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 <> 0 implies (A\B) /// a = (A///a) \ (B///a)
proof
  assume
A1: a <> 0;
A2: {a}"" = {a"} by Th37;
  thus (A\B)///a = a"**(A\B) by Th37
    .= (a"**A)\(a"**B) by A1,Th199
    .= (A///a) \ (B///a) by A2;
end;
