 reserve L for non empty LattStr;
 reserve v100,v102,v2,v1,v0,v3,v101 for Element of L;
 reserve L for WA_Lattice;
 reserve x,y,z,u for Element of L;
 reserve L for non empty LattStr;
 reserve v100,v101,v102,v0,v1,v2 for Element of L;
 reserve v101,v100,v2,v1,v0,v102,v103,v3 for Element of L;

theorem Lemma4:
(for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0) &
(for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0) &
(for v1,v0 holds (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1) &
(for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0) &
(for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0) implies
for v0,v1 holds v0 "\/" v1 = v1 "\/" v0
proof
assume A1: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0;
assume A2: for v0,v1 holds (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0;
assume A3: for v1,v0 holds (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1;
assume A4: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0;
assume A5: for v2,v1,v0 holds ((v0"/\"v1)"\/"(v2"/\"v0))"\/"v0 = v0;
assume not thesis; then
consider C,D being Element of L such that
A6: C"\/"D <> D"\/"C;
A9: for v1,v0 holds
 ((v0"/\"v1)"/\"(v0"/\"(v0"\/"v1)))"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
  (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
  hence thesis by A1;
end;

A12: for v0,v1 holds
 ((v0"/\"v0)"/\"(v1"/\"(v0"\/"v0)))"\/"((v0"/\"v0)"/\"v0) = v0"/\"v0
proof let v0,v1;
  (v0"/\"v0)"\/"(v1"/\"(v0"\/"v0)) = v0 by A2;
  hence thesis by A1;
end;

A15: for v2,v1,v101 holds
 v101"\/"(((v101"\/"v1)"/\"(v2"\/"v101))"/\"(((v101"\/"v1)"/\"
  (v2"\/"v101))"\/"v101)) = (v101"\/"v1)"/\"(v2"\/"v101)
proof let v2,v1,v101;
  ((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
  hence thesis by A1;
end;

A19: for v102,v1,v0 holds
  (v0"/\"(v102"\/"(v0"/\"v1)))"/\"(v0"/\"v1) = v0"/\"v1
proof let v102,v1,v0;
  (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
  hence thesis by A4;
end;

A27: for v102,v1,v0 holds
  (v1"/\"(v102"\/"(v0"/\"v1)))"/\"(v0"/\"v1) = v0"/\"v1
proof let v102,v1,v0;
  (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1 by A3;
  hence thesis by A4;
end;

A31: for v101,v100 holds ((v100"\/"v101)"/\"v100)"/\"v100 = v100
proof
  now let v101,v2,v1,v100;
    ((v100"/\"v1)"\/"(v2"/\"v100))"\/"v100 = v100 by A5;
    hence ((v100"\/"v101)"/\"v100)"/\"v100 = v100 by A4;
  end;
  hence thesis;
end;

A35: for v102,v2,v1,v101 holds
 (v101"\/"(v102"/\"((v101"\/"v1)"/\"(v2"\/"v101))))"\/"((v101"\/"v1)"/\"
  (v2"\/"v101)) = (v101"\/"v1)"/\"(v2"\/"v101)
proof let v102,v2,v1,v101;
  ((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
  hence thesis by A5;
end;

A39: for v101,v100 holds ((v100"/\"v101)"\/"v100)"\/"v100 = v100
proof
  now let v101,v2,v1,v100;
    ((v100"\/"v1)"/\"(v2"\/"v100))"/\"v100 = v100 by A4;
    hence ((v100"/\"v101)"\/"v100)"\/"v100 = v100 by A5;
  end;
  hence thesis;
end;

A49: for v1,v0 holds (v0"/\"(v0"/\"v1))"/\"(v0"/\"v1) = v0"/\"v1
proof let v1,v0;
  (v0"/\"v1)"\/"(v0"/\"(v0"\/"v1)) = v0 by A1;
  hence thesis by A31;
end;

A52: for v1,v101 holds
 (((v101"/\"v1)"\/"v101)"/\"v101)"\/"(((v101"/\"v1)"\/"v101)"/\"v101) =
    (v101"/\"v1)"\/"v101
proof let v1,v101;
  ((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A39;
  hence thesis by A1;
end;

A56: for v1,v101 holds
 (v101"\/"((v101"\/"v1)"/\"v101))"\/"((v101"\/"v1)"/\"v101) =
  (v101"\/"v1)"/\"v101
proof let v1,v101;
  ((v101"\/"v1)"/\"v101)"/\"v101 = v101 by A31;
  hence thesis by A39;
end;

A67: for v0 holds v0"/\"v0 = v0 by A1,A4,A5,Lemma1;

A70: for v1,v0 holds
 ((v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)))"\/"(v0"/\"(v0"/\"v1)) = v0"/\"(v0"/\"v1)
proof let v1,v0;
  (v0"/\"(v0"/\"v1))"/\"(v0"/\"v1) = v0"/\"v1 by A49;
  hence thesis by A39;
end;

A82: for v0,v1 holds
  (v0"/\"(v1"/\"(v0"\/"v0)))"\/"((v0"/\"v0)"/\"v0) = v0"/\"v0
proof let v0,v1;
  v0"/\"v0 = v0 by A67;
  hence thesis by A12;
end;

A84: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))"\/"(v0"/\"v0) = v0"/\"v0
proof let v0,v1;
  v0"/\"v0 = v0 by A67;
  hence thesis by A82;
end;

A86: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))"\/"v0 = v0"/\"v0
proof let v0,v1;
  v0"/\"v0 = v0 by A67;
  hence thesis by A84;
end;

A88: for v0,v1 holds (v0"/\"(v1"/\"(v0"\/"v0)))"\/"v0 = v0
proof let v0,v1;
  v0"/\"v0 = v0 by A67;
  hence thesis by A86;
end;

A90: for v0,v1 holds v0"\/"(v1"/\"(v0"\/"v0)) = v0
proof let v0,v1;
  v0"/\"v0 = v0 by A67;
  hence thesis by A2;
end;

A98: for v0 holds v0 = v0"\/"v0 by A1,A2,A3,A4,A5,Lemma2;

A101: for v0,v1 holds v0"\/"(v1"/\"v0) = v0
proof let v0,v1;
  v0"\/"v0 = v0 by A98;
  hence thesis by A90;
end;

A103: for v0,v1 holds (v0"/\"(v1"/\"v0))"\/"v0 = v0
proof let v0,v1;
  v0"\/"v0 = v0 by A98;
  hence thesis by A88;
end;

A105: for v1,v0 holds ((v0"/\"v1)"\/"v0)"/\"v0 = (v0"/\"v1)"\/"v0
proof let v1,v0;
  (((v0"/\"v1)"\/"v0)"/\"v0)"\/"(((v0"/\"v1)"\/"v0)"/\"v0) =
    ((v0"/\"v1)"\/"v0)"/\"v0 by A98;
  hence thesis by A52;
end;

A107: for v1,v0 holds (v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"(v0"/\"v1)
proof let v1,v0;
  (v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"v1 by A101;
  hence thesis by A70;
end;

A109: for v1,v0 holds v0"/\"v1 = v0"/\"(v0"/\"v1)
proof let v1,v0;
  (v0"/\"v1)"\/"(v0"/\"(v0"/\"v1)) = v0"/\"v1 by A101;
  hence thesis by A107;
end;

A112: for v1,v0 holds v0"\/"((v0"\/"v1)"/\"v0) = (v0"\/"v1)"/\"v0
proof let v1,v0;
  v0"\/"((v0"\/"v1)"/\"v0) = v0 by A101;
  hence thesis by A56;
end;

A114: for v1,v0 holds v0 = (v0"\/"v1)"/\"v0
proof let v1,v0;
  v0"\/"((v0"\/"v1)"/\"v0) = v0 by A101;
  hence thesis by A112;
end;

A118: for v101,v102 holds (v101"/\"(v102"\/"v101))"/\"v101 = v101
proof let v101,v102;
  v101"\/"v101 = v101 by A98;
  hence thesis by A4;
end;

A122: for v1,v101 holds
 v101"\/"((v101"\/"v1)"/\"((v101"\/"v1)"\/"v101)) = v101"\/"v1
proof let v1,v101;
  (v101"\/"v1)"/\"v101 = v101 by A114;
  hence thesis by A1;
end;

A126: for v1,v0 holds v1"/\"(v0"/\"v1) = v0"/\"v1
proof let v1,v0;
  (v0"/\"v1)"\/"(v1"/\"(v0"\/"v1)) = v1 by A3;
  hence thesis by A114;
end;

A130: for v1,v101 holds
 (v101"/\"((v101"\/"v1)"/\"((v101"\/"v1)"\/"v101)))"\/"
  (((v101"\/"v1)"/\"v101)"/\"(v101"\/"v1)) = (v101"\/"v1)"/\"v101
proof let v1,v101;
  (v101"\/"v1)"/\"v101 = v101 by A114;
  hence thesis by A9;
end;

A133: for v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"((v0"\/"v1)"\/"v0)))"\/"(v0"/\"(v0"\/"v1)) =
    (v0"\/"v1)"/\"v0
proof let v1,v0;
  (v0"\/"v1)"/\"v0 = v0 by A114;
  hence thesis by A130;
end;

A135: for v1,v0 holds
 (v0"/\"((v0"\/"v1)"/\"((v0"\/"v1)"\/"v0)))"\/"(v0"/\"(v0"\/"v1)) = v0
proof let v1,v0;
  (v0"\/"v1)"/\"v0 = v0 by A114;
  hence thesis by A133;
end;

A138: for v1,v101 holds v101"/\"((v101"/\"v1)"\/"v101) = (v101"/\"v1)"\/"v101
proof let v1,v101;
  ((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A39;
  hence thesis by A114;
end;

A141: for v0,v1 holds (v1"/\"v0)"\/"v0 = v0
proof let v0,v1;
  v0"/\"(v1"/\"v0) = v1"/\"v0 by A126;
  hence thesis by A103;
end;

A145: for v1,v100 holds
  (v100"/\"v1)"\/"(v100"/\"(v100"\/"(v100"/\"v1))) = v100
proof let v1,v100;
  v100"/\"(v100"/\"v1) = v100"/\"v1 by A109;
  hence thesis by A1;
end;

A149: for v1,v100 holds
 ((v100"/\"v1)"/\"(v100"/\"(v100"\/"(v100"/\"v1))))"\/"((v100"/\"
    (v100"/\"v1))"/\"v100) = v100"/\"(v100"/\"v1)
proof let v1,v100;
  v100"/\"(v100"/\"v1) = v100"/\"v1 by A109;
  hence thesis by A9;
end;

A152: for v1,v0 holds
 ((v0"/\"v1)"/\"(v0"/\"(v0"\/"(v0"/\"v1))))"\/"((v0"/\"v1)"/\"v0) =
    v0"/\"(v0"/\"v1)
proof let v1,v0;
  v0"/\"(v0"/\"v1) = v0"/\"v1 by A109;
  hence thesis by A149;
end;

A154: for v1,v0 holds
 ((v0"/\"v1)"/\"(v0"/\"(v0"\/"(v0"/\"v1))))"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
  v0"/\"(v0"/\"v1) = v0"/\"v1 by A109;
  hence thesis by A152;
end;

A157: for v102,v1,v101 holds
 ((v101"/\"v1)"\/"v101)"\/"((v101"/\"(v102"\/"((v101"/\"v1)"\/"v101)))"/\"
    (((((v101"/\"v1)"\/"v101)"\/"v101)"/\"(v102"\/"((v101"/\"v1)"\/"v101)))"\/"
      ((v101"/\"v1)"\/"v101))) =
   (((v101"/\"v1)"\/"v101)"\/"v101)"/\"(v102"\/"((v101"/\"v1)"\/"v101))
proof let v102,v1,v101;
  ((v101"/\"v1)"\/"v101)"\/"v101 = v101 by A39;
  hence thesis by A15;
end;

A160: for v2,v1,v0 holds
 ((v0"/\"v1)"\/"v0)"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"((v0"/\"(v2"\/"
    ((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
   (((v0"/\"v1)"\/"v0)"\/"v0)"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
  ((v0"/\"v1)"\/"v0)"\/"v0 = v0 by A39;
  hence thesis by A157;
end;

A162: for v2,v1,v0 holds
 ((v0"/\"v1)"\/"v0)"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"((v0"/\"(v2"\/"
  ((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
     v0"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
  ((v0"/\"v1)"\/"v0)"\/"v0 = v0 by A39;
  hence thesis by A160;
end;

A165: for v2,v1,v101 holds
 ((v101"\/"v1)"/\"(v2"\/"v101))"/\"(v101"\/"((v101"\/"v1)"/\"(v2"\/"v101))) =
    (((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101)"\/"((v101"\/"v1)"/\"(v2"\/"v101))
proof let v2,v1,v101;
  ((v101"\/"v1)"/\"(v2"\/"v101))"/\"v101 = v101 by A4;
  hence thesis by A138;
end;

A168: for v2,v1,v0 holds
 ((v0"\/"v1)"/\"(v2"\/"v0))"/\"(v0"\/"((v0"\/"v1)"/\"(v2"\/"v0))) =
    v0"\/"((v0"\/"v1)"/\"(v2"\/"v0))
proof let v2,v1,v0;
  ((v0"\/"v1)"/\"(v2"\/"v0))"/\"v0 = v0 by A4;
  hence thesis by A165;
end;

A171: for v1,v100 holds ((v100"/\"v1)"\/"v100)"/\"v100 = v100
proof let v1,v100;
  v100"/\"((v100"/\"v1)"\/"v100) = (v100"/\"v1)"\/"v100 by A138;
  hence thesis by A118;
end;

A174: for v1,v0 holds (v0"/\"v1)"\/"v0 = v0
proof let v1,v0;
  ((v0"/\"v1)"\/"v0)"/\"v0 = (v0"/\"v1)"\/"v0 by A105;
  hence thesis by A171;
end;

A177: for v1,v2,v0 holds
 (v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
   ((v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2))"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
  (v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2) = v0"/\"v2 by A19;
  hence thesis by A138;
end;

A179: for v1,v2,v0 holds
 (v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
   (v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
  (v0"/\"(v1"\/"(v0"/\"v2)))"/\"(v0"/\"v2) = v0"/\"v2 by A19;
  hence thesis by A177;
end;

A181: for v2,v1,v0 holds
 v0"\/"((v0"/\"(v2"\/"((v0"/\"v1)"\/"v0)))"/\"((v0"/\"(v2"\/"
   ((v0"/\"v1)"\/"v0)))"\/"((v0"/\"v1)"\/"v0))) =
      v0"/\"(v2"\/"((v0"/\"v1)"\/"v0))
proof let v2,v1,v0;
  (v0"/\"v1)"\/"v0 = v0 by A174;
  hence thesis by A162;
end;

A184: for v1,v2,v0 holds
 v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"((v0"/\"v2)"\/"v0)))"\/"
  ((v0"/\"v2)"\/"v0))) = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
  (v0"/\"v2)"\/"v0 = v0 by A174;
  hence thesis by A181;
end;

A186: for v2,v0,v1 holds
 v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"v0))"\/"((v0"/\"v2)"\/"v0))) =
   v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v2,v0,v1;
  (v0"/\"v2)"\/"v0 = v0 by A174;
  hence thesis by A184;
end;

A188: for v1,v2,v0 holds
 v0"\/"((v0"/\"(v1"\/"v0))"/\"((v0"/\"(v1"\/"v0))"\/"v0)) =
    v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
  (v0"/\"v2)"\/"v0 = v0 by A174;
  hence thesis by A186;
end;

A190: for v1,v2,v0 holds
 v0"\/"((v0"/\"(v1"\/"v0))"/\"v0) = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
  (v0"/\"(v1"\/"v0))"\/"v0 = v0 by A174;
  hence thesis by A188;
end;

A192: for v1,v2,v0 holds v0"\/"v0 = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
  (v0"/\"(v1"\/"v0))"/\"v0 = v0 by A118;
  hence thesis by A190;
end;

A194: for v1,v2,v0 holds v0 = v0"/\"(v1"\/"((v0"/\"v2)"\/"v0))
proof let v1,v2,v0;
  v0"\/"v0 = v0 by A98;
  hence thesis by A192;
end;

A196: for v0,v1 holds v0 = v0"/\"(v1"\/"v0)
proof
  now let v1,v2,v0;
    (v0"/\"v2)"\/"v0 = v0 by A174;
    hence v0 = v0"/\"(v1"\/"v0) by A194;
  end;
  hence thesis;
end;

A199: for v1,v2,v0 holds
 v0"/\"(v1"\/"(v0"/\"v2)) = (v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))
proof let v1,v2,v0;
  (v0"/\"(v1"\/"(v0"/\"v2)))"/\"((v0"/\"v2)"\/"(v0"/\"(v1"\/"(v0"/\"v2)))) =
    v0"/\"(v1"\/"(v0"/\"v2)) by A196;
  hence thesis by A179;
end;

A203: for v2,v1,v0 holds
 (v0"\/"v1)"/\"(v2"\/"v0) = v0"\/"((v0"\/"v1)"/\"(v2"\/"v0))
proof let v2,v1,v0;
  ((v0"\/"v1)"/\"(v2"\/"v0))"/\"(v0"\/"((v0"\/"v1)"/\"(v2"\/"v0))) =
    (v0"\/"v1)"/\"(v2"\/"v0) by A196;
  hence thesis by A168;
end;

A206: for v1,v0 holds v0"/\"(v0"\/"(v0"/\"v1)) = v0
proof let v1,v0;
  (v0"/\"v1)"\/"(v0"/\"(v0"\/"(v0"/\"v1))) = v0"/\"(v0"\/"(v0"/\"v1)) by A199;
  hence thesis by A145;
end;

A208: for v1,v0 holds (v0"\/"v1)"/\"((v0"\/"v1)"\/"v0) = v0"\/"v1
proof let v1,v0;
  v0"\/"((v0"\/"v1)"/\"((v0"\/"v1)"\/"v0)) =
    (v0"\/"v1)"/\"((v0"\/"v1)"\/"v0) by A203;
  hence thesis by A122;
end;

A210: for v1,v0 holds ((v0"/\"v1)"/\"v0)"\/"((v0"/\"v1)"/\"v0) = v0"/\"v1
proof let v1,v0;
  v0"/\"(v0"\/"(v0"/\"v1)) = v0 by A206;
  hence thesis by A154;
end;

A212: for v1,v0 holds (v0"/\"v1)"/\"v0 = v0"/\"v1
proof let v1,v0;
  ((v0"/\"v1)"/\"v0)"\/"((v0"/\"v1)"/\"v0) = (v0"/\"v1)"/\"v0 by A98;
  hence thesis by A210;
end;

A214: for v1,v0 holds (v0"/\"(v0"\/"v1))"\/"(v0"/\"(v0"\/"v1)) = v0
proof let v1,v0;
  (v0"\/"v1)"/\"((v0"\/"v1)"\/"v0) = v0"\/"v1 by A208;
  hence thesis by A135;
end;

A216: for v1,v0 holds v0"/\"(v0"\/"v1) = v0
proof let v1,v0;
  (v0"/\"(v0"\/"v1))"\/"(v0"/\"(v0"\/"v1)) = v0"/\"(v0"\/"v1) by A98;
  hence thesis by A214;
end;

A219: for v101,v102,v1 holds
 ((v1"\/"v102)"/\"(v101"\/"v102))"/\"(v102"/\"(v1"\/"v102)) =
    v102"/\"(v1"\/"v102)
proof let v101,v102,v1;
  v102"/\"(v1"\/"v102) = v102 by A196;
  hence thesis by A27;
end;

A222: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1"/\"(v0"\/"v1)
proof let v2,v1,v0;
  v1"/\"(v0"\/"v1) = v1 by A196;
  hence thesis by A219;
end;

A224: for v2,v1,v0 holds ((v0"\/"v1)"/\"(v2"\/"v1))"/\"v1 = v1
proof let v2,v1,v0;
  v1"/\"(v0"\/"v1) = v1 by A196;
  hence thesis by A222;
end;

A227: for v1,v101 holds (v101"\/"v1)"\/"v101 = v101"\/"v1
proof let v1,v101;
  v101"/\"(v101"\/"v1) = v101 by A216;
  hence thesis by A101;
end;

A231: for v1,v100 holds v100"\/"(v100"/\"v1) = v100
proof let v1,v100;
  (v100"/\"v1)"/\"v100 = v100"/\"v1 by A212;
  hence thesis by A101;
end;

A239: for v1,v101,v100 holds ((v100"\/"v101)"/\"(v101"\/"v1))"/\"v101 = v101
proof let v1,v101,v100;
  (v101"\/"v1)"\/"v101 = v101"\/"v1 by A227;
  hence thesis by A224;
end;

A249: for v1,v0 holds v0"/\"v1 = v1"/\"v0 by A1,A2,A3,A4,A5,Lemma3;

A251: for v2,v1,v0 holds v1"/\"((v0"\/"v1)"/\"(v1"\/"v2)) = v1
proof let v2,v1,v0;
  ((v0"\/"v1)"/\"(v1"\/"v2))"/\"v1 = v1"/\"((v0"\/"v1)"/\"(v1"\/"v2)) by A249;
  hence thesis by A239;
end;

A255: for v103,v100 holds
 (v100"\/"v103)"\/"((v100"\/"v103)"/\"(v103"\/"v100)) =
    (v100"\/"v103)"/\"(v103"\/"v100)
proof let v103,v100;
  v103"/\"((v100"\/"v103)"/\"(v103"\/"v100)) = v103 by A251;
  hence thesis by A35;
end;

A258: for v1,v0 holds v0"\/"v1 = (v0"\/"v1)"/\"(v1"\/"v0)
proof let v1,v0;
  (v0"\/"v1)"\/"((v0"\/"v1)"/\"(v1"\/"v0)) = v0"\/"v1 by A231;
  hence thesis by A255;
end;

A262: for v0,v1 holds (v1"\/"v0)"\/"(v0"\/"v1) = v1"\/"v0
proof let v0,v1;
  (v0"\/"v1)"/\"(v1"\/"v0) = v0"\/"v1 by A258;
  hence thesis by A101;
end;

A266: for v1,v0 holds (v0"\/"v1)"\/"(v1"\/"v0) = v1"\/"v0
proof let v1,v0;
  (v0"\/"v1)"/\"(v1"\/"v0) = v0"\/"v1 by A258;
  hence thesis by A141;
end;

for v1,v0 holds v0"\/"v1 = v1"\/"v0
proof let v1,v0;
  (v0"\/"v1)"\/"(v1"\/"v0) = v0"\/"v1 by A262;
  hence thesis by A266;
end;
hence thesis by A6;
end;
