
theorem
  for f being one-to-one Function, X being set
  holds (f|X)" = X|`(f") & (X|`f)" = (f")|X
proof
  let f be one-to-one Function, X be set;
  f|X is one-to-one & X|`f is one-to-one by FUNCT_1:52, FUNCT_1:58;
  then f" = (f qua Relation)~ & (f|X)" = ((f|X) qua Relation)~ &
    (X|`f)" = ((X|`f) qua Relation)~ by FUNCT_1:def 5;
  hence thesis by Th2;
end;
