reserve X for set;

theorem Th1:
  for G1,G2 being Group
  for H being Subgroup of G1
  for f being Homomorphism of G1,G2
  for h being Element of G1
  st h in H
  holds (f|H).h = f.h
proof
  let G1,G2 be Group;
  let H be Subgroup of G1;
  let f be Homomorphism of G1,G2;
  let h be Element of G1;
  assume h in H;
  then (f|(the carrier of H)).h = f.h by FUNCT_1:49;
  hence (f|H).h = f.h by GRSOLV_1:def 2;
end;
