
theorem Th3:
  for A,B,C being non empty reflexive AltGraph
  for F1,F2 being feasible FunctorStr over A,B
  for G1,G2 being FunctorStr over B,C
  st the FunctorStr of F1 = the FunctorStr of F2 &
  the FunctorStr of G1 = the FunctorStr of G2 holds G1*F1 = G2*F2
proof
  let A,B,C be non empty reflexive AltGraph;
  let F1,F2 be feasible FunctorStr over A,B;
  let G1,G2 be FunctorStr over B,C such that
A1: the FunctorStr of F1 = the FunctorStr of F2 and
A2: the FunctorStr of G1 = the FunctorStr of G2;
A3: the ObjectMap of (G1*F1) = (the ObjectMap of G1)*the ObjectMap of F1 by
FUNCTOR0:def 36;
  the MorphMap of (G1*F1) = ((the MorphMap of G1)*the ObjectMap of F1)**
  the MorphMap of F1 by FUNCTOR0:def 36;
  hence thesis by A1,A2,A3,FUNCTOR0:def 36;
end;
