
theorem
  for T, S1, S2 being non empty TopStruct st S1, S2 are_homeomorphic &
  S1 is_Retract_of T holds S2 is_Retract_of T
proof
  let T, S1, S2 be non empty TopStruct such that
A1: S1, S2 are_homeomorphic and
A2: S1 is_Retract_of T;
  consider G being Function of S1,S2 such that
A3: G is being_homeomorphism by A1;
  consider H being Function of T,T such that
A4: H is continuous and
A5: H*H = H and
A6: Image H, S1 are_homeomorphic by A2;
  take H;
  consider F being Function of Image H,S1 such that
A7: F is being_homeomorphism by A6;
  G*F is being_homeomorphism by A3,A7,TOPS_2:57;
  hence thesis by A4,A5;
end;
