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 Th101:
  F///G = {w1/w2: w1 in F & w2 in G}
proof
  thus F///G c= {w1/w2: w1 in F & w2 in G}
  proof
    let e be object;
    assume e in F///G;
    then consider w1,w2 such that
A1: e = w1*w2 and
A2: w1 in F and
A3: w2 in G"";
    consider w such that
A4: w2 = w" and
A5: w in G by A3;
    e = w1/w by A1,A4;
    hence thesis by A2,A5;
  end;
  let e be object;
  assume e in {w1/w2: w1 in F & w2 in G};
  then consider w1,w2 such that
A6: e = w1/w2 & w1 in F and
A7: w2 in G;
  w2" in G"" by A7;
  hence thesis by A6;
end;
