proposition: Lemma lker_proj U : lker (projv U) = (U^C)%VS.
proof: Proof. apply/eqP; rewrite eqEdim andbC; apply/andP; split. by rewrite dimv_compl -(limg_ker_dim (projv U) fullv) limg_proj addnK capfv. by apply/subvP=> v; rewrite memv_ker -{2}[v]subr0 => /eqP <-; apply: memv_projC. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop finfun tuple) mathcomp(ssralg matrix mxalgebra zmodp)