proposition: Lemma OT_prod2_pr2 a b: order a -> order b -> OT_prod2 (order_type_of a) (order_type_of b) = order_type_of (order_prod2 a b).
proof: Proof. move => oa ob; symmetry. rewrite /OT_prod2 OT_prop4 // OT_prop4 //; apply: order_type_unique. by apply: orprod_invariant4; apply: order_type_exists. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype)