Notation fun_of_perm := PermDef.fun_of_perm.Notation "@ 'perm'" := (@PermDef.perm) (at level 10, format "@ 'perm'").Notation perm := (@PermDef.perm _ _).Canonical fun_of_perm_unlock := Unlockable PermDef.fun_of_permE.Canonical perm_unlock := Unlockable PermDef.permE.Implicit Types (x y : T) (s t : {perm T}) (S : {set T}).

(* Specifications: *)
Lemma permP s t : s =1 t <-> s = t.
Lemma pvalE s : pval s = s :> (T -> T).
Lemma permE f f_inj : @perm T f f_inj =1 f.
Lemma perm_inj {s} : injective s.
Lemma perm_onto s : codom s =i predT.