Definition get_val_equiv s s' : Prop :=
forall k, get_val k s = get_val k s'.

(* Specifications: *)
Lemma poram_lift_change_post {X Y}
(Pre Post Post' : state -> state -> Prop)
{P : X -> Y -> Prop} (m : Poram X) (m' : Poram Y) :
(forall s s', well_formed s -> well_formed s' -> Post s s' -> Post' s s') ->
poram_lift2 Pre Post P m m' ->
poram_lift2 Pre Post' P m m'.
Lemma get_val_equiv_state_equiv : forall s s',
well_formed s -> well_formed s' ->
get_val_equiv s s' ->
state_equiv s s'.
Lemma blk_in_state_imp_kv_rel s k v:
blk_in_state k v s -> kv_rel k v s.
Lemma undef_imp_kv_rel s k :
undef k s -> kv_rel k 0 s.
Lemma state_equiv_get_val_equiv : forall s s',
well_formed s -> well_formed s' ->
state_equiv s s' ->
get_val_equiv s s'.
Lemma read_wf k :
poram_lift
triv
triv
triv
(read k).
Lemma read_pres_state k v k' :
poram_lift
(blk_in_state k v)
(blk_in_state k v)
triv
(read k').
Lemma read_undef k k' :
poram_lift
(undef k)
(undef k)
triv
(read k').
Lemma read_undef_0 k :
poram_lift
(undef k)
triv
(eq 0)
(read k).
Lemma read_pres_kv k v k' :
poram_lift
(kv_rel k v)
(kv_rel k v)
triv
(read k').
Lemma read_state_val k v :
poram_lift
(blk_in_state k v)
triv
(eq v)
(read k).
Lemma read_val k v :
poram_lift
(kv_rel k v)
triv
(eq v)
(read k).
Lemma read_val_kv k v :
poram_lift
(kv_rel k v)
(kv_rel k v)
(eq v)
(read k).
Lemma write_wf k v :
poram_lift
triv
triv
triv
(write k v).
Lemma write_undef k k' v :
k <> k' ->
poram_lift
(undef k')
(undef k')
triv
(write k v).
Lemma state_plift_pre {S X}
(Pre Pre' Post : S -> Prop) (P : X -> Prop) (m : StateT S dist X) :
(forall s, Pre' s -> Pre s) ->
state_plift Pre Post P m ->
state_plift Pre' Post P m.
Lemma write_state_val_eq k v :
poram_lift
triv
(blk_in_state k v)
triv
(write k v).
Lemma write_val_eq k v :
poram_lift
triv
(kv_rel k v)
triv
(write k v).
Lemma write_state_val_neq k v k' v' :
k <> k' ->
poram_lift
(blk_in_state k' v')
(blk_in_state k' v')
triv
(write k v).
Lemma write_val_neq k v k' v' :
k <> k' ->
poram_lift
(kv_rel k' v')
(kv_rel k' v')
triv
(write k v).