proposition: Lemma eq_in_limg V f g : {in V, f =1 g} -> (f @: V = g @: V)%VS.
proof: Proof. move=> eq_fg; apply/vspaceP=> y. by apply/memv_imgP/memv_imgP=> [][x Vx ->]; exists x; rewrite ?eq_fg. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)