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

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