proposition: Lemma codom_val sT x : (x \in codom (val : sT -> T)) = P x.
proof: Proof. by apply/codomP/idP=> [[u ->]|Px]; last exists (Sub x Px); rewrite ?valP ?SubK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(path div)