reserve i for object;
reserve S for non empty ManySortedSign;
reserve D for non empty set,
  n for Nat;

theorem Th2:
  for C being set, A,B being non empty set, F being PartFunc of C,A
  , G being Function of A,B holds G*F is Function of dom F,B
proof
  let C be set;
  let A,B be non empty set;
  let F be PartFunc of C,A;
  let G be Function of A,B;
  dom G = A by FUNCT_2:def 1;
  then rng F c= dom G by RELAT_1:def 19;
  then
A1: dom(G*F) = dom F by RELAT_1:27;
  rng(G*F) c= B by RELAT_1:def 19;
  hence thesis by A1,FUNCT_2:def 1,RELSET_1:4;
end;
