proposition: Lemma dim_cosetv_unit V u : u \is a GRing.unit -> \dim (V * <[u]>) = \dim V.
proof: Proof. by move/lker0_amulr/eqP=> Uu; rewrite -limg_amulr limg_dim_eq // Uu capv0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype div tuple finfun bigop ssralg) mathcomp(finalg zmodp matrix vector poly)