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

Theorem write_commute : forall k1 k2 v1 v2,
k1 <> k2 ->
poram_equiv
eq
(write k1 v1;; write k2 v2)
(write k2 v2;; write k1 v1).