
theorem Th23:
  for C1,C2 being Category, F being Functor of C1,C2 for a,b,c
  being Object of C1 holds (Psi F).compsym(a,b,c) = compsym(F.a,F.b,F.c)
proof
  let C1,C2 be Category, F be Functor of C1,C2;
  let a,b,c be Object of C1;
A1: dom Obj F = the carrier of C1 by FUNCT_2:def 1;
  (compsym(a,b,c))`1 = 2 & (compsym(a,b,c))`2 = <*a,b,c*>;
  hence (Psi F).compsym(a,b,c) = [2,(Obj F)*<*a,b,c*>] by Def12
    .= [2,<*(Obj F).a,(Obj F).b,(Obj F).c*>] by A1,FINSEQ_2:126
    .= [2,<*F.a,(Obj F).b,(Obj F).c*>]
    .= [2,<*F.a,F.b,(Obj F).c*>]
    .= compsym(F.a,F.b,F.c);
end;
