Commit 532a9ed0 authored by Robbert Krebbers's avatar Robbert Krebbers

Some clean up to Hai's commit.

parent 6f1a23cb
......@@ -187,35 +187,30 @@ Section curry_uncurry.
apply map_eq; intros [i j]. by rewrite lookup_gmap_curry, lookup_gmap_uncurry.
Qed.
Lemma gmap_uncurry_nonempty (m : gmap (K1 * K2) A):
i x, gmap_uncurry m !! i = Some x x .
Lemma gmap_uncurry_non_empty (m : gmap (K1 * K2) A) i x :
gmap_uncurry m !! i = Some x x .
Proof.
apply (map_fold_ind (λ mr m, i x, mr !! i = Some x x )); [done|].
intros [i j] x m12 mr Hij IH i' x'.
destruct (decide (i = i')) as [->|];
[rewrite lookup_partial_alter
|rewrite lookup_partial_alter_ne; [apply IH|done]].
inversion 1. apply insert_non_empty.
intros Hm ->. revert m Hm.
apply (map_fold_ind (λ mr _, mr !! i = Some False)); [done|].
intros [i' j] x m mr ??. destruct (decide (i = i')) as [->|].
- rewrite lookup_partial_alter. intros [= []%insert_non_empty].
- by rewrite lookup_partial_alter_ne by done.
Qed.
Lemma gmap_uncurry_curry_nonempty (m : gmap K1 (gmap K2 A))
(NE: i x, m !! i = Some x x ) :
Lemma gmap_uncurry_curry_non_empty (m : gmap K1 (gmap K2 A)) :
( i x, m !! i = Some x x )
gmap_uncurry (gmap_curry m) = m.
Proof.
apply map_eq; intros i. destruct (m !! i) as [x'|] eqn:Eqx'.
- destruct (gmap_uncurry (gmap_curry m) !! i) as [x2|] eqn:Eq2.
intros Hne. apply map_eq; intros i. destruct (m !! i) as [m2|] eqn:Hm.
- destruct (gmap_uncurry (gmap_curry m) !! i) as [m2'|] eqn:Hcurry.
+ f_equal. apply map_eq. intros j.
assert (Eq3: x' !! j = (m !! i : option (gmap _ _)) = (!! j)).
{ by rewrite Eqx'. }
assert (Eq4: x2 !! j = (
gmap_uncurry (gmap_curry m) !! i : option (gmap _ _)) = (!! j)).
{ by rewrite Eq2. }
by rewrite Eq3, <- lookup_gmap_curry, Eq4, lookup_gmap_uncurry.
+ revert Eq2. rewrite lookup_gmap_uncurry_None.
setoid_rewrite lookup_gmap_curry. rewrite Eqx'.
intros Eq2. exfalso. apply (NE _ _ Eqx'), map_eq, Eq2.
- apply lookup_gmap_uncurry_None.
intros j. by rewrite lookup_gmap_curry, Eqx'.
trans ((gmap_uncurry (gmap_curry m) !! i : option (gmap _ _)) = (!! j)).
{ by rewrite Hcurry. }
by rewrite lookup_gmap_uncurry, lookup_gmap_curry, Hm.
+ rewrite lookup_gmap_uncurry_None in Hcurry.
exfalso; apply (Hne i m2), map_eq; [done|intros j].
by rewrite lookup_empty, <-(Hcurry j), lookup_gmap_curry, Hm.
- apply lookup_gmap_uncurry_None; intros j. by rewrite lookup_gmap_curry, Hm.
Qed.
End curry_uncurry.
......
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