proposition: Lemma has_algid1 U : 1 \in U -> has_algid U.
proof: Proof. move=> U1; apply/has_algidP; exists 1; split; rewrite ?oner_eq0 // => u _. by rewrite mulr1 mul1r. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype div tuple finfun bigop ssralg) mathcomp(finalg zmodp matrix vector poly)