proposition: Lemma auxbij_inj (p : intpart) : injective (@auxbij p).
proof: Proof. move=> y z /(congr1 val) /= => HRS2. have HRS1 : RS (std y) = RS (std z). apply/eqP; rewrite -plactic_RS. apply: std_plact; rewrite (yam_plactic_shape _ (yamevalP y)). split; first exact: yamevalP. by rewrite !eval_yameval. apply val_inj; apply perm_stdE => /=. - by rewrite perm_evalseq !eval_yameval. - rewrite -[std y]RSmapK -[std z]RSmapK /=. have RSE (x : seq nat) : RSmap x = (RS x, (RSmap x).2). by rewrite -RSmapE; case RSmap. by rewrite [RSmap (std y)]RSE [RSmap (std z)]RSE HRS1 !RSmap_std HRS2. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq fintype) mathcomp(tuple finfun finset path bigop order) tools partition Yamanouchi ordtype std tableau stdtab Schensted congr plactic Greene_inv stdplact