theorem Th227:
  A///a = {c/a: c in A}
proof
  thus A///a c= {c/a: c in A}
  proof
    let e be object;
    assume e in A///a;
    then consider c1,c2 such that
A1: e = c1*c2 & c1 in A and
A2: c2 in {a}"";
    {a}"" = {a"} by Th37;
    then c1*c2 = c1/(c2") & c2 = a" by A2,TARSKI:def 1;
    hence thesis by A1;
  end;
  let e be object;
  assume e in {c/a: c in A};
  then ex c st e = c/a & c in A;
  hence thesis by Th226;
end;
