Commit 3013536d authored by Ralf Jung's avatar Ralf Jung

use ssreflect's apply where it saves underscores

parent 4763600e
......@@ -62,7 +62,7 @@ Proof.
Qed.
Global Instance map_timeless `{ a : A, Timeless a} m : Timeless m.
Proof. by intros m' ? i; apply (timeless _). Qed.
Proof. by intros m' ? i; apply: timeless. Qed.
Instance map_empty_timeless : Timeless ( : gmap K A).
Proof.
......@@ -71,7 +71,7 @@ Proof.
Qed.
Global Instance map_lookup_timeless m i : Timeless m Timeless (m !! i).
Proof.
intros ? [x|] Hx; [|by symmetry; apply (timeless _)].
intros ? [x|] Hx; [|by symmetry; apply: timeless].
assert (m {0} <[i:=x]> m)
by (by symmetry in Hx; inversion Hx; cofe_subst; rewrite insert_id).
by rewrite (timeless m (<[i:=x]>m)) // lookup_insert.
......@@ -80,8 +80,8 @@ Global Instance map_insert_timeless m i x :
Timeless x Timeless m Timeless (<[i:=x]>m).
Proof.
intros ?? m' Hm j; destruct (decide (i = j)); simplify_map_eq.
{ by apply (timeless _); rewrite -Hm lookup_insert. }
by apply (timeless _); rewrite -Hm lookup_insert_ne.
{ by apply: timeless; rewrite -Hm lookup_insert. }
by apply: timeless; rewrite -Hm lookup_insert_ne.
Qed.
Global Instance map_singleton_timeless i x :
Timeless x Timeless ({[ i := x ]} : gmap K A) := _.
......
......@@ -49,7 +49,7 @@ Section iprod_cofe.
Definition iprod_lookup_empty x : x = := eq_refl.
Global Instance iprod_empty_timeless :
( x : A, Timeless ( : B x)) Timeless ( : iprod B).
Proof. intros ? f Hf x. by apply (timeless _). Qed.
Proof. intros ? f Hf x. by apply: timeless. Qed.
End empty.
(** Properties of iprod_insert. *)
......@@ -78,7 +78,7 @@ Section iprod_cofe.
intros ? y ?.
cut (f iprod_insert x y f).
{ by move=> /(_ x)->; rewrite iprod_lookup_insert. }
by apply (timeless _)=>x'; destruct (decide (x = x')) as [->|];
by apply: timeless=>x'; destruct (decide (x = x')) as [->|];
rewrite ?iprod_lookup_insert ?iprod_lookup_insert_ne.
Qed.
Global Instance iprod_insert_timeless f x y :
......@@ -86,9 +86,9 @@ Section iprod_cofe.
Proof.
intros ?? g Heq x'; destruct (decide (x = x')) as [->|].
- rewrite iprod_lookup_insert.
apply (timeless _). by rewrite -(Heq x') iprod_lookup_insert.
apply: timeless. by rewrite -(Heq x') iprod_lookup_insert.
- rewrite iprod_lookup_insert_ne //.
apply (timeless _). by rewrite -(Heq x') iprod_lookup_insert_ne.
apply: timeless. by rewrite -(Heq x') iprod_lookup_insert_ne.
Qed.
(** Properties of iprod_singletom. *)
......
......@@ -80,7 +80,7 @@ Proof.
by destruct inG_prf.
Qed.
Lemma own_valid_r γ a : own γ a (own γ a a).
Proof. apply (uPred.always_entails_r _ _), own_valid. Qed.
Proof. apply: uPred.always_entails_r. apply own_valid. Qed.
Lemma own_valid_l γ a : own γ a ( a own γ a).
Proof. by rewrite comm -own_valid_r. Qed.
Global Instance own_timeless γ a : Timeless a TimelessP (own γ a).
......
......@@ -31,7 +31,7 @@ Proof. by intros P P' HP e ? <- Φ Φ' HΦ; apply ht_mono. Qed.
Lemma ht_alt E P Φ e : (P wp E e Φ) {{ P }} e @ E {{ Φ }}.
Proof.
intros; rewrite -{1}always_const. apply (always_intro _ _), impl_intro_l.
intros; rewrite -{1}always_const. apply: always_intro. apply impl_intro_l.
by rewrite always_const right_id.
Qed.
......@@ -43,7 +43,7 @@ Lemma ht_vs E P P' Φ Φ' e :
((P ={E}=> P') {{ P' }} e @ E {{ Φ' }} v, Φ' v ={E}=> Φ v)
{{ P }} e @ E {{ Φ }}.
Proof.
apply (always_intro _ _), impl_intro_l.
apply: always_intro. apply impl_intro_l.
rewrite (assoc _ P) {1}/vs always_elim impl_elim_r.
rewrite assoc pvs_impl_r pvs_always_r wp_always_r.
rewrite -(pvs_wp E e Φ) -(wp_pvs E e Φ); apply pvs_mono, wp_mono=> v.
......@@ -55,7 +55,7 @@ Lemma ht_atomic E1 E2 P P' Φ Φ' e :
((P ={E1,E2}=> P') {{ P' }} e @ E2 {{ Φ' }} v, Φ' v ={E2,E1}=> Φ v)
{{ P }} e @ E1 {{ Φ }}.
Proof.
intros ??; apply (always_intro _ _), impl_intro_l.
intros ??; apply: always_intro. apply impl_intro_l.
rewrite (assoc _ P) {1}/vs always_elim impl_elim_r.
rewrite assoc pvs_impl_r pvs_always_r wp_always_r.
rewrite -(wp_atomic E1 E2) //; apply pvs_mono, wp_mono=> v.
......@@ -66,7 +66,7 @@ Lemma ht_bind `{LanguageCtx Λ K} E P Φ Φ' e :
({{ P }} e @ E {{ Φ }} v, {{ Φ v }} K (of_val v) @ E {{ Φ' }})
{{ P }} K e @ E {{ Φ' }}.
Proof.
intros; apply (always_intro _ _), impl_intro_l.
intros; apply: always_intro. apply impl_intro_l.
rewrite (assoc _ P) {1}/ht always_elim impl_elim_r.
rewrite wp_always_r -wp_bind //; apply wp_mono=> v.
by rewrite (forall_elim v) /ht always_elim impl_elim_r.
......
......@@ -26,7 +26,7 @@ Lemma ht_lift_step E1 E2
{{ Φ2 e2 σ2 ef }} ef ?@ {{ λ _, True }})
{{ P }} e1 @ E2 {{ Ψ }}.
Proof.
intros ?? Hsafe Hstep; apply (always_intro _ _), impl_intro_l.
intros ?? Hsafe Hstep; apply: always_intro. apply impl_intro_l.
rewrite (assoc _ P) {1}/vs always_elim impl_elim_r pvs_always_r.
rewrite -(wp_lift_step E1 E2 φ _ e1 σ1) //; apply pvs_mono.
rewrite always_and_sep_r -assoc; apply sep_mono; first done.
......@@ -62,8 +62,8 @@ Proof.
apply and_intro; [by rewrite -vs_reflexive; apply const_intro|].
apply forall_mono=>e2; apply forall_mono=>σ2; apply forall_mono=>ef.
apply and_intro; [|apply and_intro; [|done]].
- rewrite -vs_impl; apply (always_intro _ _),impl_intro_l; rewrite and_elim_l.
rewrite !assoc; apply sep_mono; last done.
- rewrite -vs_impl; apply: always_intro. apply impl_intro_l.
rewrite and_elim_l !assoc; apply sep_mono; last done.
rewrite -!always_and_sep_l -!always_and_sep_r; apply const_elim_l=>-[??].
by repeat apply and_intro; try apply const_intro.
- apply (always_intro _ _), impl_intro_l; rewrite and_elim_l.
......@@ -82,7 +82,7 @@ Lemma ht_lift_pure_step E (φ : expr Λ → option (expr Λ) → Prop) P P' Ψ e
{{ φ e2 ef P' }} ef ?@ {{ λ _, True }})
{{ (P P') }} e1 @ E {{ Ψ }}.
Proof.
intros ? Hsafe Hstep; apply (always_intro _ _), impl_intro_l.
intros ? Hsafe Hstep; apply: always_intro. apply impl_intro_l.
rewrite -(wp_lift_pure_step E φ _ e1) //.
rewrite (later_intro ( _, _)) -later_and; apply later_mono.
apply forall_intro=>e2; apply forall_intro=>ef; apply impl_intro_l.
......@@ -110,11 +110,11 @@ Proof.
intros ? Hsafe Hdet.
rewrite -(ht_lift_pure_step _ (λ e2' ef', e2 = e2' ef = ef')); eauto.
apply forall_intro=>e2'; apply forall_intro=>ef'; apply and_mono.
- apply (always_intro' _ _), impl_intro_l.
- apply: always_intro. apply impl_intro_l.
rewrite -always_and_sep_l -assoc; apply const_elim_l=>-[??]; subst.
by rewrite /ht always_elim impl_elim_r.
- destruct ef' as [e'|]; simpl; [|by apply const_intro].
apply (always_intro _ _), impl_intro_l.
apply: always_intro. apply impl_intro_l.
rewrite -always_and_sep_l -assoc; apply const_elim_l=>-[??]; subst.
by rewrite /= /ht always_elim impl_elim_r.
Qed.
......
......@@ -40,7 +40,7 @@ Proof. by destruct 1. Qed.
Global Instance pst_ne n : Proper (dist n ==> dist n) (@pst Λ Σ A).
Proof. by destruct 1. Qed.
Global Instance pst_ne' n : Proper (dist n ==> ()) (@pst Λ Σ A).
Proof. destruct 1; apply (timeless _), dist_le with n; auto with lia. Qed.
Proof. destruct 1; apply: timeless; apply dist_le with n; auto with lia. Qed.
Global Instance pst_proper : Proper (() ==> (=)) (@pst Λ Σ A).
Proof. by destruct 1; unfold_leibniz. Qed.
Global Instance gst_ne n : Proper (dist n ==> dist n) (@gst Λ Σ A).
......@@ -69,7 +69,7 @@ Qed.
Canonical Structure resC : cofeT := CofeT res_cofe_mixin.
Global Instance res_timeless r :
Timeless (wld r) Timeless (gst r) Timeless r.
Proof. by destruct 3; constructor; try apply (timeless _). Qed.
Proof. by destruct 3; constructor; try apply: timeless. Qed.
Instance res_op : Op (res Λ Σ A) := λ r1 r2,
Res (wld r1 wld r2) (pst r1 pst r2) (gst r1 gst r2).
......@@ -157,7 +157,7 @@ Lemma lookup_wld_op_r n r1 r2 i P :
{n} (r1r2) wld r2 !! i {n} Some P (wld r1 wld r2) !! i {n} Some P.
Proof. rewrite (comm _ r1) (comm _ (wld r1)); apply lookup_wld_op_l. Qed.
Global Instance Res_timeless eσ m : Timeless m Timeless (Res eσ m).
Proof. by intros ? ? [???]; constructor; apply (timeless _). Qed.
Proof. by intros ? ? [???]; constructor; apply: timeless. Qed.
(** Internalized properties *)
Lemma res_equivI {M} r1 r2 :
......
......@@ -24,7 +24,7 @@ Implicit Types N : namespace.
Lemma vs_alt E1 E2 P Q : (P pvs E1 E2 Q) P ={E1,E2}=> Q.
Proof.
intros; rewrite -{1}always_const. apply (always_intro _ _), impl_intro_l.
intros; rewrite -{1}always_const. apply: always_intro. apply impl_intro_l.
by rewrite always_const right_id.
Qed.
......@@ -51,7 +51,7 @@ Proof. by intros ?; apply vs_alt, pvs_timeless. Qed.
Lemma vs_transitive E1 E2 E3 P Q R :
E2 E1 E3 ((P ={E1,E2}=> Q) (Q ={E2,E3}=> R)) (P ={E1,E3}=> R).
Proof.
intros; rewrite -always_and; apply (always_intro _ _), impl_intro_l.
intros; rewrite -always_and; apply: always_intro. apply impl_intro_l.
rewrite always_and assoc (always_elim (P _)) impl_elim_r.
by rewrite pvs_impl_r; apply pvs_trans.
Qed.
......@@ -91,7 +91,7 @@ Lemma vs_open_close N E P Q R :
nclose N E
(inv N R ( R P ={E nclose N}=> R Q)) (P ={E}=> Q).
Proof.
intros; apply (always_intro _ _), impl_intro_l.
intros; apply: always_intro. apply impl_intro_l.
rewrite always_and_sep_r assoc [(P _)%I]comm -assoc.
eapply pvs_open_close; [by eauto with I..|].
rewrite sep_elim_r. apply wand_intro_l.
......
Markdown is supported
0%
or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment