proposition: Lemma prod_similar : forall I A1 A2 (F1:family I A1) (F2:family I A2), prod2 (similar F1) (similar F2) = similar (prod_family F1 F2).
proof: Proof. Proof using. intros. unfold prod_family, prod_family_sim, similar. simpl. apply fun_ext_2. intros [x1 x2] [y1 y2]. simpls. apply pred_conj_forall_distrib. Qed.
imports: TLC(LibTactics LibLogic LibReflect LibEpsilon LibInt LibProd LibSum LibOperation LibRelation LibWf LibOrder LibMin)