proposition: Lemma lpreim_cap_limg f W : (f @^-1: (W :&: limg f))%VS = (f @^-1: W)%VS.
proof: Proof. by rewrite /lfun_preim -capvA capvv. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)