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

theorem Th13:
  for A, B being transitive with_units non empty AltCatStr for F
being contravariant Functor of A, B for a being Object of A holds F.idm a = idm
  (F.a)
proof
  let A, B be transitive with_units non empty AltCatStr, F be contravariant
  Functor of A, B;
  let a be Object of A;
  thus F.idm a = Morph-Map(F,a,a).idm a by FUNCTOR0:def 16
    .= idm (F.a) by FUNCTOR0:def 20;
end;
