proposition: Lemma poly_mulm1 : right_id 1%:MP mpoly_mul.
proof: Proof. move=> p; apply/mpoly_eqP/esym; rewrite /mpoly_mul /=. rewrite msupp1 big_allpairs exchange_big big_seq1 {1}[p]freeg_mpoly /=. by apply: eq_bigr=> i _; rewrite mpolyCK !simpm. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype tuple finfun bigop finset binomial) mathcomp(order fingroup perm ssralg zmodp poly ssrint) mathcomp(matrix vector) mathcomp(bigenough) ssrcomplements freeg