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