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 Th86:
  {f}**{g} = {f*g}
proof
  let i;
  hereby
    assume i in {f}**{g};
    then consider w1,w2 such that
A1: i = w1*w2 and
A2: w1 in {f} & w2 in {g};
    w1 = f & w2 = g by A2,TARSKI:def 1;
    hence i in {f*g} by A1,TARSKI:def 1;
  end;
A3: f in {f} & g in {g} by TARSKI:def 1;
  assume i in {f*g};
  then
A4: i = f*g by TARSKI:def 1;
  f in ExtREAL & g in ExtREAL by XXREAL_0:def 1;
  hence thesis by A4,A3;
end;
