reserve x,y for set;

theorem Th35:
  for A,B being non empty reflexive AltGraph for F being feasible
Contravariant FunctorStr over A,B st F is faithful for a,b being Object of A st
  <^a,b^> <> {} for f,g being Morphism of a,b st F.f = F.g holds f = g
proof
  let A,B be non empty reflexive AltGraph;
  let F be feasible Contravariant FunctorStr over A,B such that
A1: for i being set, f being Function st i in dom the MorphMap of F & (
  the MorphMap of F).i = f holds f is one-to-one;
  let a,b be Object of A such that
A2: <^a,b^> <> {};
  let f,g be Morphism of a,b;
  dom the MorphMap of F = [:the carrier of A, the carrier of A:] & [a,b]
  in [: the carrier of A, the carrier of A:] by PARTFUN1:def 2,ZFMISC_1:def 2;
  then
A3: Morph-Map(F,a,b) is one-to-one by A1;
A4: <^F.b, F.a^> <> {} by A2,FUNCTOR0:def 19;
  then F.f = Morph-Map(F,a,b).f & F.g = Morph-Map(F,a,b).g by A2,
FUNCTOR0:def 16;
  hence thesis by A2,A4,A3,FUNCT_2:19;
end;
