
theorem Th6:
  for S,T being RelStr, R being SubRelStr of S for f being Function
  of the carrier of S, the carrier of T holds f|R = f|the carrier of R & for x
  being set st x in the carrier of R holds (f|R).x = f.x
proof
  let S,T be RelStr, R be SubRelStr of S;
  let f be Function of the carrier of S, the carrier of T;
  the carrier of R c= the carrier of S by YELLOW_0:def 13;
  hence f|R = f|the carrier of R by TMAP_1:def 3;
  hence thesis by FUNCT_1:49;
end;
