reserve C for category,
  o1, o2, o3 for Object of C;

theorem Th16:
  for C1, C2 being non empty AltCatStr for F being Covariant
FunctorStr over C1, C2 for o1, o2 being Object of C1, Fm being Morphism of F.o1
, F.o2 st <^o1,o2^> <> {} & F is full feasible ex m being Morphism of o1, o2 st
  Fm = F.m
proof
  let C1, C2 be non empty AltCatStr, F be Covariant FunctorStr over C1, C2, o1
  , o2 be Object of C1, Fm be Morphism of F.o1, F.o2 such that
A1: <^o1,o2^> <> {};
  assume F is full;
  then Morph-Map(F,o1,o2) is onto by FUNCTOR1:15;
  then
A2: rng Morph-Map(F,o1,o2) = <^F.o1,F.o2^>;
  assume F is feasible;
  then
A3: <^F.o1,F.o2^> <> {} by A1;
  then consider m being object such that
A4: m in dom Morph-Map(F,o1,o2) and
A5: Fm = Morph-Map(F,o1,o2).m by A2,FUNCT_1:def 3;
  reconsider m as Morphism of o1, o2 by A3,A4,FUNCT_2:def 1;
  take m;
  thus thesis by A1,A3,A5,FUNCTOR0:def 15;
end;
