Section EXTEN.
Variable valu1: valuation.
Variable upto: valnum.
Variable valu2: valuation.
Hypothesis AGREE: valu_agree valu1 valu2 upto.
Variable ge: genv.
Variable sp: val.
Variable rs: regset.
Variable m: mem.

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.