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 Th214:
  a///A = {a/c: c in A}
proof
  thus a///A c= {a/c: c in A}
  proof
    let e be object;
    assume e in a///A;
    then consider c1,c2 such that
A1: e = c1*c2 and
A2: c1 in {a} & c2 in A"";
A3: c1*c2 = c1/(c2");
    c2" in A & c1 = a by A2,Th29,TARSKI:def 1;
    hence thesis by A1,A3;
  end;
  let e be object;
  assume e in {a/c: c in A};
  then ex c st e = a/c & c in A;
  hence thesis by Th213;
end;
