proposition: Lemma mem_sfilterleqK n v i : i \in (sfilterleq n v) = (i + n \in v).
proof: Proof. rewrite /=; elim: v => [// | v0 v IHv] /=. case: leqP => H /=; rewrite !inE IHv. - by congr (_ || _); rewrite -{2}(subnK H) eqn_add2r. - suff -> : (i + n == v0) = false by []. by apply: gtn_eqF; exact: ltn_addl. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype finfun fintype choice) mathcomp(order seq tuple finset perm binomial bigop) tools vectNK subseq partition Yamanouchi ordtype std tableau stdtab Schensted plactic Greene_inv stdplact