Definition dummy {X Y} (P : X -> Prop) (Q : Y -> Prop) : X -> Y -> Prop :=
  fun x y => P x /\ Q y.

Lemma poram_lift2_kv_stable {X Y} (m : Poram X) (m' : Poram Y) : kv_stable m -> kv_stable m' -> poram_lift2 state_equiv state_equiv triv2 m m'.