 reserve L for non empty LattStr;
 reserve v100,v102,v2,v1,v0,v3,v101 for Element of L;

theorem
  (for v0 holds v0"\/"v0 = v0) &
  (for v1,v2,v0 holds v0"/\"(v1"\/"(v0"\/"v2)) = v0) implies
  for v1,v2 holds v1"/\"(v1"\/"v2) = v1
proof
  assume A1: for v0 holds v0"\/"v0 = v0;
  assume A2: for v1,v2,v0 holds v0"/\"(v1"\/"(v0"\/"v2)) = v0;
  for v102,v100 holds v100"/\"(v100"\/"v102) = v100
  proof
    let v102,v100;
    (v100"\/"v102)"\/"(v100"\/"v102) = v100"\/"v102 by A1;
    hence thesis by A2;
  end;
  hence thesis;
end;
