Definition prod_ordMixin := OrdMixin irr_lex trans_lex total_lex.Canonical Structure prod_ordType := Eval hnf in OrdType (K * T) prod_ordMixin.Definition ordf : rel T :=
  fun x y => index x (enum T) < index y (enum T).

(* Specifications: *)
Lemma irr_ordf : irreflexive ordf.
Lemma trans_ordf : transitive ordf.