theorem
  h is one-to-one & c in Image h implies h.(h".c) = c
proof
  reconsider h9 = h as Function of G,Image h by Th49;
  assume that
A1: h is one-to-one and
A2: c in Image h;
A3: rng h9 = the carrier of Image h by Th44;
  c in the carrier of Image h by A2;
  hence thesis by A1,A3,FUNCT_1:35;
end;
