(** Succeed iff [x] is in the list [ls], represented with left-associated nested tuples. *)
Ltac inList x ls :=
  match ls with
    | x => idtac
    | (_, x) => idtac
    | (?LS, _) => inList x LS
  end.(** Try calling tactic function [f] on every element of tupled list [ls], keeping the first call not to fail. *)
Ltac app f ls :=
  match ls with
    | (?LS, ?X) => f X || app f LS || fail 1
    | _ => f ls
  end.(** Run [f] on every element of [ls], not just the first that doesn't fail. *)
Ltac all f ls :=
  match ls with
    | (?LS, ?X) => f X; all f LS
    | (_, _) => fail 1
    | _ => f ls
  end.

Lemma sorted_term_index_le : forall l e e', sorted l -> In e l -> In e' l -> eTerm e' < eTerm e -> eIndex e' <= eIndex e.