(** * 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 numbering_holds_exten: forall n, numbering_holds valu1 ge sp rs m n -> Ple n.(num_next) upto -> numbering_holds valu2 ge sp rs m n.