proposition: Lemma dimv_add_leqif U V : \dim (U + V) <= \dim U + \dim V ?= iff (U :&: V <= 0)%VS.
proof: Proof. by rewrite /dimv /subV !mxrank_gen vs2mx0 genmxE; apply: mxrank_adds_leqif. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)