1"/\"(v0"\/"(v0"/\"v1))))=(v0"\/"((v0"/\"v1)"\/"(v1
"/\"(v0"\/"
(v0"/\"v1))))) by A181;
hence thesis by A1040;
end;

A1047: for v1,v0 holds
 (v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"\/"(v0"/\"v1))))))=(v0"/\"(v1"\/"v0))
proof let v1,v0;
((v0"/\"v1)"\/"(v1"/\"(v0"\/"(v0"/\"v1))))=(v1"/\"(v0"\/"(v0"\/"(v0"/\"v1))))
by A6;
hence thesis by A1045;
end;

A1049: for v1,v0 holds
 (v0"/\"(v0"\/"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1))))))=(v0"/\"(v1"\/"v0))
proof let v1,v0;
(v0"\/"(v1"/\"(v0"\/"(v0"\/"(v0"/\"v1)))))=(v0"\/"(v0"\/"(v1"/\"(v0"\/"(v0"/\"
v1))))) by
 A956;
hence thesis by A1047;
end;

A1054: for v100,v2,v1 holds
 (v100"/\"(v100"/\"(v100"\/"(v1"\/"(v1"/\"v2)))))=(v100"/\"(v100"\/"(v1"/\"(
v100"\/"
(v100"/\"v2)))))
proof let v100,v2,v1;
(v100"/\"(v1"\/"(v1"/\"v2)))=(v1"/\"(v100"\/"(v100"/\"v2))) by A1005;
hence thesis by A534;
end;

A1057: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"/\"
v2)))))
proof let v0,v2,v1;
(v0"/\"(v0"/\"(v0"\/"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"
v2))))) by
 A534;
hence thesis by A1054;
end;

A1059: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v1"/\"(v0"/\"v2))))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v2)))))=(v0"/\"(v0"\/"(v1"/\"(v0"/\"v2))))
by A896;
hence thesis by A1057;
end;

A1061: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v0"/\"(v2"/\"v1))))
proof let v0,v2,v1;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1059;
end;

A1066: for v103,v102,v2,v100 holds
 (v100"\/"(((v100"/\"v2)"/\"v102)"\/"(v100"/\"(v103"\/"(v103"/\"v2)))))=(v100
"\/"(
(v100"/\"v2)"/\"(v103"\/"v102)))
proof let v103,v102,v2,v100;
(v103"/\"(v100"\/"(v100"/\"v2)))=(v100"/\"(v103"\/"(v103"/\"v2))) by A1005;
hence thesis by A106;
end;

A1072: for v3,v2,v0,v1 holds
 (v0"\/"((v2"/\"(v1"/\"v0))"\/"(v0"/\"(v3"\/"(v3"/\"v2)))))=(v0"\/"((v0"/\"v2)
"/\"
(v3"\/"v1)))
proof let v3,v2,v0,v1;
(v1"/\"(v0"/\"v2))=(v2"/\"(v1"/\"v0)) by A14;
hence thesis by A1066;
end;

A1077: for v3,v0,v1,v2 holds
 (v0"\/"((v0"/\"(v2"/\"v1))"\/"(v0"/\"(v3"\/"(v3"/\"v1)))))=(v0"\/"((v0"/\"v1)
"/\"
(v3"\/"v2)))
proof let v3,v0,v1,v2;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1072;
end;

A1085: for v0,v3,v2,v1 holds
 (v0"\/"(v0"/\"((v1"/\"v2)"\/"(v3"\/"(v1"/\"v3)))))=(v0"\/"((v0"/\"v1)"/\"(v3
"\/"v2)))
proof let v0,v3,v2,v1;
((v0"/\"(v1"/\"v2))"\/"(v0"/\"(v3"\/"(v1"/\"v3))))=(v0"/\"((v1"/\"v2)"\/"(v3
"\/"
(v1"/\"v3)))) by A6;
hence thesis by A1077;
end;

A1087: for v0,v2,v3,v1 holds
 (v0"\/"(v0"/\"(v3"\/"((v1"/\"v3)"\/"(v1"/\"v2)))))=(v0"\/"((v0"/\"v1)"/\"(v3
"\/"v2)))
proof let v0,v2,v3,v1;
(v3"\/"((v1"/\"v3)"\/"(v1"/\"v2)))=((v1"/\"v2)"\/"(v3"\/"(v1"/\"v3))) by A8;
hence thesis by A1085;
end;

A1090: for v0,v2,v3,v1 holds
 (v0"\/"(v0"/\"(v1"\/"(v2"/\"(v1"\/"v3)))))=(v0"\/"((v0"/\"v2)"/\"(v1"\/"v3)))
proof let v0,v2,v3,v1;
((v2"/\"v1)"\/"(v2"/\"v3))=(v2"/\"(v1"\/"v3)) by A6;
hence thesis by A1087;
end;

A1096: for v0,v2,v1,v3 holds
 (v0"\/"(v0"/\"(v1"\/"(v2"/\"(v3"\/"v1)))))=(v0"\/"(v0"/\"(v2"/\"(v3"\/"v1))))
proof let v0,v2,v1,v3;
((v0"/\"v2)"/\"(v3"\/"v1))=(v0"/\"(v2"/\"(v3"\/"v1))) by A292;
hence thesis by A1090;
end;

A1099: for v100,v101,v2,v103 holds
 (v100"\/"((v101"/\"(v103"/\"v2))"\/"(v103"/\"(v100"\/"v101))))=(v100"\/"(v103
"/\"
(v101"\/"(v101"/\"v2))))
proof let v100,v101,v2,v103;
(v101"/\"(v103"\/"(v103"/\"v2)))=(v103"/\"(v101"\/"(v101"/\"v2))) by A1005;
hence thesis by A106;
end;

A1102: for v2,v3,v1,v0 holds
 (v0"\/"(v2"/\"((v0"\/"v1)"\/"(v1"/\"v3))))=(v0"\/"(v2"/\"(v1"\/"(v1"/\"v3))))
proof let v2,v3,v1,v0;
((v1"/\"(v2"/\"v3))"\/"(v2"/\"(v0"\/"v1)))=(v2"/\"((v0"\/"v1)"\/"(v1"/\"v3)))
by A123;
hence thesis by A1099;
end;

A1105: for v1,v0,v3,v2 holds
 (v0"\/"(v1"/\"(v0"\/"(v2"\/"(v2"/\"v3)))))=(v0"\/"(v1"/\"(v2"\/"(v2"/\"v3))))
proof let v1,v0,v3,v2;
((v0"\/"v2)"\/"(v2"/\"v3))=(v0"\/"(v2"\/"(v2"/\"v3))) by A181;
hence thesis by A1102;
end;

A1107: for v0,v1,v3,v2 holds
 (v0"\/"(v0"\/"(v1"/\"(v2"\/"(v2"/\"v3)))))=(v0"\/"(v1"/\"(v2"\/"(v2"/\"v3))))
proof let v0,v1,v3,v2;
(v0"\/"(v1"/\"(v0"\/"(v2"\/"(v2"/\"v3)))))=(v0"\/"(v0"\/"(v1"/\"(v2"\/"(v2"/\"
v3))))) by
 A956;
hence thesis by A1105;
end;

A1109: for v1,v0 holds (v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1)))))=(v0"/\"(v0
"\/"v1))
proof let v1,v0;
(v0"\/"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1))))
by A1107;
hence thesis by A1049;
end;

A1111: for v1,v0 holds (v0"/\"(v0"\/"(v1"/\"(v0"/\"v1))))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"/\"(v0"\/"(v0"/\"v1)))))=(v0"/\"(v0"\/"(v1"/\"(v0"/\"v1))))
by A896;
hence thesis by A1109;
end;

A1113: for v1,v0 holds (v0"/\"(v0"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
hence thesis by A1111;
end;

A1115: for v1,v0 holds (v0"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v0"\/"(v0"/\"v1)));
hence thesis by A1113;
end;

A1117: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v1"\/"(v1"/\"v2))))=(v0"/\"(v0"\/"(v0"/\"(v1"/\"v2))))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))=(v0"/\"(v0"\/"(v1"\/"(v1"/\"v2))))
by A1115;
hence thesis by A1061;
end;

A1119: for v0,v2,v1 holds
 (v0"/\"(v0"\/"(v1"\/"(v1"/\"v2))))=(v0"/\"(v0"\/"(v1"/\"v2)))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v0"/\"(v1"/\"v2))))=(v0"/\"(v0"\/"(v1"/\"v2))) by A1115;
hence thesis by A1117;
end;

A1121: for v1,v2,v0 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v1"/\"(v1"\/"(v1"/\"v2)))=(v1"/\"(v1"\/"v2)) by A1115;
hence thesis by A932;
end;

A1126: for v1,v0 holds (v0"/\"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v0"\/"v1)) by A1115;
hence thesis by A534;
end;

A1159: for v102,v1,v100 holds
 (v100"/\"((v100"\/"(v100"/\"v1))"/\"v102))=(v102"/\"(v100"/\"(v100"\/"v1)))
proof let v102,v1,v100;
(v100"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1115;
hence thesis by A14;
end;

A1165: for v1,v2,v0 holds
 (v0"/\"(v1"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"((v0"\/"v2)"/\"v1))
proof let v1,v2,v0;
(v0"/\"((v0"\/"v2)"/\"v1))=(v1"/\"(v0"/\"(v0"\/"v2))) by A14;
hence thesis by A1159;
end;

A1170: for v101,v1,v100 holds
 ((v100"\/"v101)"/\"(v101"\/"(v100"\/"(v100"/\"v1))))=(v101"\/"(v100"/\"(v100
"\/"v1)))
proof let v101,v1,v100;
(v100"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1115;
hence thesis by A4;
end;

A1173: for v1,v2,v0 holds
 ((v0"\/"v1)"/\"(v0"\/"((v0"/\"v2)"\/"v1)))=(v1"\/"(v0"/\"(v0"\/"v2)))
proof let v1,v2,v0;
(v0"\/"((v0"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v2))) by A8;
hence thesis by A1170;
end;

A1177: for v1,v2,v0 holds
 (v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))=(v1"\/"(v0"/\"(v0"\/"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v0"/\"v2))))=(v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))
by A4;
hence thesis by A1173;
end;

A1180: for v1,v2,v0 holds
 ((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1"\/"(v0"/\"v2))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A1115;
end;

A1182: for v1,v2,v0 holds
 ((v0"\/"v1)"/\"(v1"\/"((v0"/\"v2)"\/"(v0"\/"v1))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
(v1"\/"((v0"/\"v2)"\/"(v0"\/"v1)))=((v0"\/"v1)"\/"(v1"\/"(v0"/\"v2))) by A8;
hence thesis by A1180;
end;

A1184: for v1,v2,v0 holds
 ((v0"\/"v1)"/\"(v1"\/"(v1"\/"((v0"/\"v2)"\/"v0))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
((v0"/\"v2)"\/"(v0"\/"v1))=(v1"\/"((v0"/\"v2)"\/"v0)) by A8;
hence thesis by A1182;
end;

A1188: for v1,v2,v0 holds
 ((v0"\/"v1)"/\"(v1"\/"(v0"\/"((v0"/\"v2)"\/"v1))))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
(v0"\/"((v0"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v2))) by A8;
hence thesis by A1184;
end;

A1192: for v1,v2,v0 holds
 ((v0"\/"v1)"/\"(v0"\/"((v1"\/"(v0"/\"v2))"\/"v1)))=((v0"\/"v1)"/\"((v0"\/"v1)
"\/"
(v1"\/"v2)))
proof let v1,v2,v0;
(v0"\/"((v1"\/"(v0"/\"v2))"\/"v1))=(v1"\/"(v0"\/"(v1"\/"(v0"/\"v2)))) by A8;
hence thesis by A1188;
end;

A1196: for v1,v2,v0 holds
 (v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1
"\/"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"
(v0"/\"v2))))) by A4;
hence thesis by A1192;
end;

A1198: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v1"\/"v2)))
proof let v0,v2,v1;
(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"v2))) by A1121;
hence thesis by A1196;
end;

A1200: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"(v2"\/"((v0"\/"v1)"\/"v1)))
proof let v0,v2,v1;
((v0"\/"v1)"\/"(v1"\/"v2))=(v2"\/"((v0"\/"v1)"\/"v1)) by A8;
hence thesis by A1198;
end;

A1204: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"(v2"\/"(v0"\/"(v1"\/"v1))))
proof let v0,v2,v1;
(v0"\/"(v1"\/"v1))=(v1"\/"(v0"\/"v1)) by A8;
hence thesis by A1200;
end;

A1206: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"(v0"\/"((v1"\/"v1)"\/"v2)))
proof let v0,v2,v1;
(v0"\/"((v1"\/"v1)"\/"v2))=(v2"\/"(v0"\/"(v1"\/"v1))) by A8;
hence thesis by A1204;
end;

A1210: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"v2)))=((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v2"\/"v1))))
proof let v0,v2,v1;
(v2"\/"(v1"\/"v1))=(v1"\/"(v2"\/"v1)) by A8;
hence thesis by A1206;
end;

A1214: for v0,v2,v1 holds
 (v0"\/"(v1"/\"(v1"\/"v2)))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2))))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v1"\/"v2))))=(v0"\/"(v1"/\"(v1"\/"(v1"\/"v2))))
by A4;
hence thesis by A1210;
end;

A1267: for v102,v103,v1,v100 holds
 ((v100"/\"(v100"\/"v1))"/\"(v102"\/"v103))=(v100"/\"((v100"\/"(v100"/\"v1))
"/\"
(v102"\/"v103)))
proof let v102,v103,v1,v100;
(v100"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1115;
hence thesis by A292;
end;

A1270: for v2,v3,v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"(v2"\/"v3)))=(v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2"\/"v3)))
proof let v2,v3,v1,v0;
((v0"/\"(v0"\/"v1))"/\"(v2"\/"v3))=(v0"/\"((v0"\/"v1)"/\"(v2"\/"v3))) by A292;
hence thesis by A1267;
end;

A1272: for v2,v3,v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"(v2"\/"v3)))=(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"v3))))
proof let v2,v3,v1,v0;
(v0"/\"((v0"\/"(v0"/\"v1))"/\"(v2"\/"v3)))=(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"
v3)))) by
 A912;
hence thesis by A1270;
end;

A1377: for v102,v1,v100 holds
 (v100"\/"(((v100"/\"v1)"/\"v102)"\/"(v100"/\"(v100"\/"v1))))=(v100"\/"((v100
"/\"v1)"/\"
(v100"\/"v102)))
proof let v102,v1,v100;
(v100"/\"(v100"\/"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1115;
hence thesis by A106;
end;

A1383: for v2,v0,v1 holds
 (v0"\/"((v2"/\"(v1"/\"v0))"\/"(v0"/\"(v0"\/"v2))))=(v0"\/"((v0"/\"v2)"/\"(v0
"\/"v1)))
proof let v2,v0,v1;
(v1"/\"(v0"/\"v2))=(v2"/\"(v1"/\"v0)) by A14;
hence thesis by A1377;
end;

A1388: for v0,v1,v2 holds
 (v0"\/"((v0"/\"(v2"/\"v1))"\/"(v0"/\"(v0"\/"v1))))=(v0"\/"((v0"/\"v1)"/\"(v0
"\/"v2)))
proof let v0,v1,v2;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1383;
end;

A1394: for v0,v2,v1 holds
 (v0"\/"(v0"/\"((v1"/\"v2)"\/"(v0"\/"v1))))=(v0"\/"((v0"/\"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
((v0"/\"(v1"/\"v2))"\/"(v0"/\"(v0"\/"v1)))=(v0"/\"((v1"/\"v2)"\/"(v0"\/"v1)))
by A6;
hence thesis by A1388;
end;

A1396: for v0,v2,v1 holds
 (v0"\/"(v0"/\"(v1"\/"((v1"/\"v2)"\/"v0))))=(v0"\/"((v0"/\"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
((v1"/\"v2)"\/"(v0"\/"v1))=(v1"\/"((v1"/\"v2)"\/"v0)) by A8;
hence thesis by A1394;
end;

A1400: for v0,v2,v1 holds
 (v0"\/"(v0"/\"(v0"\/"((v1"/\"v2)"\/"v1))))=(v0"\/"((v0"/\"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
(v0"\/"((v1"/\"v2)"\/"v1))=(v1"\/"(v0"\/"(v1"/\"v2))) by A8;
hence thesis by A1396;
end;

A1404: for v0,v2,v1 holds
 (v0"\/"(v0"/\"(v0"\/"(v1"/\"v2))))=(v0"\/"((v0"/\"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v1"\/"(v1"/\"v2))))=(v0"/\"(v0"\/"(v1"/\"v2))) by A1119;
hence thesis by A1400;
end;

A1406: for v0,v2,v1 holds
 (v0"\/"(v0"/\"(v0"\/"(v1"/\"v2))))=(v0"\/"(v0"/\"(v1"/\"(v0"\/"v2))))
proof let v0,v2,v1;
((v0"/\"v1)"/\"(v0"\/"v2))=(v0"/\"(v1"/\"(v0"\/"v2))) by A292;
hence thesis by A1404;
end;

A1410: for v103,v100,v1,v101 holds
 ((v100"/\"(v101"/\"(v101"\/"v1)))"\/"(v101"/\"v103))=(v101"/\"(v103"\/"(v100
"/\"
(v101"\/"(v101"/\"v1)))))
proof let v103,v100,v1,v101;
(v101"/\"(v101"\/"(v101"/\"v1)))=(v101"/\"(v101"\/"v1)) by A1115;
hence thesis by A123;
end;

A1413: for v3,v0,v2,v1 holds
 (v1"/\"(v3"\/"(v0"/\"(v1"\/"v2))))=(v1"/\"(v3"\/"(v0"/\"(v1"\/"(v1"/\"v2)))))
proof let v3,v0,v2,v1;
((v0"/\"(v1"/\"(v1"\/"v2)))"\/"(v1"/\"v3))=(v1"/\"(v3"\/"(v0"/\"(v1"\/"v2))))
by A123;
hence thesis by A1410;
end;

A1443: for v1,v2,v0 holds
 (v0"/\"(v1"/\"(v0"\/"v2)))=(v0"/\"(v0"/\"(v1"/\"(v0"\/"v2))))
proof let v1,v2,v0;
(v0"/\"(v1"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v1"/\"(v0"\/"v2))) by A1165;
hence thesis by A833;
end;

A1455: for v1,v2,v0 holds
 (v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))=(v0"\/"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v0"\/"(v1"/\"(v1"\/"(v1"\/"(v0"/\"v2)))))=(v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))
by A1214;
hence thesis by A1121;
end;

A1457: for v1,v2,v0 holds (v1"\/"(v0"/\"(v0"\/"v2)))=(v0"\/"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v0"\/"(v1"/\"(v1"\/"(v0"/\"v2))))=(v1"\/"(v0"/\"(v0"\/"v2))) by A1177;
hence thesis by A1455;
end;

A1470: for v2,v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"(v2"\/"(v0"/\"(v1
"/\"v1))))
proof let v2,v1,v0;
(v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1))))))=(v0"/\"((v0"\/"v1)
"/\"(v2"\/"
(v0"/\"(v1"/\"v1))))) by A1272;
hence thesis by A714;
end;

A1472: for v3,v1,v2,v0 holds
 (v0"/\"((v1"/\"(v0"\/"v2))"\/"(v3"/\"(v0"\/"v2))))=(v0"/\"((v0"\/"v2)"/\"(v1
"\/"
(v3"/\"v0))))
proof let v3,v1,v2,v0;
(v0"/\"((v1"/\"(v0"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v2)))))=(v0"/\"((v1"/\"(v0
"\/"v2))"\/"
(v3"/\"(v0"\/"v2)))) by A1413;
hence thesis by A994;
end;

A1474: for v1,v3,v2,v0 holds
 (v0"/\"((v0"\/"v2)"/\"(v1"\/"v3)))=(v0"/\"((v0"\/"v2)"/\"(v1"\/"(v3"/\"v0))))
proof let v1,v3,v2,v0;
((v1"/\"(v0"\/"v2))"\/"(v3"/\"(v0"\/"v2)))=((v0"\/"v2)"/\"(v1"\/"v3)) by A523;
hence thesis by A1472;
end;

A1482: for v1,v0 holds
 (v0"\/"(v0"/\"(v1"\/"(v0"/\"(v1"/\"(v0"\/"v1))))))=(v0"/\"(v0"\/"(v1"\/"v1)))
proof let v1,v0;
(v0"/\"(v0"/\"(v1"/\"(v0"\/"v1))))=(v0"/\"(v1"/\"(v0"\/"v1))) by A1443;
hence thesis by A816;
end;

A1484: for v1,v0 holds
 (v0"\/"(v0"/\"(v1"\/"(v1"/\"(v0"\/"v1)))))=(v0"/\"(v0"\/"(v1"\/"v1)))
proof let v1,v0;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"(v0"\/"v1)))))=(v0"/\"(v1"\/"(v1"/\"(v0"\/"v1))))
by A378;
hence thesis by A1482;
end;

A1486: for v1,v0 holds (v0"\/"(v0"/\"(v1"/\"(v0"\/"v1))))=(v0"/\"(v0"\/"(v1"\/"
v1)))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"\/"(v1"/\"(v0"\/"v1)))))=(v0"\/"(v0"/\"(v1"/\"(v0"\/"v1))))
by A1096;
hence thesis by A1484;
end;

A1488: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"\/"
v1)))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"/\"(v0"\/"v1))))=(v0"\/"(v0"/\"(v0"\/"(v1"/\"v1)))) by A1406;
hence thesis by A1486;
end;

A1490: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"(v1"\/"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"/\"v1)))=(v0"/\"(v0"\/"v1));
hence thesis by A1488;
end;

A1499: for v2,v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"(v2"\/"(v1"/\"v1))))=(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1))))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"((v0"\/"v1)"/\"(v2
"\/"
(v1"/\"v1)))) by A1474;
hence thesis by A1470;
end;

A1501: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"v1)))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"\/"v1)))=(v0"/\"(v0"\/"v1));
hence thesis by A1490;
end;

A1504: for v102,v1,v100 holds
 ((v100"/\"(v100"\/"v1))"\/"((v100"/\"(v100"\/"v1))"/\"v102))=((v100"/\"
(v100"\/"v1))"/\"(v100"\/"v102))
proof let v102,v1,v100;
(v100"/\"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"v1)) by A1126;
hence thesis by A6;
end;

A1509: for v2,v1,v0 holds
 ((v0"/\"(v0"\/"v1))"\/"(v0"/\"((v0"\/"v1)"/\"v2)))=((v0"/\"(v0"\/"v1))"/\"(v0
"\/"v2))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"v2))=(v2"/\"(v0"/\"(v0"\/"v1))) by A14;
hence thesis by A1504;
end;

A1513: for v2,v1,v0 holds
 (v0"/\"((v0"\/"v1)"\/"(v2"/\"(v0"\/"v1))))=((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))
proof let v2,v1,v0;
((v0"/\"(v0"\/"v1))"\/"(v0"/\"(v2"/\"(v0"\/"v1))))=(v0"/\"((v0"\/"v1)"\/"(v2
"/\"
(v0"\/"v1)))) by A6;
hence thesis by A1509;
end;

A1515: for v2,v1,v0 holds
 (v0"/\"(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))))=((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))
proof let v2,v1,v0;
((v0"\/"v1)"\/"(v2"/\"(v0"\/"v1)))=(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))) by A181;
hence thesis by A1513;
end;

A1517: for v0,v2,v1 holds
 (v0"\/"(v0"/\"(v1"/\"v2)))=((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))
proof let v0,v2,v1;
(v0"/\"(v0"\/"(v1"\/"(v2"/\"(v0"\/"v1)))))=(v0"\/"(v0"/\"(v1"/\"v2))) by A1027;
hence thesis by A1515;
end;

A1519: for v0,v2,v1 holds
 (v0"\/"(v0"/\"(v1"/\"v2)))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2)))
proof let v0,v2,v1;
((v0"/\"(v0"\/"v1))"/\"(v0"\/"v2))=(v0"/\"((v0"\/"v1)"/\"(v0"\/"v2))) by A292;
hence thesis by A1517;
end;

A1521: for v0,v2,v1 holds (v0"\/"(v0"/\"(v1"/\"v2)))=(v0"/\"(v0"\/"(v1"/\"v2)))
proof let v0,v2,v1;
((v0"\/"v1)"/\"(v0"\/"v2))=(v0"\/"(v1"/\"v2)) by A4;
hence thesis by A1519;
end;

A1580: for v1,v0 holds (v0"\/"(v0"/\"(v0"/\"v1)))=(v0"/\"(v0"\/"v1))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"/\"v1)))=(v0"\/"(v0"/\"(v0"/\"v1))) by A1521;
hence thesis by A1115;
end;

A1582: for v1,v2,v0 holds
 (v0"/\"(v1"\/"(v1"/\"(v0"/\"v2))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v1,v2,v0;
(v1"/\"(v1"\/"(v0"/\"v2)))=(v1"\/"(v1"/\"(v0"/\"v2))) by A1521;
hence thesis by A730;
end;

A1584: for v0,v1,v2 holds
 (v0"/\"(v1"\/"(v0"/\"(v2"/\"v1))))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v1,v2;
(v0"/\"(v2"/\"v1))=(v1"/\"(v0"/\"v2)) by A14;
hence thesis by A1582;
end;

A1588: for v0,v2,v1 holds (v0"/\"(v1"\/"(v1"/\"v2)))=(v0"/\"(v1"/\"(v1"\/"v2)))
proof let v0,v2,v1;
(v0"/\"(v1"\/"(v0"/\"(v1"/\"v2))))=(v0"/\"(v1"\/"(v1"/\"v2))) by A378;
hence thesis by A1584;
end;

A1622: for v102,v1,v100 holds
 (v100"\/"((v100"/\"(v100"\/"v1))"\/"v102))=(v102"\/"(v100"/\"(v100"\/"v1)))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v100"\/"v1)))=(v100"/\"(v100"\/"v1)) by A1501;
hence thesis by A8;
end;

A1669: for v0,v2,v1 holds
 (v0"/\"(v0"/\"(v2"\/"(v1"/\"(v1"\/"v2)))))=(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v0,v2,v1;
(v1"\/"(v2"\/"(v1"/\"(v1"\/"v2))))=(v2"\/"(v1"/\"(v1"\/"v2))) by A1622;
hence thesis by A1037;
end;

A1672: for v0,v1,v2 holds
 (v0"/\"(v1"\/"(v0"/\"(v2"/\"(v2"\/"v1)))))=(v0"/\"(v2"\/"(v0"/\"v1)))
proof let v0,v1,v2;
(v0"/\"(v0"/\"(v1"\/"(v2"/\"(v2"\/"v1)))))=(v0"/\"(v1"\/"(v0"/\"(v2"/\"(v2"\/"
v1))))) by
 A398;
hence thesis by A1669;
end;

A1674: for v0,v1,v2 holds
 (v0"/\"(v1"\/"(v0"/\"(v2"\/"(v2"/\"v1)))))=(v0"/\"(v2"\/"(v0"/\"v1)))
proof let v0,v1,v2;
(v0"/\"(v2"/\"(v2"\/"v1)))=(v0"/\"(v2"\/"(v2"/\"v1))) by A1588;
hence thesis by A1672;
end;

A1677: for v102,v1,v100 holds
 ((v100"/\"(v100"\/"v1))"/\"((v100"/\"(v1"/\"v1))"\/"v102))=((v100"/\"(v1"/\"v1
))"\/"
(v100"/\"v102))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v1"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1521;
hence thesis by A4;
end;

A1682: for v2,v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1)))))=((v0"/\"(v1"/\"v1))"\/"(v0
"/\"v2))
proof let v2,v1,v0;
((v0"/\"(v0"\/"v1))"/\"(v2"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"((v0"\/"v1)"/\"(v2
"\/"(v0"/\"
(v1"/\"v1))))) by A292;
hence thesis by A1677;
end;

A1684: for v2,v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"(v2"\/"(v1"/\"v1))))=((v0"/\"(v1"/\"v1))"\/"(v0"/\"v2))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"((v0"\/"v1)"/\"(v2
"\/"
 (v1"/\"v1)))) by A1474;
hence thesis by A1682;
end;

A1686: for v2,v1,v0 holds
 (v0"/\"(v2"\/"(v0"/\"(v1"/\"v1))))=((v0"/\"(v1"/\"v1))"\/"(v0"/\"v2))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v1"/\"v1))))=(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1))))
by A1499;
hence thesis by A1684;
end;

A1689: for v1,v2,v0 holds
 (v0"/\"(v1"\/"(v0"/\"(v2"/\"v2))))=(v0"/\"((v2"/\"v2)"\/"v1))
proof let v1,v2,v0;
((v0"/\"(v2"/\"v2))"\/"(v0"/\"v1))=(v0"/\"((v2"/\"v2)"\/"v1)) by A6;
hence thesis by A1686;
end;

A1694: for v101,v103 holds
 ((v103"/\"v101)"/\"((v103"/\"v101)"\/"v103))=(v103"/\"(v101"\/"(
(v103"/\"v101)"/\"v103)))
proof let v101,v103;
((v103"/\"v101)"\/"((v103"/\"v101)"/\"(v103"/\"v103)))=((v103"/\"v101)"/\"(
(v103"/\"v101)"\/"v103)) by A1521;
hence thesis by A159;
end;

A1699: for v1,v0 holds
 (v0"/\"(v1"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"((v0"/\"v1)"/\"v0)))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v1"/\"(v0"\/"(v0"/\"v1)))) by A292;
hence thesis by A1694;
end;

A1701: for v1,v0 holds (v0"/\"(v1"/\"(v0"\/"v1)))=(v0"/\"(v1"\/"((v0"/\"v1)"/\"
v0)))
proof let v1,v0;
(v0"/\"(v1"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"/\"(v0"\/"v1))) by A1165;
hence thesis by A1699;
end;

A1707: for v102,v103,v1,v101 holds
 ((v101"/\"(v1"/\"v1))"\/"((v101"/\"v102)"\/"(v103"/\"(v101"/\"(v101"\/"v1)))))
=(
(v101"/\"(v1"/\"v1))"\/"(v101"/\"(v103"\/"v102)))
proof let v102,v103,v1,v101;
(v101"\/"(v101"/\"(v1"/\"v1)))=(v101"/\"(v101"\/"v1)) by A1521;
hence thesis by A150;
end;

A1710: for v2,v3,v1,v0 holds
 ((v0"/\"(v1"/\"v1))"\/"((v0"/\"v2)"\/"(v3"/\"(v0"\/"(v0"/\"v1)))))=((v0"/\"(v1
"/\"v1))"\/"
(v0"/\"(v3"\/"v2)))
proof let v2,v3,v1,v0;
(v3"/\"(v0"/\"(v0"\/"v1)))=(v3"/\"(v0"\/"(v0"/\"v1))) by A1588;
hence thesis by A1707;
end;

A1712: for v3,v0,v2,v1 holds
 ((v0"/\"((v1"/\"v1)"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=((v0"/\"(v1"/\"v1))
"\/"(v0"/\"
(v3"\/"v2)))
proof let v3,v0,v2,v1;
((v0"/\"(v1"/\"v1))"\/"((v0"/\"v2)"\/"(v3"/\"(v0"\/"(v0"/\"v1)))))=((v0"/\"(
(v1"/\"v1)"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1)))) by A341;
hence thesis by A1710;
end;

A1719: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"\/"(v2"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"((v2"/\"v2)
"\/"
(v1"\/"v3)))
proof let v3,v0,v2,v1;
((v0"/\"(v2"/\"v2))"\/"(v0"/\"(v1"\/"v3)))=(v0"/\"((v2"/\"v2)"\/"(v1"\/"v3)))
by A6;
hence thesis by A1712;
end;

A1721: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"\/"(v2"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v3"\/"(
(v2"/\"v2)"\/"v1)))
proof let v3,v0,v2,v1;
((v2"/\"v2)"\/"(v1"\/"v3))=(v3"\/"((v2"/\"v2)"\/"v1)) by A8;
hence thesis by A1719;
end;

A1725: for v3,v0,v2,v1 holds
 ((v0"/\"(v1"\/"(v2"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v1"\/"(
(v2"/\"v2)"\/"v3)))
proof let v3,v0,v2,v1;
(v1"\/"((v2"/\"v2)"\/"v3))=(v3"\/"(v1"\/"(v2"/\"v2))) by A8;
hence thesis by A1721;
end;

A1729: for v2,v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"(v2"\/"(v1"/\"v1))))=(v0"/\"(v2"\/"(v1"/\"v1)))
proof let v2,v1,v0;
(v0"/\"(v2"\/"(v0"/\"(v1"/\"v1))))=(v0"/\"(v2"\/"(v1"/\"v1))) by A1689;
hence thesis by A1499;
end;

A1732: for v102,v1,v100 holds
 (v100"/\"(((v100"/\"v1)"\/"v102)"/\"(v100"/\"(v100"\/"v1))))=(v100"/\"((v100
"/\"v1)"\/"
(v100"/\"v102)))
proof let v102,v1,v100;
(v100"\/"(v100"/\"(v100"/\"v1)))=(v100"/\"(v100"\/"v1)) by A1580;
hence thesis by A82;
end;

A1738: for v1,v2,v0 holds
 (v0"/\"((v0"\/"v2)"/\"((v1"\/"(v0"/\"v2))"/\"v0)))=(v0"/\"((v0"/\"v2)"\/"(v0
"/\"v1)))
proof let v1,v2,v0;
((v1"\/"(v0"/\"v2))"/\"(v0"/\"(v0"\/"v2)))=((v0"\/"v2)"/\"((v1"\/"(v0"/\"v2))
"/\"v0)) by
 A14;
hence thesis by A1732;
end;

A1743: for v2,v1,v0 holds
 (v0"/\"(v0"/\"((v2"\/"(v0"/\"v1))"/\"(v0"\/"v1))))=(v0"/\"((v0"/\"v1)"\/"(v0
"/\"v2)))
proof let v2,v1,v0;
(v0"/\"((v2"\/"(v0"/\"v1))"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v0"/\"(v2"\/"(v0"/\"
v1)))) by
 A14;
hence thesis by A1738;
end;

A1749: for v2,v1,v0 holds
 (v0"/\"(v0"/\"((v0"\/"v1)"/\"(v2"\/"v1))))=(v0"/\"((v0"/\"v1)"\/"(v0"/\"v2)))
proof let v2,v1,v0;
(v0"/\"((v0"\/"v1)"/\"(v2"\/"(v0"/\"v1))))=(v0"/\"((v0"\/"v1)"/\"(v2"\/"v1)))
by A1474;
hence thesis by A1743;
end;

A1753: for v1,v2,v0 holds
 (v0"/\"(v0"/\"(v1"\/"(v0"/\"v2))))=(v0"/\"((v0"/\"v1)"\/"(v0"/\"v2)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A1749;
end;

A1755: for v1,v2,v0 holds
 (v0"/\"(v1"\/"(v0"/\"(v0"/\"v2))))=(v0"/\"((v0"/\"v1)"\/"(v0"/\"v2)))
proof let v1,v2,v0;
(v0"/\"(v0"/\"(v1"\/"(v0"/\"v2))))=(v0"/\"(v1"\/"(v0"/\"(v0"/\"v2)))) by A398;
hence thesis by A1753;
end;

A1757: for v1,v2,v0 holds
 (v0"/\"(v1"\/"(v0"/\"(v0"/\"v2))))=(v0"/\"(v0"/\"(v1"\/"v2)))
proof let v1,v2,v0;
((v0"/\"v1)"\/"(v0"/\"v2))=(v0"/\"(v1"\/"v2)) by A6;
hence thesis by A1755;
end;

A1795: for v102,v103,v1,v101 holds
 ((v101"/\"(v101"/\"v1))"\/"((v101"/\"v102)"\/"(v103"/\"(v101"/\"(v101"\/"v1)))
))=(
(v101"/\"(v101"/\"v1))"\/"(v101"/\"(v103"\/"v102)))
proof let v102,v103,v1,v101;
(v101"\/"(v101"/\"(v101"/\"v1)))=(v101"/\"(v101"\/"v1)) by A1580;
hence thesis by A150;
end;

A1798: for v2,v3,v1,v0 holds
 ((v0"/\"(v0"/\"v1))"\/"((v0"/\"v2)"\/"(v3"/\"(v0"\/"(v0"/\"v1)))))=((v0"/\"(v0
"/\"v1))"\/"
(v0"/\"(v3"\/"v2)))
proof let v2,v3,v1,v0;
(v3"/\"(v0"/\"(v0"\/"v1)))=(v3"/\"(v0"\/"(v0"/\"v1))) by A1588;
hence thesis by A1795;
end;

A1800: for v3,v2,v1,v0 holds
 ((v0"/\"((v0"/\"v1)"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=((v0"/\"(v0"/\"v1))
"\/"(v0"/\"
(v3"\/"v2)))
proof let v3,v2,v1,v0;
((v0"/\"(v0"/\"v1))"\/"((v0"/\"v2)"\/"(v3"/\"(v0"\/"(v0"/\"v1)))))=((v0"/\"(
(v0"/\"v1)"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1)))) by A341;
hence thesis by A1798;
end;

A1807: for v3,v1,v2,v0 holds
 ((v0"/\"(v1"\/"(v0"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"((v0"/\"v2)
"\/"
(v1"\/"v3)))
proof let v3,v1,v2,v0;
((v0"/\"(v0"/\"v2))"\/"(v0"/\"(v1"\/"v3)))=(v0"/\"((v0"/\"v2)"\/"(v1"\/"v3)))
by A6;
hence thesis by A1800;
end;

A1809: for v3,v1,v2,v0 holds
 ((v0"/\"(v1"\/"(v0"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v3"\/"(
(v0"/\"v2)"\/"v1)))
proof let v3,v1,v2,v0;
  ((v0"/\"v2)"\/"(v1"\/"v3))=(v3"\/"((v0"/\"v2)"\/"v1)) by A8;
  hence thesis by A1807;
end;

A1813: for v3,v1,v2,v0 holds
 ((v0"/\"(v1"\/"(v0"/\"v2)))"\/"(v3"/\"(v0"\/"(v0"/\"v2))))=(v0"/\"(v1"\/"(
(v0"/\"v2)"\/"v3)))
proof let v3,v1,v2,v0;
(v1"\/"((v0"/\"v2)"\/"v3))=(v3"\/"(v1"\/"(v0"/\"v2))) by A8;
hence thesis by A1809;
end;

A1817: for v1,v0 holds v0"/\"(v0"/\"(v1"\/"v1))=v0"/\"(v1"/\"(v0"\/"v1))
proof let v1,v0;
  v0"/\"(v1"\/"(v0"/\"(v0"/\"v1)))=v0"/\"(v0"/\"(v1"\/"v1)) by A1757;
  hence thesis by A1701;
end;

A2027: for v1,v0 holds v0"/\"(v0"\/"v1)=v0"\/"(v1"/\"v0)
proof let v1,v0;
  v0"\/"(v0"/\"(v1"/\"v1))=v0"/\"(v0"\/"v1) by A1521;
  hence thesis;
end;

A2080: for v102,v100 holds
 (v102"/\"((v100"\/"v102)"\/"((v100"\/"v102)"/\"(v100"\/"v102))))=(v102"\/"
(v100"/\"v102))
proof let v102,v100;
(v102"/\"((v100"\/"v102)"\/"((v100"\/"v102)"/\"(v100"\/"v102))))=((v100"\/"v102
)"/\"
(v102"\/"v102));
hence thesis by A4;
end;

A2089: for v1,v0 holds (v0"/\"((v0"\/"v1)"\/"(v0"\/"(v1"/\"v1))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
  ((v0"\/"v1)"/\"(v0"\/"v1))=(v0"\/"(v1"/\"v1));
  hence thesis by A2080;
end;

A2091: for v1,v0 holds (v0"/\"(v0"\/"((v1"/\"v1)"\/"(v0"\/"v1))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
  (v0"\/"((v1"/\"v1)"\/"(v0"\/"v1)))=((v0"\/"v1)"\/"(v0"\/"(v1"/\"v1))) by A8;
  hence thesis by A2089;
end;

A2097: for v1,v0 holds (v0"/\"(v0"\/"(v0"\/"((v1"/\"v1)"\/"v1))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
  (v0"\/"((v1"/\"v1)"\/"v1))=(v1"\/"(v0"\/"(v1"/\"v1))) by A8;
  hence thesis by A2091;
end;

A2101: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"(v1"\/"(v1"/\"v1)))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
(v0"/\"(v0"\/"(v0"\/"(v1"\/"(v1"/\"v1)))))=(v0"\/"(v0"/\"(v0"\/"(v1"\/"(v1"/\"
v1))))) by
 A2027;
hence thesis by A2097;
end;

A2103: for v1,v0 holds (v0"\/"(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1)))))=(v0"\/"(v1
"/\"v0))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"\/"(v1"/\"v1))))=(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1)))) by A2027;
hence thesis by A2101;
end;

A2105: for v1,v0 holds (v0"\/"(v0"\/"(v0"/\"(v1"/\"v1))))=(v0"\/"(v1"/\"v0))
proof let v1,v0;
(v0"\/"(v0"/\"(v1"\/"(v1"/\"v1))))=(v0"\/"(v0"/\"(v1"/\"v1)));
hence thesis by A2103;
end;

A2107: for v1,v0 holds (v0"\/"(v0"/\"(v0"\/"v1)))=(v0"\/"(v1"/\"v0))
proof let v1,v0;
  (v0"\/"(v0"/\"(v1"/\"v1)))=(v0"/\"(v0"\/"v1)) by A1521;
  hence thesis by A2105;
end;

A2109: for v1,v0 holds (v0"\/"(v0"\/"(v0"/\"v1)))=(v0"\/"(v1"/\"v0))
proof let v1,v0;
  (v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"v1)) by A2027;
  hence thesis by A2107;
end;

A2117: for v1,v0 holds ((v0"/\"v1)"\/"(v0"/\"(v1"/\"v0)))=(v0"/\"(v1"\/"v1))
proof let v1,v0;
(v1"/\"(v0"/\"v0))=(v0"/\"(v1"/\"v0)) by A14;
hence thesis;
end;

A2121: for v1,v0 holds (v0"/\"(v1"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v1))
proof let v1,v0;
((v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)))=(v0"/\"(v1"\/"(v0"/\"v1))) by A6;
hence thesis by A2117;
end;

A2148: for v1,v0 holds v0"/\"(v0"/\"(v1"\/"v1))=v1"/\"(v0"\/"v0)
proof let v1,v0;
  v1"/\"(v0"\/"(v0"/\"v0))=v1"/\"(v0"\/"v0);
  hence thesis by A292;
end;

A2170: for v2,v1,v0 holds
 ((v0"\/"(v1"/\"(v0"\/"v0)))"/\"(v2"\/"(v0"/\"(v1"\/"v1))))=(v0"/\"(v1"\/"(
(v1"/\"v1)"\/"v2)))
proof let v2,v1,v0;
  (v1"\/"((v1"/\"v1)"\/"v2))=(v2"\/"(v1"\/"(v1"/\"v1))) by A8;
  hence thesis by A85;
end;

A2178: for v1,v0 holds ((v0"\/"(v0"/\"v1))"/\"(v1"/\"(v0"\/"v1)))=(v1"/\"(v0
"\/"v0))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"((v1"/\"v1)"\/"(v0"/\"v1)))=((v0"\/"(v0"/\"v1))"/\"(v1
"/\"
(v0"\/"v1))) by A336;
hence thesis by A85;
end;

A2180: for v1,v0 holds ((v0"\/"v1)"/\"((v0"\/"(v0"/\"v1))"/\"v1))=(v1"/\"(v0
"\/"v0))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"/\"(v1"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"((v0"\/"(v0"/\"v1))
"/\"v1)) by A14;
hence thesis by A2178;
end;

A2184: for v1,v0 holds (v1"/\"((v0"\/"(v0"/\"v1))"/\"(v0"\/"v1)))=(v1"/\"(v0
"\/"v0))
proof let v1,v0;
(v1"/\"((v0"\/"(v0"/\"v1))"/\"(v0"\/"v1)))=((v0"\/"v1)"/\"(v1"/\"(v0"\/"(v0"/\"
v1)))) by A14;
  hence thesis by A2180;
end;

A2189: for v0,v1 holds (v0"/\"(v1"\/"(v0"/\"(v1"/\"v0))))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
  ((v1"\/"v0)"/\"(v1"\/"(v1"/\"v0)))=(v1"\/"(v0"/\"(v1"/\"v0))) by A4;
  hence thesis by A2184;
end;

A2191: for v0,v1 holds (v0"/\"(v1"\/"(v1"/\"(v0"/\"v0))))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
  (v1"/\"(v0"/\"v0))=(v0"/\"(v1"/\"v0)) by A14;
  hence thesis by A2189;
end;

A2193: for v0,v1 holds (v0"/\"(v1"/\"(v1"\/"v0)))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
  (v1"\/"(v1"/\"(v0"/\"v0)))=(v1"/\"(v1"\/"v0)) by A1521;
  hence thesis by A2191;
end;

A2195: for v0,v1 holds (v0"/\"(v1"\/"(v1"/\"v0)))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
  (v1"/\"(v1"\/"v0))=(v1"\/"(v1"/\"v0)) by A2027;
  hence thesis by A2193;
end;

A2212: for v101,v100 holds
 ((v100"/\"v101)"/\"((v100"\/"(v100"/\"v101))"\/"((v100"\/"(v100"/\"v101))"/\"(
v100"\/"
(v100"/\"v101)))))=(v100"/\"(v101"\/"(v100"/\"v101)))
proof let v101,v100;
((v100"/\"v101)"/\"((v100"\/"(v100"/\"v101))"\/"((v100"\/"(v100"/\"v101))"/\"(
v100"\/"
(v100"/\"v101)))))=((v100"\/"(v100"/\"v101))"/\"((v100"/\"v101)"\/"(v100"/\"
v101)));
hence thesis by A85;
end;

A2215: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"((v0"/\"v1)"/\"(v0"/\"v1)))))=(v0
"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
  ((v0"\/"(v0"/\"v1))"/\"(v0"\/"(v0"/\"v1)))=
    (v0"\/"((v0"/\"v1)"/\"(v0"/\"v1)));
  hence thesis by A2212;
end;

A2217: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v1"/\"((v0"/\"v1)"/\"v0)))))=
 (v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
  ((v0"/\"v1)"/\"(v0"/\"v1))=(v1"/\"((v0"/\"v1)"/\"v0)) by A14;
  hence thesis by A2215;
end;

A2221: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"((v0"/\"v1)"/\"v1)))))=
 (v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
  (v0"/\"((v0"/\"v1)"/\"v1))=(v1"/\"(v0"/\"(v0"/\"v1))) by A14;
  hence thesis by A2217;
end;

A2225: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"(v0"/\"(v1"/\"v1))))))=
 (v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
  (v0"/\"(v1"/\"v1))=(v1"/\"(v0"/\"v1)) by A14;
  hence thesis by A2221;
end;

A2227: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"\/"(v1"/\"v1)))))=
 v0"/\"(v1"\/"(v0"/\"v1))
proof let v1,v0;
  (v0"\/"(v0"/\"(v0"/\"(v1"/\"v1))))=(v0"/\"(v0"\/"(v1"/\"v1))) by A1580;
  hence thesis by A2225;
end;

A2229: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"(v1"/\"v1)))))=(v0"/\"(v1
"\/"
(v0"/\"v1)))
proof let v1,v0;
(v0"/\"(v0"\/"(v1"/\"v1)))=(v0"\/"(v0"/\"(v1"/\"v1))) by A2027;
hence thesis by A2227;
end;

A2231: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"/\"(v0"\/"v1))))=(v0"/\"(v1"\/"(v0
"/\"v1)))
proof let v1,v0;
  (v0"\/"(v0"/\"(v1"/\"v1)))=(v0"/\"(v0"\/"v1)) by A1521;
  hence thesis by A2229;
end;

A2233: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v0
"/\"v1)))
proof let v1,v0;
  (v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"v1)) by A2027;
  hence thesis by A2231;
end;

A2235: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"/\"v1)"\/"((v0"\/"(v0"/\"v1))"\/"v0)))=(v0"/\"(v1"\/"(v0
"/\"v1)))
proof let v1,v0;
((v0"\/"(v0"/\"v1))"\/"(v0"\/"(v0"/\"v1)))=((v0"/\"v1)"\/"((v0"\/"(v0"/\"v1))
"\/"v0)) by
 A8;
hence thesis by A2233;
end;

A2239: for v1,v0 holds
 ((v0"/\"v1)"/\"((v0"/\"v1)"\/"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
  (v0"\/"(v0"\/"(v0"/\"v1)))=(v0"\/"(v0"/\"v1)) by A2109;
  hence thesis by A2235;
end;

A2241: for v1,v0 holds
 ((v0"/\"v1)"/\"(v0"\/"((v0"/\"v1)"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
(v0"\/"((v0"/\"v1)"\/"(v0"/\"v1)))=((v0"/\"v1)"\/"(v0"\/"(v0"/\"v1))) by A8;
hence thesis by A2239;
end;

A2243: for v1,v0 holds
 ((v0"/\"v1)"/\"(v0"\/"(v0"/\"(v1"\/"v1))))=(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
  ((v0"/\"v1)"\/"(v0"/\"v1))=(v0"/\"(v1"\/"v1));
  hence thesis by A2241;
end;

A2245: for v1,v0 holds ((v0"/\"v1)"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"(v0"/\"
v1)))
proof let v1,v0;
  (v0"\/"(v0"/\"(v1"\/"v1)))=(v0"\/"(v0"/\"v1));
  hence thesis by A2243;
end;

A2247: for v1,v0 holds (v0"/\"(v1"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"(v1"\/"(v0"/\"
v1)))
proof let v1,v0;
((v0"/\"v1)"/\"(v0"\/"(v0"/\"v1)))=(v0"/\"(v1"/\"(v0"\/"(v0"/\"v1)))) by A292;
hence thesis by A2245;
end;

A2249: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))=(v0"/\"(v1"\/"(v0"/\"v1)))
proof let v0,v1;
  (v1"/\"(v0"\/"(v0"/\"v1)))=(v1"/\"(v0"\/"v0)) by A2195;
  hence thesis by A2247;
end;

A2251: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))=(v0"/\"(v1"\/"v1))
proof let v0,v1;
  (v0"/\"(v1"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v1)) by A2121;
  hence thesis by A2249;
end;

A2340: for v1,v0 holds (v0"\/"(v1"/\"(v0"\/"v1)))=(v0"\/"((v0"/\"v0)"\/"v1))
proof let v1,v0;
(v0"\/"((v0"/\"v0)"\/"v1))=(v1"\/"(v0"\/"(v0"/\"v0))) by A8;
hence thesis by A1457;
end;

A2355: for v2,v1,v0 holds
 ((v0"\/"v1)"/\"(v0"\/"((v0"/\"v0)"\/"v2)))=(v0"\/"(v1"/\"v2))
proof let v2,v1,v0;
(v0"\/"((v0"/\"v0)"\/"v2))=(v2"\/"(v0"\/"(v0"/\"v0))) by A8;
hence thesis by A4;
end;

A2359: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v0"\/"(v0"\/"v2)))=(v0"\/"(v1"/\"v2))
proof let v2,v1,v0;
((v0"\/"v1)"/\"(v0"\/"(v2"\/"(v0"/\"v0))))=((v0"\/"v1)"/\"(v0"\/"(v0"\/"v2)))
;
hence thesis by A2355;
end;

A2361: for v1,v2,v0 holds (v0"\/"(v1"/\"(v0"\/"v2)))=(v0"\/"(v1"/\"v2))
proof let v1,v2,v0;
  ((v0"\/"v1)"/\"(v0"\/"(v0"\/"v2)))=(v0"\/"(v1"/\"(v0"\/"v2))) by A4;
  hence thesis by A2359;
end;

A2369: for v1,v0 holds (v0"/\"(v1"/\"(v0"\/"v1)))=(v1"/\"(v0"\/"v0))
proof let v1,v0;
(v0"/\"(v0"/\"(v1"\/"v1)))=(v1"/\"(v0"\/"v0)) by A2148;
hence thesis by A1817;
end;

A2371: for v2,v1,v0 holds
 ((v0"\/"(v1"/\"v0))"/\"(v2"\/"(v0"/\"(v1"\/"v1))))=(v0"/\"(v1"\/"(v2"\/"(v1
"/\"v1))))
proof let v2,v1,v0;
(v0"\/"(v1"/\"(v0"\/"v0)))=(v0"\/"(v1"/\"v0));
hence thesis by A2170;
end;

A2375: for v2,v1,v0 holds
 ((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"(v1"\/"v1))))=(v0"/\"(v1"\/"(v1"\/"v2)))
proof let v2,v1,v0;
  (v0"/\"(v1"\/"(v2"\/"(v1"/\"v1))))=(v0"/\"(v1"\/"(v1"\/"v2)));
  hence thesis by A2371;
end;

A2397: for v0,v1 holds (v0"\/"(v1"\/"(v0"/\"v0)))=(v0"\/"(v1"/\"v1))
proof let v0,v1;
(v0"\/"(v1"/\"(v0"\/"v1)))=(v0"\/"(v1"/\"v1)) by A2361;
hence thesis by A2340;
end;

A2408: (c2"\/"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4))))=(c2"\/"((c3"\/"c4)"/\"(c3"/\"
c4))) by A2361;

A2411:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"((c2"\/"c3)"/\"(
c1"\/"
(c2"/\"c3))))))=((c2"\/"(c4"/\"((c3"\/"c4)"/\"c3)))"/\"(c1"\/"(c2"/\"((c3"\/"c4
)"/\"(c2"\/"
(c3"/\"c4)))))) by A14,A2408,A368;

A2415:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"((c2"\/"c3)"/\"(
c1"\/"
(c2"/\"c3))))))=((c2"\/"(c4"/\"(c3"\/"(c3"/\"c4))))"/\"(c1"\/"(c2"/\"((c3"\/"c4
)"/\"(c2"\/"
(c3"/\"c4)))))) by A2027,A2411;

A2417:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"((c2"\/"c3)"/\"(
c1"\/"
(c2"/\"c3))))))=((c2"\/"(c4"/\"(c3"\/"c3)))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2
"\/"
(c3"/\"c4)))))) by A2195,A2415;

A2431: for v2,v0,v1 holds
 ((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v1"/\"v0)))=(v0"/\"(v1"\/"(v1"\/"v2)))
proof let v2,v0,v1;
  (v2"\/"(v0"/\"(v1"\/"v1)))=(v2"\/"(v1"/\"v0));
  hence thesis by A2375;
end;

A2435: for v0,v2,v1 holds (v0"/\"(v1"\/"v2))=(v0"/\"(v1"\/"(v1"\/"v2)))
proof let v0,v2,v1;
  ((v0"\/"(v0"/\"v1))"/\"(v2"\/"(v0"/\"v1)))=(v0"/\"(v1"\/"v2)) by A85;
  hence thesis by A2431;
end;

A2490: for v1,v2,v0 holds (v0"/\"(v1"\/"(v0"/\"v2)))=(v0"/\"(v2"\/"(v1"/\"v1)))
proof let v1,v2,v0;
((v0"\/"v1)"/\"(v1"\/"v2))=(v1"\/"(v0"/\"v2)) by A4;
hence thesis by A1729;
end;

A2492: for v1,v2,v0 holds v0"/\"(v1"\/"(v0"/\"v2)) = v0"/\"(v2"\/"v1)
proof let v1,v2,v0;
  v0"/\"(v2"\/"(v1"/\"v1)) = v0"/\"(v2"\/"v1);
  hence thesis by A2490;
end;

A2498: for v0,v2,v1 holds
 v0"/\"(v1"\/"(v2"\/"(v1"/\"v2))) = v0"/\"(v2"\/"(v0"/\"v1))
proof let v0,v2,v1;
  v0"/\"(v1"\/"(v0"/\"(v2"\/"(v1"/\"v2)))) = v0"/\"(v1"\/"(v2"\/"(v1"/\"v2)))
    by A2492;
  hence thesis by A1674;
end;

A2500: for v0,v2,v1 holds v0"/\"(v1"\/"(v2"\/"(v1"/\"v2))) = v0"/\"(v2"\/"v1)
proof let v0,v2,v1;
  v0"/\"(v2"\/"(v0"/\"v1)) = v0"/\"(v2"\/"v1) by A2492;
  hence thesis by A2498;
end;

A2504: for v3,v0,v2,v1 holds
 (v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v2))) =
   v0"/\"(v1"\/"(v3"\/"(v0"/\"v2)))
proof let v3,v0,v2,v1;
  v0"/\"(v1"\/"(v0"/\"v2)) = v0"/\"(v1"\/"v2) by A2492;
  hence thesis by A1813;
end;

A2506: for v0,v1,v2,v3 holds
 v0"/\"(v1"\/"(v3"\/"(v2"/\"v2))) = v0"/\"(v1"\/"(v3"\/"(v0"/\"v2)))
proof let v0,v1,v2,v3;
  (v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v2))) =
    v0"/\"(v1"\/"(v3"\/"(v2"/\"v2))) by A1725;
  hence thesis by A2504;
end;

A2509: for v3,v0,v2,v1 holds
 (v0"/\"(v1"\/"(v1"/\"v2)))"\/"(v1"/\"(v2"\/"v3)) =
    v1"/\"(v0"\/"(v3"\/"(v2"/\"v2)))
proof let v3,v0,v2,v1;
  (v1"/\"(v0"\/"v2))"\/"(v3"/\"(v1"\/"(v1"/\"v2))) =
    v1"/\"(v0"\/"(v3"\/"(v2"/\"v2))) by A1725;
  hence thesis by A444;
end;

A2512: for v102,v100 holds
 Tern(v100,(v100"\/"v102)
,v102)=((v100"\/"v102)"\/"((v100"\/"v102)"/\"(v100"/\"v102)))
proof let v102,v100;
  (v100"\/"v102)"/\"((v100"\/"v102)"\/"(v100"/\"v102)) =
    (v100"\/"v102)"\/"((v100"\/"v102)"/\"(v100"/\"v102)) by A2027;
  hence thesis by A63;
end;

A2515: for v1,v0 holds
 ((v0"\/"v1)"/\"((v0"\/"v1)"\/"(v0"/\"v1)))=((v0"\/"v1)"\/"((v0"\/"v1)"/\"(v0
"/\"v1)))
proof let v1,v0;
  Tern(v0,(v0"\/"v1),v1) = (v0"\/"v1)"/\"((v0"\/"v1)"\/"(v0"/\"v1)) by A63;
  hence thesis by A2512;
end;

A2517: for v1,v0 holds
 ((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v0"/\"v1))))=((v0"\/"v1)"\/"((v0"\/"v1)"/\"(v0
"/\"v1)))
proof let v1,v0;
((v0"\/"v1)"\/"(v0"/\"v1))=(v0"\/"(v1"\/"(v0"/\"v1))) by A181;
hence thesis by A2515;
end;

A2519: for v1,v0 holds
 ((v0"\/"v1)"/\"(v0"\/"v1))=((v0"\/"v1)"\/"((v0"\/"v1)"/\"(v0"/\"v1)))
proof let v1,v0;
((v0"\/"v1)"/\"(v0"\/"(v1"\/"(v0"/\"v1))))=((v0"\/"v1)"/\"(v0"\/"v1)) by A2500;
hence thesis by A2517;
end;

A2521: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"((v0"\/"v1)"/\"(v0"/\"
v1)))
proof let v1,v0;
((v0"\/"v1)"/\"(v0"\/"v1))=(v0"\/"(v1"/\"v1));
hence thesis by A2519;
end;

A2523: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"(v1"/\"((v0"\/"v1)"/\"
v0)))
proof let v1,v0;
  ((v0"\/"v1)"/\"(v0"/\"v1))=(v1"/\"((v0"\/"v1)"/\"v0)) by A14;
  hence thesis by A2521;
end;

A2527: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"(v1"/\"(v0"\/"(v0"/\"
v1))))
proof let v1,v0;
  (v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"v1)) by A2027;
  hence thesis by A2523;
end;

A2529: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"(v1"/\"(v0"\/"v0)))
proof let v1,v0;
(v1"/\"(v0"\/"(v0"/\"v1)))=(v1"/\"(v0"\/"v0)) by A2195;
hence thesis by A2527;
end;

A2531: for v1,v0 holds (v0"\/"(v1"/\"v1))=((v0"\/"v1)"\/"(v0"/\"v1))
proof let v1,v0;
  ((v0"\/"v1)"\/"(v1"/\"(v0"\/"v0)))=((v0"\/"v1)"\/"(v0"/\"v1));
  hence thesis by A2529;
end;

A2533: for v1,v0 holds (v0"\/"(v1"/\"v1))=(v0"\/"(v1"\/"(v0"/\"v1)))
proof let v1,v0;
  ((v0"\/"v1)"\/"(v0"/\"v1))=(v0"\/"(v1"\/"(v0"/\"v1))) by A181;
  hence thesis by A2531;
end;

A2549: for v103,v100,v1,v101 holds
 ((v100"/\"(v101"\/"(v101"/\"v1)))"\/"(v101"/\"v103))=(v101"/\"(v103"\/"(v100
"/\"
(v101"\/"v1))))
proof let v103,v100,v1,v101;
(v101"/\"(v101"\/"v1))=(v101"\/"(v101"/\"v1)) by A2027;
hence thesis by A123;
end;

A2553: for v101,v102,v1,v100 holds
 ((v100"/\"v101)"\/"(v102"/\"(v100"\/"(v100"/\"v1))))=(v100"/\"(v101"\/"(v102
"/\"
(v100"\/"v1))))
proof let v101,v102,v1,v100;
  (v100"/\"(v100"\/"v1))=(v100"\/"(v100"/\"v1)) by A2027;
  hence thesis by A159;
end;

A2556: for v3,v0,v2,v1 holds
 (v1"/\"((v2"\/"v3)"\/"(v0"/\"(v1"\/"v2))))=(v1"/\"(v0"\/"(v3"\/"(v2"/\"v2))))
proof let v3,v0,v2,v1;
((v0"/\"(v1"\/"(v1"/\"v2)))"\/"(v1"/\"(v2"\/"v3)))=(v1"/\"((v2"\/"v3)"\/"(v0
"/\"
(v1"\/"v2)))) by A2549;
hence thesis by A2509;
end;

A2559: for v2,v3,v1,v0 holds
 (v0"/\"(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))))=(v0"/\"(v3"\/"(v2"\/"(v1"/\"v1))))
proof let v2,v3,v1,v0;
((v1"\/"v2)"\/"(v3"/\"(v0"\/"v1)))=(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))) by A181;
hence thesis by A2556;
end;

A2561: for v2,v3,v1,v0 holds
 (v0"/\"((v1"\/"v2)"\/"(v3"/\"(v0"\/"v1))))=(v0"/\"(v1"\/"(v2"\/"v3)))
proof let v2,v3,v1,v0;
((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v0"\/"(v0"/\"v1))))=(v0"/\"((v1"\/"v2)"\/"(v3
"/\"
(v0"\/"v1)))) by A2553;
hence thesis by A458;
end;

A2563: for v2,v3,v1,v0 holds
 (v0"/\"(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))))=(v0"/\"(v1"\/"(v2"\/"v3)))
proof let v2,v3,v1,v0;
((v1"\/"v2)"\/"(v3"/\"(v0"\/"v1)))=(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))) by A181;
hence thesis by A2561;
end;

A2565: for v0,v3,v1,v2 holds
 (v0"/\"(v3"\/"(v2"\/"(v1"/\"v1))))=(v0"/\"(v1"\/"(v2"\/"v3)))
proof let v0,v3,v1,v2;
(v0"/\"(v1"\/"(v2"\/"(v3"/\"(v0"\/"v1)))))=(v0"/\"(v3"\/"(v2"\/"(v1"/\"v1))))
by A2559;
hence thesis by A2563;
end;

A2574: for v0,v3,v2,v1 holds
 (v0"/\"(v3"\/"(v1"\/"v2)))=(v0"/\"(v1"\/"(v2"\/"(v0"/\"v3))))
proof let v0,v3,v2,v1;
  (v0"/\"(v1"\/"(v2"\/"(v3"/\"v3))))=(v0"/\"(v3"\/"(v1"\/"v2))) by A2565;
  hence thesis by A2506;
end;

A2577: for v0,v3,v2,v1 holds
 (v0"/\"(v3"\/"(v1"\/"v2)))=(v0"/\"(v2"\/"(v3"\/"(v0"/\"v1))))
proof let v0,v3,v2,v1;
(v1"\/"(v2"\/"v3))=(v3"\/"(v1"\/"v2)) by A8;
hence thesis by A2574;
end;

A2583: for v0,v2,v1,v3 holds
 (v0"/\"(v2"\/"(v3"\/"v1)))=(v0"/\"(v2"\/"(v1"\/"(v0"/\"v3))))
proof let v0,v2,v1,v3;
  (v2"\/"(v3"\/"v1))=(v1"\/"(v2"\/"v3)) by A8;
  hence thesis by A2577;
end;

A2591: for v102,v103,v1,v101 holds
 ((v101"\/"v1)"/\"((v101"\/"v102)"/\"(v103"\/"(v101"/\"(v101"\/"v1)))))=(v101
"\/"(v1"/\"
(v103"/\"v102)))
proof let v102,v103,v1,v101;
((v101"\/"v1)"/\"(v101"\/"(v103"/\"v102)))=(v101"\/"(v1"/\"(v103"/\"v102))) by
 A4;
hence thesis by A241;
end;

A2594: for v2,v3,v1,v0 holds
 ((v0"\/"v1)"/\"((v0"\/"v2)"/\"(v3"\/"(v0"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v3
"/\"v2)))
proof let v2,v3,v1,v0;
(v0"/\"(v0"\/"v1))=(v0"\/"(v0"/\"v1)) by A2027;
hence thesis by A2591;
end;

A2596: for v2,v3,v1,v0 holds
 ((v0"\/"v1)"/\"((v0"\/"v2)"/\"(v0"\/"((v0"/\"v1)"\/"v3))))=(v0"\/"(v1"/\"(v3
"/\"v2)))
proof let v2,v3,v1,v0;
(v0"\/"((v0"/\"v1)"\/"v3))=(v3"\/"(v0"\/"(v0"/\"v1))) by A8;
hence thesis by A2594;
end;

A2600: for v2,v3,v1,v0 holds
 ((v0"\/"v1)"/\"(v0"\/"(v2"/\"(v3"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v3"/\"v2)))
proof let v2,v3,v1,v0;
((v0"\/"v2)"/\"(v0"\/"(v3"\/"(v0"/\"v1))))=(v0"\/"(v2"/\"(v3"\/"(v0"/\"v1))))
by A4;
hence thesis by A2596;
end;

A2602: for v2,v3,v1,v0 holds
 (v0"\/"(v1"/\"(v2"/\"(v3"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v3"/\"v2)))
proof let v2,v3,v1,v0;
((v0"\/"v1)"/\"(v0"\/"(v2"/\"(v3"\/"(v0"/\"v1)))))=(v0"\/"(v1"/\"(v2"/\"(v3"\/"
(v0"/\"v1))))) by A4;
hence thesis by A2600;
end;

A2618: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))=(v1"/\"(v0"\/"v0))
proof let v0,v1;
  (v0"/\"(v1"\/"v1))=(v0"/\"(v1"/\"(v0"\/"v0))) by A2251;
  hence thesis;
end;

A2652: for v1,v2,v100,v102,v101 holds
 ((v100"\/"(v101"\/"v102))"/\"(v101"\/"(v1"/\"v2)))=(v101"\/"((v1"/\"(v101"\/"
v2))"/\"
(v100"\/"v102)))
proof let v1,v2,v100,v102,v101;
(v101"\/"(v1"/\"(v101"\/"v2)))=(v101"\/"(v1"/\"v2)) by A2361;
hence thesis by A109;
end;

A2655: for v1,v0,v2,v4,v3 holds
 (v1"\/"((v3"/\"v4)"/\"(v0"\/"v2)))=(v1"\/"((v3"/\"(v1"\/"v4))"/\"(v0"\/"v2)))
proof let v1,v0,v2,v4,v3;
((v0"\/"(v1"\/"v2))"/\"(v1"\/"(v3"/\"v4)))=(v1"\/"((v3"/\"v4)"/\"(v0"\/"v2)))
by A109;
hence thesis by A2652;
end;

A2658: for v0,v1,v2,v4,v3 holds
 (v0"\/"(v1"/\"(v2"/\"(v3"\/"v4))))=(v0"\/"((v1"/\"(v0"\/"v2))"/\"(v3"\/"v4)))
proof let v0,v1,v2,v4,v3;
  ((v1"/\"v2)"/\"(v3"\/"v4))=(v1"/\"(v2"/\"(v3"\/"v4))) by A292;
  hence thesis by A2655;
end;

A2660: for v0,v1,v2,v4,v3 holds
 (v0"\/"(v1"/\"(v2"/\"(v3"\/"v4))))=(v0"\/"(v1"/\"((v0"\/"v2)"/\"(v3"\/"v4))))
proof let v0,v1,v2,v4,v3;
((v1"/\"(v0"\/"v2))"/\"(v3"\/"v4))=(v1"/\"((v0"\/"v2)"/\"(v3"\/"v4))) by A292;
hence thesis by A2658;
end;

A2663:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c4"/\"(c3"/\"(c1"\/"(c2
"/\"c3))))))=
((c2"\/"(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by
 A2660,A2417;

A2667:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c3"/\"(c4"/\"(c1"\/"(c2
"/\"c3))))))=
((c2"\/"(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by
 A2663,A14;

A2669:  not
 ((c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3))))"/\"(c2"\/"(c3"/\"(c4"/\"c1))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A2602,
A2667;

A2677:  not
 ((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"\/"c3)"/\"(c1"\/"(c2"/\"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(
  c2"\/"(c3"/\"c4)))))) by A14,A2669;

A2680: for v103,v101,v100 holds
 ((v101"/\"(v100"\/"v100))"\/"((v100"\/"v101)"/\"v103))=((v100"\/"v101)"/\"(
v103"\/"
(v100"/\"v101)))
proof let v103,v101,v100;
(v100"/\"(v101"/\"(v100"\/"v101)))=(v101"/\"(v100"\/"v100)) by A2369;
hence thesis by A131;
end;

A2692: for v103,v100,v1,v101 holds
 ((v100"\/"(v101"\/"(v1"/\"v1)))"/\"((v1"\/"(v101"/\"v101))"\/"v103))=((v1"\/"
(v101"/\"v101))"\/"(v103"/\"(v100"\/"v101)))
proof let v103,v100,v1,v101;
(v101"\/"(v1"\/"(v101"/\"v101)))=(v101"\/"(v1"/\"v1)) by A2397;
hence thesis by A117;
end;

A2697: for v3,v0,v2,v1 holds
 ((v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v2"\/"((v1"/\"v1)"\/"v3)))=((v2"\/"(v1"/\"v1))
"\/"(v3"/\"
(v0"\/"v1)))
proof let v3,v0,v2,v1;
(v2"\/"((v1"/\"v1)"\/"v3))=(v3"\/"(v2"\/"(v1"/\"v1))) by A8;
hence thesis by A2692;
end;

A2701: for v3,v0,v2,v1 holds
 ((v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v1"\/"(v2"\/"v3)))=((v2"\/"(v1"/\"v1))"\/"(v3
"/\"
(v0"\/"v1)))
proof let v3,v0,v2,v1;
((v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v2"\/"(v3"\/"(v1"/\"v1))))=((v0"\/"(v1"\/"(v2
"/\"v2)))"/\"
(v1"\/"(v2"\/"v3))) by A2565;
hence thesis by A2697;
end;

A2703: for v1,v0,v3,v2 holds
 (v1"\/"((v2"\/"v3)"/\"(v0"\/"(v2"/\"v2))))=((v2"\/"(v1"/\"v1))"\/"(v3"/\"(v0
"\/"v1)))
proof let v1,v0,v3,v2;
((v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v1"\/"(v2"\/"v3)))=(v1"\/"((v2"\/"v3)"/\"(v0
"\/"(v2"/\"v2)))) by A109;
hence thesis by A2701;
end;

A2706: for v0,v3,v2,v1 holds
 v0"\/"((v1"\/"v2)"/\"(v3"\/"v1)) = (v1"\/"(v0"/\"v0))"\/"(v2"/\"(v3"\/"v0))
proof let v0,v3,v2,v1;
  (v1"\/"v2)"/\"(v3"\/"(v1"/\"v1)) = (v1"\/"v2)"/\"(v3"\/"v1);
  hence thesis by A2703;
end;

A2708: for v0,v1,v2,v3 holds
 v0"\/"(v1"\/"(v3"/\"v2)) = (v1"\/"(v0"/\"v0))"\/"(v2"/\"(v3"\/"v0))
proof let v0,v1,v2,v3;
  v0"\/"((v1"\/"v2)"/\"(v3"\/"v1)) = v0"\/"(v1"\/"(v3"/\"v2)) by A223;
  hence thesis by A2706;
end;

A2711: for v0,v1,v3,v2 holds
 v0"\/"(v1"\/"(v2"/\"v3)) = v1"\/"((v0"/\"v0)"\/"(v3"/\"(v2"\/"v0)))
proof let v0,v1,v3,v2;
  (v1"\/"(v0"/\"v0))"\/"(v3"/\"(v2"\/"v0)) =
    v1"\/"((v0"/\"v0)"\/"(v3"/\"(v2"\/"v0))) by A181;
  hence thesis by A2708;
end;

A2713: for v0,v1,v3,v2 holds
 v0"\/"(v1"\/"(v2"/\"v3)) = v1"\/"(v0"\/"(v3"/\"(v2"\/"v0)))
proof let v0,v1,v3,v2;
  (v0"/\"v0)"\/"(v3"/\"(v2"\/"v0)) = v0"\/"(v3"/\"(v2"\/"v0));
  hence thesis by A2711;
end;

A2715: for v0,v1,v3,v2 holds
 (v0"\/"(v1"\/"(v2"/\"v3)))=(v0"\/"((v3"/\"(v2"\/"v0))"\/"v1))
proof let v0,v1,v3,v2;
(v0"\/"((v3"/\"(v2"\/"v0))"\/"v1))=(v1"\/"(v0"\/"(v3"/\"(v2"\/"v0)))) by A8;
hence thesis by A2713;
end;

A2721: for v0,v1 holds (v0"\/"(v1"\/"(v0"/\"v0)))=(v1"\/"(v0"/\"v0))
proof let v0,v1;
(v0"\/"(v1"\/"(v0"/\"v0)))=(v0"\/"(v1"/\"v1)) by A2397;
hence thesis;
end;

A2773: for v2,v1,v0 holds
 (v1"/\"v0)"\/"(v2"/\"(v0"\/"v1)) = (v0"\/"v1)"/\"(v2"\/"(v0"/\"v1))
proof let v2,v1,v0;
  (v0"/\"(v1"\/"v1))"\/"(v2"/\"(v0"\/"v1)) = (v1"/\"v0)"\/"(v2"/\"(v0"\/"v1));
  hence thesis by A2680;
end;

A2780:  not
 ((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"\/"c4)"/\"(c2"\/"(c3"/\"c4)))))) by A2773,
A2677;

A2782:  not
 ((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"/\"c4)"\/"(c2"/\"(c3"\/"c4)))))) by A2773,
A2780;

A2784:  not
 ((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"((c3"/\"c4)"\/"(c3"\/"c4))))) by A2492,A2782;

A2788:  not
 ((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"(c3"\/"(c4"\/"(c3"/\"c4)))))) by A181,A2784;

A2790:  not
 ((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"\/"
(c3"/\"c4))"/\"(c1"\/"(c2"/\"(c3"\/"(c4"/\"c4))))) by A2533,A2788;

A2795: for v101,v102,v2,v3,v1,v0 holds
 (((v0"/\"(v1"/\"v2))"\/"v101)"/\"(v102"\/"(v2"/\"(v3"\/"(v0"/\"v1)))))=((v0
"/\"
(v1"/\"v2))"\/"(v101"/\"(v102"\/"(v2"/\"v3))))
proof let v101,v102,v2,v3,v1,v0;
((v0"/\"(v1"/\"v2))"\/"(v2"/\"v3))=(v2"/\"(v3"\/"(v0"/\"v1))) by A131;
hence thesis by A270;
end;

A2802: for v103,v102,v101 holds
 (v101"\/"v102)"/\"(v102"\/"v103) = v102"\/"(v103"/\"((v101"\/"v102)"\/"v101))
proof let v103,v102,v101;
  ((v101"\/"v102)"\/"(v101"\/"v102))"/\"(v102"\/"v103) =
    (v101"\/"v102)"/\"(v102"\/"v103);
  hence thesis by A117;
end;

A2805: for v1,v2,v0 holds (v1"\/"(v0"/\"v2))=(v1"\/"(v2"/\"((v0"\/"v1)"\/"v0)))
proof let v1,v2,v0;
  (v0"\/"v1)"/\"(v1"\/"v2) = v1"\/"(v0"/\"v2) by A4;
  hence thesis by A2802;
end;

A2810: for v0,v2,v1 holds v0"\/"(v1"/\"v2) = v0"\/"(v2"/\"(v1"\/"v0))
proof let v0,v2,v1;
  v2"/\"(v1"\/"(v1"\/"v0)) = v2"/\"(v1"\/"v0) by A2435;
  hence thesis by A2805;
end;

A2815: for v1,v2,v100,v102,v101 holds
 ((v100"/\"(v101"/\"v102))"\/"(v101"/\"(v1"\/"v2)))=(v101"/\"((v1"\/"(v101"/\"
v2))"\/"
(v100"/\"v102)))
proof let v1,v2,v100,v102,v101;
(v101"/\"(v1"\/"(v101"/\"v2)))=(v101"/\"(v1"\/"v2)) by A2492;
hence thesis by A123;
end;

A2818: for v1,v0,v2,v4,v3 holds
 (v1"/\"((v3"\/"v4)"\/"(v0"/\"v2)))=(v1"/\"((v3"\/"(v1"/\"v4))"\/"(v0"/\"v2)))
proof let v1,v0,v2,v4,v3;
((v0"/\"(v1"/\"v2))"\/"(v1"/\"(v3"\/"v4)))=(v1"/\"((v3"\/"v4)"\/"(v0"/\"v2)))
by A123;
hence thesis by A2815;
end;

A2821: for v0,v1,v2,v4,v3 holds
 v0"/\"(v1"\/"(v2"\/"(v3"/\"v4))) = v0"/\"((v1"\/"(v0"/\"v2))"\/"(v3"/\"v4))
proof let v0,v1,v2,v4,v3;
  (v1"\/"v2)"\/"(v3"/\"v4) = v1"\/"(v2"\/"(v3"/\"v4)) by A181;
  hence thesis by A2818;
end;

A2823: for v0,v1,v2,v4,v3 holds
 (v0"/\"(v1"\/"(v2"\/"(v3"/\"v4))))=(v0"/\"(v1"\/"((v0"/\"v2)"\/"(v3"/\"v4))))
proof let v0,v1,v2,v4,v3;
((v1"\/"(v0"/\"v2))"\/"(v3"/\"v4))=(v1"\/"((v0"/\"v2)"\/"(v3"/\"v4))) by A181;
hence thesis by A2821;
end;

A2838: for v102,v100,v1 holds
 (v1"/\"(v100"\/"v100))"\/"(v100"/\"v102) =
   v100"/\"((v1"/\"(v100"\/"v100))"\/"v102)
proof let v102,v100,v1;
  v100"/\"(v1"/\"(v100"\/"v100)) = v1"/\"(v100"\/"v100) by A2618;
  hence thesis by A6;
end;

A2847: for v1,v2,v0 holds v1"/\"(v0"\/"v2) = v1"/\"((v0"/\"(v1"\/"v1))"\/"v2)
proof let v1,v2,v0;
  (v0"/\"v1)"\/"(v1"/\"v2) = v1"/\"(v0"\/"v2) by A6;
  hence thesis by A2838;
end;

A2852: for v0,v2,v1 holds v0"/\"(v1"\/"v2) = v0"/\"(v2"\/"(v0"/\"v1))
proof let v0,v2,v1;
  v2"\/"(v1"/\"(v0"\/"v0)) = v2"\/"(v0"/\"v1);
  hence thesis by A2847;
end;

A2859: for v103,v100,v101,v1 holds
 (v100"/\"(v1"/\"(v101"\/"v101)))"\/"(v101"/\"v103) =
    v101"/\"(v103"\/"(v100"/\"(v1"/\"(v101"\/"v101))))
proof let v103,v100,v101,v1;
  v101"/\"(v1"/\"(v101"\/"v101)) = v1"/\"(v101"\/"v101) by A2618;
  hence thesis by A123;
end;

A2862: for v2,v3,v1,v0 holds
 (v2"/\"(v3"\/"(v0"/\"v1)))=(v2"/\"(v3"\/"(v0"/\"(v1"/\"(v2"\/"v2)))))
proof let v2,v3,v1,v0;
((v0"/\"(v1"/\"(v2"\/"v2)))"\/"(v2"/\"v3))=(v2"/\"(v3"\/"(v0"/\"v1))) by A123;
hence thesis by A2859;
end;

A2865: for v0,v1,v3,v2 holds
 (v0"/\"(v1"\/"(v2"/\"v3)))=(v0"/\"(v1"\/"(v0"/\"(v2"/\"v3))))
proof let v0,v1,v3,v2;
(v1"\/"(v2"/\"(v3"/\"(v0"\/"v0))))=(v1"\/"(v0"/\"(v2"/\"v3))) by A14;
hence thesis by A2862;
end;

A2867: for v0,v1,v3,v2 holds
 (v0"/\"(v1"\/"(v2"/\"v3)))=(v0"/\"(v1"\/"(v3"/\"(v0"/\"v2))))
proof let v0,v1,v3,v2;
(v0"/\"(v2"/\"v3))=(v3"/\"(v0"/\"v2)) by A14;
hence thesis by A2865;
end;

A2886: for v3,v2,v1,v0 holds
 ((v0"/\"(v1"\/"v2))"\/"(v3"/\"(v2"\/"(v0"/\"v1))))=((v0"/\"v1)"\/"(v2"/\"(v0
"\/"v3)))
proof let v3,v2,v1,v0;
((v2"\/"(v0"/\"v1))"/\"(v0"\/"(v3"\/"(v0"/\"v1))))=((v0"/\"v1)"\/"(v2"/\"(v0
"\/"v3))) by A305;
hence thesis by A511;
end;

A2889: for v103,v100,v101,v1 holds
 (v100"\/"(v1"\/"(v101"/\"v101)))"/\"(v101"\/"v103) =
  v101"\/"(v103"/\"(v100"\/"(v1"\/"(v101"/\"v101))))
proof let v103,v100,v101,v1;
  v101"\/"(v1"\/"(v101"/\"v101)) = v1"\/"(v101"/\"v101) by A2721;
  hence thesis by A109;
end;

A2892: for v2,v3,v1,v0 holds
 (v2"\/"(v3"/\"(v0"\/"v1)))=(v2"\/"(v3"/\"(v0"\/"(v1"\/"(v2"/\"v2)))))
proof let v2,v3,v1,v0;
  (v0"\/"(v1"\/"(v2"/\"v2)))"/\"(v2"\/"v3) = v2"\/"(v3"/\"(v0"\/"v1)) by A109;
  hence thesis by A2889;
end;

A2895: for v0,v1,v3,v2 holds
 v0"\/"(v1"/\"(v2"\/"v3)) = v0"\/"(v1"/\"(v0"\/"(v2"\/"v3)))
proof let v0,v1,v3,v2;
  v1"/\"(v2"\/"(v3"\/"(v0"/\"v0))) = v1"/\"(v0"\/"(v2"\/"v3)) by A2565;
  hence thesis by A2892;
end;

A2897: for v0,v1,v3,v2 holds
 v0"\/"(v1"/\"(v2"\/"v3)) = v0"\/"(v1"/\"(v3"\/"(v0"\/"v2)))
proof let v0,v1,v3,v2;
  v0"\/"(v2"\/"v3) = v3"\/"(v0"\/"v2) by A8;
  hence thesis by A2895;
end;

A2907: for v102,v1,v100,v2 holds
 ((v100"/\"(v2"\/"v1))"\/"((v1"\/"(v2"/\"v100))"/\"v102))=((v1"\/"(v2"/\"v100))
"/\"
(v100"\/"v102))
proof let v102,v1,v100,v2;
  v100"/\"(v1"\/"(v2"/\"v100)) = v100"/\"(v2"\/"v1) by A2852;
  hence thesis by A6;
end;

A2914: for v1,v2,v3,v0 holds
 (v0"/\"v1)"\/"(v2"/\"(v0"\/"v3)) = (v2"\/"(v1"/\"v0))"/\"(v0"\/"v3)
proof let v1,v2,v3,v0;
  (v0"/\"(v1"\/"v2))"\/"(v3"/\"(v2"\/"(v0"/\"v1))) =
    (v0"/\"v1)"\/"(v2"/\"(v0"\/"v3)) by A2886;
  hence thesis by A2907;
end;

A2921: for v102,v101,v1,v0 holds
 ((v102"/\"v101)"\/"(v101"/\"(v0"\/"v1)))=(v101"/\"((v0"\/"(v1"\/"(v102"/\"v101
)))"\/"(
(v0"\/"(v1"\/"(v102"/\"v101)))"/\"v102)))
proof let v102,v101,v1,v0;
((v0"\/"(v1"\/"(v102"/\"v101)))"/\"(v101"\/"(v102"/\"v101)))=((v102"/\"v101)
"\/"
(v101"/\"(v0"\/"v1))) by A346;
hence thesis by A1005;
end;

A2924: for v1,v0,v3,v2 holds
 v1"/\"(v0"\/"(v2"\/"v3)) =
    v1"/\"((v2"\/"(v3"\/"(v0"/\"v1)))"\/"((v2"\/"(v3"\/"(v0"/\"v1)))"/\"v0))
proof let v1,v0,v3,v2;
  (v0"/\"v1)"\/"(v1"/\"(v2"\/"v3)) = v1"/\"(v0"\/"(v2"\/"v3)) by A6;
  hence thesis by A2921;
end;

A2929: for v0,v1,v3,v2 holds
 v0"/\"(v1"\/"(v2"\/"v3)) =
  v0"/\"((v2"\/"(v3"\/"(v1"/\"v0)))"\/"(v1"/\"(v2"\/"(v3"\/"v0))))
proof let v0,v1,v3,v2;
  v1"/\"(v2"\/"(v3"\/"(v1"/\"v0))) = v1"/\"(v2"\/"(v3"\/"v0)) by A2583;
  hence thesis by A2924;
end;

A2933: for v0,v1,v3,v2 holds
 v0"/\"(v1"\/"(v2"\/"v3)) =
   v0"/\"((v2"\/"(v3"\/"(v1"/\"v0)))"\/"(v1"/\"(v0"\/"(v3"\/"v2))))
proof let v0,v1,v3,v2;
  v0"\/"(v3"\/"v2) = v2"\/"(v0"\/"v3) by A8;
  hence thesis by A2929;
end;

A2937: for v0,v1,v3,v2 holds
 v0"/\"(v1"\/"(v2"\/"v3)) =
   v0"/\"(v2"\/"((v3"\/"(v1"/\"v0))"\/"(v1"/\"(v0"\/"(v2"\/"v3)))))
proof let v0,v1,v3,v2;
  (v2"\/"(v3"\/"(v1"/\"v0)))"\/"(v1"/\"(v0"\/"(v2"\/"v3))) =
    v2"\/"((v3"\/"(v1"/\"v0))"\/"(v1"/\"(v0"\/"(v2"\/"v3)))) by A181;
  hence thesis by A2933;
end;

A2939: for v0,v1,v3,v2 holds
 v0"/\"(v1"\/"(v2"\/"v3)) =
   v0"/\"(v2"\/"(v3"\/"((v1"/\"v0)"\/"(v1"/\"(v0"\/"(v2"\/"v3))))))
proof let v0,v1,v3,v2;
  (v3"\/"(v1"/\"v0))"\/"(v1"/\"(v0"\/"(v2"\/"v3))) =
     v3"\/"((v1"/\"v0)"\/"(v1"/\"(v0"\/"(v2"\/"v3)))) by A181;
  hence thesis by A2937;
end;

A2941: for v0,v1,v3,v2 holds v0"/\"(v1"\/"(v2"\/"v3)) =
  v0"/\"(v2"\/"(v3"\/"(v1"/\"(v0"\/"(v0"\/"(v2"\/"v3))))))
proof let v0,v1,v3,v2;
  (v1"/\"v0)"\/"(v1"/\"(v0"\/"(v2"\/"v3))) =
    v1"/\"(v0"\/"(v0"\/"(v2"\/"v3))) by A6;
  hence thesis by A2939;
end;

A2943: for v0,v1,v3,v2 holds
 v0"/\"(v1"\/"(v2"\/"v3)) = v0"/\"(v2"\/"(v3"\/"(v1"/\"(v0"\/"(v2"\/"v3)))))
proof let v0,v1,v3,v2;
  v1"/\"(v0"\/"(v0"\/"(v2"\/"v3))) = v1"/\"(v0"\/"(v2"\/"v3)) by A2435;
  hence thesis by A2941;
end;

A2945: for v0,v1,v3,v2 holds
 v0"/\"(v1"\/"(v2"\/"v3)) = v0"/\"(v2"\/"(v3"\/"(v1"/\"(v0"\/"v2))))
proof let v0,v1,v3,v2;
  v3"\/"(v1"/\"(v0"\/"(v2"\/"v3))) = v3"\/"(v1"/\"(v0"\/"v2)) by A2897;
  hence thesis by A2943;
end;

A2947: for v0,v1,v3,v2 holds
 v0"/\"(v1"\/"(v2"\/"v3)) = v0"/\"(v2"\/"(v3"\/"(v0"/\"v1)))
proof let v0,v1,v3,v2;
  v2"\/"(v3"\/"(v1"/\"(v0"\/"v2))) = v2"\/"(v3"\/"(v0"/\"v1)) by A2715;
  hence thesis by A2945;
end;

A2969:  not
 ((c2"\/"(c1"/\"(c3"/\"c4)))"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=((
c2"/\"
(c3"\/"c4))"\/"(c1"/\"(c2"\/"(c3"/\"c4)))) by A2914,A2790;

A2972: for v101,v102,v1,v3,v2 holds
 (v1"\/"(v2"/\"(v3"/\"v102)))"/\"(v101"\/"(v102"/\"(v1"\/"(v2"/\"v3)))) =
  (v1"\/"(v2"/\"(v3"/\"v102)))"/\"(v102"\/"v101)
proof let v101,v102,v1,v3,v2;
  v102"/\"(v1"\/"(v2"/\"(v3"/\"v102))) = v102"/\"(v1"\/"(v2"/\"v3)) by A2867;
  hence thesis by A2852;
end;

A2975: for v0,v4,v1,v3,v2 holds
 (v1"/\"(v2"/\"v3))"\/"(v0"/\"(v4"\/"(v3"/\"v0))) =
   (v0"\/"(v1"/\"(v2"/\"v3)))"/\"(v3"\/"v4)
proof let v0,v4,v1,v3,v2;
  (v0"\/"(v1"/\"(v2"/\"v3)))"/\"(v4"\/"(v3"/\"(v0"\/"(v1"/\"v2)))) =
   (v1"/\"(v2"/\"v3))"\/"(v0"/\"(v4"\/"(v3"/\"v0))) by A2795;
  hence thesis by A2972;
end;

A2980: for v4,v3,v0,v2,v1 holds
 (v0"/\"(v1"/\"v2))"\/"(v3"/\"(v4"\/"v2)) =
   (v3"\/"(v0"/\"(v1"/\"v2)))"/\"(v2"\/"v4)
proof let v4,v3,v0,v2,v1;
  v3"/\"(v4"\/"(v3"/\"v2)) = v3"/\"(v4"\/"v2) by A2492;
  hence thesis by A2975;
end;

A2986:  not
 ((c1"/\"(c3"/\"c4))"\/"(c2"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3))))))=((
c2"/\"
(c3"\/"c4))"\/"(c1"/\"(c2"\/"(c3"/\"c4)))) by A2980,A2969;

A2987:
 (c2"/\"(c4"\/"((c2"/\"c3)"\/"(c1"/\"(c2"\/"c3)))))=(c2"/\"(c4"\/"(c3"\/"(c1
"/\"
(c2"\/"c3))))) by A2823;

A2992:  not
 ((c1"/\"(c3"/\"c4))"\/"(c2"/\"(c4"\/"(c3"\/"(c1"/\"c2)))))=((c2"/\"(c3"\/"c4))
"\/"(c1"/\"
(c2"\/"(c3"/\"c4)))) by A2810,A2987,A2986;

A2998:  not
 ((c1"/\"(c3"/\"c4))"\/"(c2"/\"(c1"\/"(c3"\/"c4))))=((c2"/\"(c3"\/"c4))"\/"(c1
"/\"(c2"\/"
(c3"/\"c4)))) by A2947,A2992;

A3002: for v2,v100,v102,v101 holds
 ((v100"\/"(v101"/\"v102))"/\"(v101"\/"(v100"/\"v2)))=((v101"/\"v102)"\/"(v100
"/\"
(v101"\/"v2)))
proof let v2,v100,v102,v101;
(v100"/\"(v101"\/"(v100"/\"v2)))=(v100"/\"(v101"\/"v2)) by A2492;
hence thesis by A2914;
end;

A3005: for v3,v0,v2,v1 holds
 ((v0"/\"v3)"\/"(v1"/\"(v0"\/"(v1"/\"v2))))=((v1"/\"v2)"\/"(v0"/\"(v1"\/"v3)))
proof let v3,v0,v2,v1;
((v0"\/"(v1"/\"v2))"/\"(v1"\/"(v0"/\"v3)))=((v0"/\"v3)"\/"(v1"/\"(v0"\/"(v1"/\"
v2)))) by
 A2914;
hence thesis by A3002;
end;

for v1,v2,v3,v0 holds
 (v0"/\"v1)"\/"(v2"/\"(v0"\/"v3)) = (v2"/\"v3)"\/"(v0"/\"(v2"\/"v1))
proof let v1,v2,v3,v0;
  v2"/\"(v0"\/"(v2"/\"v3)) = v2"/\"(v0"\/"v3) by A2492;
  hence thesis by A3005;
end;
hence thesis by A2998;
end;
