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 Th81:
  F c= G & H c= I implies F**H c= G**I
proof
  assume
A1: F c= G & H c= I;
  let i;
  assume i in F**H;
  then ex w,w1 st i = w*w1 & w in F & w1 in H;
  hence thesis by A1;
end;
