reserve G for Robbins join-associative join-commutative non empty
  ComplLLattStr;
reserve x, y, z, u, v for Element of G;

theorem Th42:
  x _4 + x _0 = x _3 + x _1
proof
  thus x _4 + x _0 = (x _0 + Double x) + Double x + x _0 by LATTICES:def 5
    .= (x _0 + Double x) + x + x + x _0 by LATTICES:def 5
    .= x _3 + x + x _0 by LATTICES:def 5
    .= x _3 + x _1 by LATTICES:def 5;
end;
