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
  r <> 0 implies r ** (F\+\G) = (r**F) \+\ (r**G)
proof
  assume
A1: r <> 0;
  thus r ** (F \+\ G) = (r**(F\G)) \/ (r**(G\F)) by Th82
    .= ((r**F)\(r**G)) \/ (r**(G\F)) by A1,Th191
    .= (r**F) \+\ (r**G) by A1,Th191;
end;
