
theorem
  for f1,f2 being Function st f1 c= f2 for g1 being rng-retract of f1 ex
  g2 being rng-retract of f2 st g1 c= g2
proof
  let f1,f2 be Function such that
A1: f1 c= f2;
A2: f2+*f1 = f2 by A1,FUNCT_4:98;
  set g = the rng-retract of f2;
  let g1 be rng-retract of f1;
  f1 tolerates f2 by A1,PARTFUN1:52;
  then reconsider g2 = g+*g1 as rng-retract of f2 by A2,Th27;
  take g2;
  thus thesis by FUNCT_4:25;
end;
