proposition: Lemma dimv_sum_cap U V : (\dim (U + V) + \dim (U :&: V) = \dim U + \dim V)%N.
proof: Proof. by rewrite /dimv !mxrank_gen mxrank_sum_cap. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)