Remark in_remove:
  forall (A: Type) (eq: forall (x y: A), {x=y}+{x<>y}) x y l,
  In y (List.remove eq x l) <-> x <> y /\ In y l.

Lemma set_res_unknown_holds: forall valu ge sp rs m n r v, numbering_holds valu ge sp rs m n -> numbering_holds valu ge sp (regmap_setres r v rs) m (set_res_unknown n r).