no actual use of the End(vT)    *)
(* algebra structure). Also note that theQed.

Prenex Implicits comp_lfunA comp_lfun1l comp_lfun1r comp_lfunDl comp_lfunDr.Definition lfun_comp_ringMixin :=RingMixin comp_lfunA comp_lfun1l comp_lfun1r comp_lfunDl comp_lfunDr
            lfun1_neq0.
Definition lfun_comp_ringType := RingType 'End(vT) lfun_comp_ringMixin.(* In the standard endomorphism ring product is categorical composition.Section Projection.Implicit Types U V : {vspace vT}.

(* Specifications: *)
Lemma projv_id U u : u \in U -> projv U u = u.
by rewrite addrC addKr memv_pi.
by exists (projv U u); rewrite ?projv_id ?memv
by apply/subvP=> v; rewrite memv_ker -{2}[v]subr0 => /eqP <-; apply: m
Lemma addv_pi2_id U V v : v \in V -> addv_pi2 U V v = v.