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

theorem Th53: :: Lemma 8
  \delta (\beta x, x) = -(x _1 + x _3)
proof
  thus -(x _1 + x _3) = \delta (-(x _1 + x _3) + (x + -(x _3)), \delta (x + -(
  x _3), -(x _1 + x _3))) by Th36
    .= \delta (\beta x, \delta (x + -(x _3), -(x _1 + x _3))) by LATTICES:def 5
    .= \delta (\beta x, \delta (x _1 + x _3, \delta (x _3, x))) by Th47
    .= \delta (\beta x, \delta (x _1 + x _3, x _0)) by Th48
    .= \delta (\beta x, x) by Th51;
end;
