
theorem Th25:
  for C1 being non empty AltGraph, C2 being non empty reflexive AltGraph,
  o2 being Object of C2, m be Morphism of o2,o2,
  F being Covariant feasible FunctorStr over C1,C2 st F = C1 --> m
  for o,o9 being Object of C1, f being Morphism of o,o9 st <^o,o9^> <> {}
  holds F.f = m
proof
  let C1 be non empty AltGraph, C2 be non empty reflexive AltGraph,
  o2 be Object of C2;
A1: <^o2,o2^> <> {} by ALTCAT_2:def 7;
  let m be Morphism of o2,o2,
  F be Covariant feasible FunctorStr over C1,C2 such that
A2: F = C1 --> m;
  let o,o9 be Object of C1, f be Morphism of o,o9;
  assume
A3: <^o,o9^> <> {};
  then <^F.o,F.o9^> <> {} by Def18;
  hence F.f = Morph-Map(F,o,o9).f by A3,Def15
    .= m by A1,A2,A3,Th24;
end;
