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 c= B & C c= D implies A**C c= B**D
proof
  assume
A1: A c= B & C c= D;
  let a;
  assume a in A**C;
  then ex c,c1 st a = c*c1 & c in A & c1 in C;
  hence thesis by A1;
end;
