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

theorem Th52: :: Lemma 7
  \delta (\beta x, x) = -x _3
proof
  thus -x _3 = \delta (\beta x, \delta (-(x _1 + x _3) + x, -(x _3))) by Th36
    .= \delta (\beta x, \delta (x _3, \delta (x _1 + x _3, x))) by Th47
    .= \delta (\beta x, \delta (x _3, x _0)) by Th49
    .= \delta (\beta x, x) by Th45;
end;
