reserve w, w1, w2 for Element of ExtREAL;
reserve c, c1, c2 for Complex;
reserve A, B, C, D for complex-membered set;
reserve F, G, H, I for ext-real-membered set;
reserve a, b, s, t, z for Complex;
reserve f, g, h, i, j for ExtReal;
reserve r for Real;
reserve e for set;

theorem
  (A\+\B) -- a = (A--a) \+\ (B--a)
proof
  thus (A\+\B) -- a = --(a--(A\+\B)) by Th71
    .= --((a--A) \+\ (a--B)) by Th167
    .= (--(a--A)) \+\ (--(a--B)) by Th18
    .= (--(a--A)) \+\ (B--a) by Th71
    .= (A--a) \+\ (B--a) by Th71;
end;
