proposition: Fact intro_unit (x y : R) : y * x = 1 -> x != 0.
proof: Proof. move=> yx1; apply: contraNneq (@oner_neq0 R) => x0. by rewrite -yx1 x0 mulr0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)