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 Th187:
  f**F = {f*w: w in F}
proof
  thus f**F c= {f*w: w in F}
  proof
    let e be object;
    assume e in f**F;
    then consider w1,w2 such that
A1: e = w1*w2 and
A2: w1 in {f} and
A3: w2 in F;
    w1 = f by A2,TARSKI:def 1;
    hence thesis by A1,A3;
  end;
  let e be object;
  assume e in {f*w: w in F};
  then ex w st e = f*w & w in F;
  hence thesis by Th186;
end;
