Definition triv2 {X Y} : X -> Y -> Prop :=
  fun _ _ => True.Definition pforall {I X} (P : I -> X -> Prop) : X -> Prop :=
  fun x => forall i, P i x.

Lemma kv_rel_functional : forall s, well_formed s -> forall k v v', kv_rel k v s -> kv_rel k v' s -> v = v'.