proposition: Lemma addv_diff_cap U V : (U :\: V + U :&: V)%VS = U.
proof: Proof. apply/vs2mxP; rewrite vs2mxD -genmx_adds !genmxE. exact/eqmxP/addsmx_diff_cap_eq. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)