(** * Soundness of operations over value numberings *)

Remark wf_equation_incr:
  forall next1 next2 e,
  wf_equation next1 e -> Ple next1 next2 -> wf_equation next2 e.(** Extensionality with respect to valuations. *)

Definition valu_agree (valu1 valu2: valuation) (upto: valnum) :=
  forall v, Plt v upto -> valu2 v = valu1 v.

Lemma valnums_val_exten: forall vl, (forall v, In v vl -> Plt v upto) -> map valu2 vl = map valu1 vl.