(** ** Merging two sorted lists *)

   Inductive merge_lem (l1 l2:list A) : Type :=
    merge_exist :
    forall l:list A,
      Sorted leA l ->
      meq (list_contents _ eqA_dec l)
      (munion (list_contents _ eqA_dec l1) (list_contents _ eqA_dec l2)) ->
      (forall a, HdRel leA a l1 -> HdRel leA a l2 -> HdRel leA a l) ->
      merge_lem l1 l2.(** ** Merging two sorted lists *)

   Inductive merge_lem (l1 l2:list A) : Type :=
    merge_exist :
    forall l:list A,
      Sorted leA l ->
      meq (list_contents _ eqA_dec l)
      (munion (list_contents _ eqA_dec l1) (list_contents _ eqA_dec l2)) ->
      (forall a, HdRel leA a l1 -> HdRel leA a l2 -> HdRel leA a l) ->
      merge_lem l1 l2.Instance: Proper (@meq A ++> @meq _ ++> @meq _) (@munion A).

#[deprecated(since="8.3", note="Use mergesort.v")] Lemma merge : forall l1:list A, Sorted leA l1 -> forall l2:list A, Sorted leA l2 -> merge_lem l1 l2.