theorem
  for F being Injections_family of b,I, G being Function of I,the
  carrier' of C st doms F = cods G holds F"*"G is Injections_family of b,I
proof
  let F be Injections_family of b,I;
  let G be Function of I,the carrier' of C;
  assume doms F = cods G;
  then cods(F"*"G) = cods F by Th18;
  hence cods(F"*"G) = I --> b by Def16;
end;
