Commit 411de288 authored by Robbert Krebbers's avatar Robbert Krebbers

Now compiles with 8.5 beta 3.

parent a123e160
......@@ -92,7 +92,7 @@ Solve Obligations with naive_solver eauto 2 using (dist_le (A:=B)).
Program Definition iprop_sep {A} (P Q : iProp A) : iProp A :=
{| iprop_holds n x := x1 x2, x ={n}= x1 x2 P n x1 Q n x2 |}.
Next Obligation.
by intros A P Q x y n (x1&x2&?&?&?) Hxy; exists x1 x2; rewrite <-Hxy.
by intros A P Q x y n (x1&x2&?&?&?) Hxy; exists x1, x2; rewrite <-Hxy.
Qed.
Next Obligation.
intros A P Q x y n1 n2 Hxy ?? (x1&x2&Hx&?&?).
......@@ -100,7 +100,7 @@ Next Obligation.
{ rewrite ra_included_spec in Hxy; destruct Hxy as [z Hy].
exists (x2 z); split; eauto using ra_included_l.
apply dist_le with n1; auto. by rewrite (associative op), <-Hx, Hy. }
exists x1 x2'; split_ands; auto.
exists x1, x2'; split_ands; auto.
* apply iprop_weaken with x1 n1; auto.
by apply cmra_valid_op_l with x2'; rewrite <-Hy.
* apply iprop_weaken with x2 n1; auto.
......@@ -194,7 +194,7 @@ Global Instance iprop_sep_ne n :
Proper (dist n ==> dist n ==> dist n) (@iprop_sep A).
Proof.
intros P P' HP Q Q' HQ x n' ? Hx'; split; intros (x1&x2&Hx&?&?);
exists x1 x2; rewrite Hx in Hx'; split_ands; try apply HP; try apply HQ;
exists x1, x2; rewrite Hx in Hx'; split_ands; try apply HP; try apply HQ;
eauto using cmra_valid_op_l, cmra_valid_op_r.
Qed.
Global Instance iprop_wand_ne n :
......@@ -262,27 +262,27 @@ Proof.
intros P x n Hvalid; split.
* intros (x1&x2&Hx&_&?); rewrite Hx in Hvalid |- *.
apply iprop_weaken with x2 n; auto using ra_included_r.
* by intros ?; exists (unit x) x; rewrite ra_unit_l.
* by intros ?; exists (unit x), x; rewrite ra_unit_l.
Qed.
Global Instance iprop_sep_commutative : Commutative () (@iprop_sep A).
Proof.
by intros P Q x n ?; split;
intros (x1&x2&?&?&?); exists x2 x1; rewrite (commutative op).
intros (x1&x2&?&?&?); exists x2, x1; rewrite (commutative op).
Qed.
Global Instance iprop_sep_associative : Associative () (@iprop_sep A).
Proof.
intros P Q R x n ?; split.
* intros (x1&x2&Hx&?&y1&y2&Hy&?&?); exists (x1 y1) y2; split_ands; auto.
* intros (x1&x2&Hx&?&y1&y2&Hy&?&?); exists (x1 y1), y2; split_ands; auto.
+ by rewrite <-(associative op), <-Hy, <-Hx.
+ by exists x1 y1.
* intros (x1&x2&Hx&(y1&y2&Hy&?&?)&?); exists y1 (y2 x2); split_ands; auto.
+ by exists x1, y1.
* intros (x1&x2&Hx&(y1&y2&Hy&?&?)&?); exists y1, (y2 x2); split_ands; auto.
+ by rewrite (associative op), <-Hy, <-Hx.
+ by exists y2 x2.
+ by exists y2, x2.
Qed.
Lemma iprop_wand_intro P Q R : (R P)%I Q R (P - Q)%I.
Proof.
intros HPQ x n ?? x' n' ???; apply HPQ; auto.
exists x x'; split_ands; auto.
exists x, x'; split_ands; auto.
eapply iprop_weaken with x n; eauto using cmra_valid_op_l.
Qed.
Lemma iprop_wand_elim P Q : ((P - Q) P)%I Q.
......@@ -291,21 +291,21 @@ Proof.
Qed.
Lemma iprop_sep_or P Q R : ((P Q) R)%I ((P R) (Q R))%I.
Proof.
split; [by intros (x1&x2&Hx&[?|?]&?); [left|right]; exists x1 x2|].
intros [(x1&x2&Hx&?&?)|(x1&x2&Hx&?&?)]; exists x1 x2; split_ands;
split; [by intros (x1&x2&Hx&[?|?]&?); [left|right]; exists x1, x2|].
intros [(x1&x2&Hx&?&?)|(x1&x2&Hx&?&?)]; exists x1, x2; split_ands;
first [by left | by right | done].
Qed.
Lemma iprop_sep_and P Q R : ((P Q) R)%I ((P R) (Q R))%I.
Proof. by intros x n ? (x1&x2&Hx&[??]&?); split; exists x1 x2. Qed.
Proof. by intros x n ? (x1&x2&Hx&[??]&?); split; exists x1, x2. Qed.
Lemma iprop_sep_exist {B} (P : B iProp A) Q :
(( b, P b) Q)%I ( b, P b Q)%I.
Proof.
split; [by intros (x1&x2&Hx&[b ?]&?); exists b x1 x2|].
intros [b (x1&x2&Hx&?&?)]; exists x1 x2; split_ands; by try exists b.
split; [by intros (x1&x2&Hx&[b ?]&?); exists b, x1, x2|].
intros [b (x1&x2&Hx&?&?)]; exists x1, x2; split_ands; by try exists b.
Qed.
Lemma iprop_sep_forall `(P : B iProp A) Q :
(( b, P b) Q)%I ( b, P b Q)%I.
Proof. by intros x n ? (x1&x2&Hx&?&?); intros b; exists x1 x2. Qed.
Proof. by intros x n ? (x1&x2&Hx&?&?); intros b; exists x1, x2. Qed.
(* Later *)
Global Instance iprop_later_contractive : Contractive (@iprop_later A).
......@@ -345,12 +345,12 @@ Qed.
Lemma iprop_later_sep P Q : ( (P Q))%I ( P Q)%I.
Proof.
intros x n ?; split.
* destruct n as [|n]; simpl; [by exists x x|intros (x1&x2&Hx&?&?)].
* destruct n as [|n]; simpl; [by exists x, x|intros (x1&x2&Hx&?&?)].
destruct (cmra_extend_op x x1 x2 n)
as ([y1 y2]&Hx'&Hy1&Hy2); auto using cmra_valid_S; simpl in *.
exists y1 y2; split; [by rewrite Hx'|by rewrite Hy1, Hy2].
exists y1, y2; split; [by rewrite Hx'|by rewrite Hy1, Hy2].
* destruct n as [|n]; simpl; [done|intros (x1&x2&Hx&?&?)].
exists x1 x2; eauto using (dist_S (A:=A)).
exists x1, x2; eauto using (dist_S (A:=A)).
Qed.
(* Always *)
......@@ -378,7 +378,7 @@ Lemma iprop_always_exist `(P : B → iProp A) : (□ ∃ b, P b)%I ≡ (∃ b,
Proof. done. Qed.
Lemma iprop_always_and_always_box P Q : ( P Q)%I ( P Q)%I.
Proof.
intros x n ? [??]; exists (unit x) x; simpl in *.
intros x n ? [??]; exists (unit x), x; simpl in *.
by rewrite ra_unit_l, ra_unit_idempotent.
Qed.
......
......@@ -656,7 +656,7 @@ Lemma map_choose {A} (m : M A) : m ≠ ∅ → ∃ i x, m !! i = Some x.
Proof.
intros Hemp. destruct (map_to_list m) as [|[i x] l] eqn:Hm.
{ destruct Hemp; eauto using map_to_list_empty_inv. }
exists i x. rewrite <-elem_of_map_to_list, Hm. by left.
exists i, x. rewrite <-elem_of_map_to_list, Hm. by left.
Qed.
(** Properties of the imap function *)
......@@ -777,7 +777,7 @@ Proof.
split; [|intros (i&x&?&?) Hm; specialize (Hm i x); tauto].
rewrite map_Forall_to_list. intros Hm.
apply (not_Forall_Exists _), Exists_exists in Hm.
destruct Hm as ([i x]&?&?). exists i x. by rewrite <-elem_of_map_to_list.
destruct Hm as ([i x]&?&?). exists i, x. by rewrite <-elem_of_map_to_list.
Qed.
End map_Forall.
......
......@@ -85,7 +85,7 @@ Proof.
rewrite elem_of_list_intersection in Hx; naive_solver. }
intros [(l&?&?) (k&?&?)]. assert (x list_intersection l k)
by (by rewrite elem_of_list_intersection).
exists (list_intersection l k); split; [exists l k|]; split_ands; auto.
exists (list_intersection l k); split; [exists l, k|]; split_ands; auto.
by rewrite option_guard_True by eauto using elem_of_not_nil.
* unfold elem_of, hashset_elem_of, intersection, hashset_intersection.
intros [m1 ?] [m2 ?] x; simpl.
......@@ -95,7 +95,7 @@ Proof.
intros [(l&?&?) Hm2]; destruct (m2 !! hash x) as [k|] eqn:?; eauto.
destruct (decide (x k)); [destruct Hm2; eauto|].
assert (x list_difference l k) by (by rewrite elem_of_list_difference).
exists (list_difference l k); split; [right; exists l k|]; split_ands; auto.
exists (list_difference l k); split; [right; exists l,k|]; split_ands; auto.
by rewrite option_guard_True by eauto using elem_of_not_nil.
* unfold elem_of at 2, hashset_elem_of, elements, hashset_elems.
intros [m Hm] x; simpl. setoid_rewrite elem_of_list_bind. split.
......
......@@ -487,8 +487,8 @@ Lemma list_lookup_other l i x :
length l 1 l !! i = Some x j y, j i l !! j = Some y.
Proof.
intros. destruct i, l as [|x0 [|x1 l]]; simplify_equality'.
* by exists 1 x1.
* by exists 0 x0.
* by exists 1, x1.
* by exists 0, x0.
Qed.
Lemma alter_app_l f l1 l2 i :
i < length l1 alter f i (l1 ++ l2) = alter f i l1 ++ l2.
......@@ -604,7 +604,7 @@ Proof. induction 1; rewrite ?elem_of_nil, ?elem_of_cons; intuition. Qed.
Lemma elem_of_list_split l x : x l l1 l2, l = l1 ++ x :: l2.
Proof.
induction 1 as [x l|x y l ? [l1 [l2 ->]]]; [by eexists [], l|].
by exists (y :: l1) l2.
by exists (y :: l1), l2.
Qed.
Lemma elem_of_list_lookup_1 l x : x l i, l !! i = Some x.
Proof.
......@@ -1621,7 +1621,7 @@ Proof.
split.
* intros Hlk. induction k as [|y k IH]; inversion Hlk.
+ eexists [], k. by repeat constructor.
+ destruct IH as (k1&k2&->&?); auto. by exists (y :: k1) k2.
+ destruct IH as (k1&k2&->&?); auto. by exists (y :: k1), k2.
* intros (k1&k2&->&?). by apply sublist_inserts_l, sublist_skip.
Qed.
Lemma sublist_app_r l k1 k2 :
......@@ -1633,9 +1633,9 @@ Proof.
{ eexists [], l. by repeat constructor. }
rewrite sublist_cons_r. intros [?|(l' & ? &?)]; subst.
+ destruct (IH l k2) as (l1&l2&?&?&?); trivial; subst.
exists l1 l2. auto using sublist_cons.
exists l1, l2. auto using sublist_cons.
+ destruct (IH l' k2) as (l1&l2&?&?&?); trivial; subst.
exists (y :: l1) l2. auto using sublist_skip.
exists (y :: l1), l2. auto using sublist_skip.
* intros (?&?&?&?&?); subst. auto using sublist_app.
Qed.
Lemma sublist_app_l l1 l2 k :
......@@ -1647,7 +1647,7 @@ Proof.
{ eexists [], k. by repeat constructor. }
rewrite sublist_cons_l. intros (k1 & k2 &?&?); subst.
destruct (IH l2 k2) as (h1 & h2 &?&?&?); trivial; subst.
exists (k1 ++ x :: h1) h2. rewrite <-(associative_L (++)).
exists (k1 ++ x :: h1), h2. rewrite <-(associative_L (++)).
auto using sublist_inserts_l, sublist_skip.
* intros (?&?&?&?&?); subst. auto using sublist_app.
Qed.
......@@ -1865,7 +1865,7 @@ Proof.
split.
* rewrite contains_sublist_r. intros (l'&E&Hl').
rewrite sublist_app_r in Hl'. destruct Hl' as (l1&l2&?&?&?); subst.
exists l1 l2. eauto using sublist_contains.
exists l1, l2. eauto using sublist_contains.
* intros (?&?&E&?&?). rewrite E. eauto using contains_app.
Qed.
Lemma contains_app_l l1 l2 k :
......@@ -1875,7 +1875,7 @@ Proof.
split.
* rewrite contains_sublist_l. intros (l'&Hl'&E).
rewrite sublist_app_l in Hl'. destruct Hl' as (k1&k2&?&?&?); subst.
exists k1 k2. split. done. eauto using sublist_contains.
exists k1, k2. split. done. eauto using sublist_contains.
* intros (?&?&E&?&?). rewrite E. eauto using contains_app.
Qed.
Lemma contains_app_inv_l l1 l2 k :
......@@ -2578,7 +2578,7 @@ Section fmap.
Proof.
revert l. induction k1 as [|y k1 IH]; simpl; [intros l ?; by eexists [],l|].
intros [|x l] ?; simplify_equality'.
destruct (IH l) as (l1&l2&->&->&->); [done|]. by exists (x :: l1) l2.
destruct (IH l) as (l1&l2&->&->&->); [done|]. by exists (x :: l1), l2.
Qed.
Lemma fmap_length l : length (f <$> l) = length l.
Proof. by induction l; f_equal'. Qed.
......@@ -3006,7 +3006,7 @@ Section zip_with.
{ intros l k ?. by eexists [], [], l, k. }
intros [|x l] [|y k] ?; simplify_equality'.
destruct (IH l k) as (l1&k1&l2&k2&->&->&->&->&?); [done |].
exists (x :: l1) (y :: k1) l2 k2; simpl; auto with congruence.
exists (x :: l1), (y :: k1), l2, k2; simpl; auto with congruence.
Qed.
Lemma zip_with_inj `{!Injective2 (=) (=) (=) f} l1 l2 k1 k2 :
length l1 = length k1 length l2 = length k2
......
......@@ -19,7 +19,7 @@ Lemma natmap_wf_lookup {A} (l : natmap_raw A) :
Proof.
intros Hwf Hl. induction l as [|[x|] l IH]; simpl; [done| |].
{ exists 0. simpl. eauto. }
destruct IH as (i&x&?); eauto using natmap_wf_inv; [|by exists (S i) x].
destruct IH as (i&x&?); eauto using natmap_wf_inv; [|by exists (S i), x].
intros ->. by destruct Hwf.
Qed.
......
......@@ -114,9 +114,9 @@ Proof. by destruct i. Qed.
Lemma Pmap_ne_lookup {A} (t : Pmap_raw A) : Pmap_ne t i x, t !! i = Some x.
Proof.
induction 1 as [? x ?| l r ? IHl | l r ? IHr].
* intros. by exists 1 x.
* destruct IHl as [i [x ?]]. by exists (i~0) x.
* destruct IHr as [i [x ?]]. by exists (i~1) x.
* intros. by exists 1, x.
* destruct IHl as [i [x ?]]. by exists (i~0), x.
* destruct IHr as [i [x ?]]. by exists (i~1), x.
Qed.
Lemma Pmap_wf_eq_get {A} (t1 t2 : Pmap_raw A) :
......
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