theorem
  for f being one-to-one PartFunc of C,D st c in dom f holds c = f"/.(f
  /.c) & c = (f"*f)/.c
proof
  let f be one-to-one PartFunc of C,D;
  assume
A1: c in dom f;
  hence
A2: c = f"/.(f/.c) by Th11;
  f" = f";
  then f/.c in rng f by A1,Th11;
  then f/.c in dom (f") by FUNCT_1:33;
  hence thesis by A1,A2,Th4;
end;
