reserve B,C,D for Category;

theorem
  for S1 being Contravariant_Functor of C,B, S2 being Functor of B,D
  holds S2*S1 is Contravariant_Functor of C,D
proof
  let S1 be Contravariant_Functor of C,B, S2 be Functor of B,D;
  *'S1 is Functor of C opp,B by Th53;
  then S2*(*'S1) is Functor of C opp,D by CAT_1:73;
  then /*(S2*(*'S1)) is Contravariant_Functor of C,D by Th32;
  then S2*(/*(*'S1)) is Contravariant_Functor of C,D by Lm18;
  hence thesis by Th45;
end;
