
theorem
  for S, T, X, Y being non empty TopSpace st the TopStruct of S = the
  TopStruct of T & the TopStruct of X = the TopStruct of Y & S is_Retract_of X
  holds T is_Retract_of Y
proof
  let S, T, X, Y be non empty TopSpace such that
A1: the TopStruct of S = the TopStruct of T and
A2: the TopStruct of X = the TopStruct of Y;
  given c being continuous Function of S, X, r being continuous Function of X,
  S such that
A3: r * c = id S;
  reconsider rr = r as continuous Function of Y, T by A1,A2,YELLOW12:36;
  reconsider cc = c as continuous Function of T, Y by A1,A2,YELLOW12:36;
  take cc, rr;
  thus thesis by A1,A3;
end;
