Commit c59e1f85 by Robbert Krebbers

### More solve_propers.

parent 9589d1ba
 ... @@ -42,7 +42,7 @@ Section auth. ... @@ -42,7 +42,7 @@ Section auth. Global Instance auth_own_ne n γ : Proper (dist n ==> dist n) (auth_own γ). Global Instance auth_own_ne n γ : Proper (dist n ==> dist n) (auth_own γ). Proof. rewrite auth_own_eq; solve_proper. Qed. Proof. rewrite auth_own_eq; solve_proper. Qed. Global Instance auth_own_proper γ : Proper ((≡) ==> (≡)) (auth_own γ). Global Instance auth_own_proper γ : Proper ((≡) ==> (≡)) (auth_own γ). Proof. by rewrite auth_own_eq /auth_own_def=> a b ->. Qed. Proof. by rewrite auth_own_eq; solve_proper. Qed. Global Instance auth_own_timeless γ a : TimelessP (auth_own γ a). Global Instance auth_own_timeless γ a : TimelessP (auth_own γ a). Proof. rewrite auth_own_eq. apply _. Qed. Proof. rewrite auth_own_eq. apply _. Qed. ... ...
 ... @@ -64,7 +64,7 @@ Qed. ... @@ -64,7 +64,7 @@ Qed. (** * Properties of own *) (** * Properties of own *) Global Instance own_ne γ n : Proper (dist n ==> dist n) (own γ). Global Instance own_ne γ n : Proper (dist n ==> dist n) (own γ). Proof. by intros m m' Hm; rewrite /own Hm. Qed. Proof. solve_proper. Qed. Global Instance own_proper γ : Proper ((≡) ==> (≡)) (own γ) := ne_proper _. Global Instance own_proper γ : Proper ((≡) ==> (≡)) (own γ) := ne_proper _. Lemma own_op γ a1 a2 : own γ (a1 ⋅ a2) ≡ (own γ a1 ★ own γ a2)%I. Lemma own_op γ a1 a2 : own γ (a1 ⋅ a2) ≡ (own γ a1 ★ own γ a2)%I. ... ...
 ... @@ -30,13 +30,13 @@ Global Instance ht_ne E n : ... @@ -30,13 +30,13 @@ Global Instance ht_ne E n : Proof. solve_proper. Qed. Proof. solve_proper. Qed. Global Instance ht_proper E : Global Instance ht_proper E : Proper ((≡) ==> eq ==> pointwise_relation _ (≡) ==> (≡)) (@ht Λ Σ E). Proper ((≡) ==> eq ==> pointwise_relation _ (≡) ==> (≡)) (@ht Λ Σ E). Proof. by intros P P' HP e ? <- Φ Φ' HΦ; rewrite /ht HP; setoid_rewrite HΦ. Qed. Proof. solve_proper. Qed. Lemma ht_mono E P P' Φ Φ' e : Lemma ht_mono E P P' Φ Φ' e : P ⊑ P' → (∀ v, Φ' v ⊑ Φ v) → {{ P' }} e @ E {{ Φ' }} ⊑ {{ P }} e @ E {{ Φ }}. P ⊑ P' → (∀ v, Φ' v ⊑ Φ v) → {{ P' }} e @ E {{ Φ' }} ⊑ {{ P }} e @ E {{ Φ }}. Proof. by intros; apply always_mono, impl_mono, wp_mono. Qed. Proof. by intros; apply always_mono, impl_mono, wp_mono. Qed. Global Instance ht_mono' E : Global Instance ht_mono' E : Proper (flip (⊑) ==> eq ==> pointwise_relation _ (⊑) ==> (⊑)) (@ht Λ Σ E). Proper (flip (⊑) ==> eq ==> pointwise_relation _ (⊑) ==> (⊑)) (@ht Λ Σ E). Proof. by intros P P' HP e ? <- Φ Φ' HΦ; apply ht_mono. Qed. Proof. solve_proper. Qed. Lemma ht_alt E P Φ e : (P ⊑ || e @ E {{ Φ }}) → {{ P }} e @ E {{ Φ }}. Lemma ht_alt E P Φ e : (P ⊑ || e @ E {{ Φ }}) → {{ P }} e @ E {{ Φ }}. Proof. Proof. ... ...
 ... @@ -46,7 +46,7 @@ Proof. rewrite /ownP; apply _. Qed. ... @@ -46,7 +46,7 @@ Proof. rewrite /ownP; apply _. Qed. (* ghost state *) (* ghost state *) Global Instance ownG_ne n : Proper (dist n ==> dist n) (@ownG Λ Σ). Global Instance ownG_ne n : Proper (dist n ==> dist n) (@ownG Λ Σ). Proof. by intros m m' Hm; unfold ownG; rewrite Hm. Qed. Proof. solve_proper. Qed. Global Instance ownG_proper : Proper ((≡) ==> (≡)) (@ownG Λ Σ) := ne_proper _. Global Instance ownG_proper : Proper ((≡) ==> (≡)) (@ownG Λ Σ) := ne_proper _. Lemma ownG_op m1 m2 : ownG (m1 ⋅ m2) ≡ (ownG m1 ★ ownG m2)%I. Lemma ownG_op m1 m2 : ownG (m1 ⋅ m2) ≡ (ownG m1 ★ ownG m2)%I. Proof. by rewrite /ownG -uPred.ownM_op Res_op !left_id. Qed. Proof. by rewrite /ownG -uPred.ownM_op Res_op !left_id. Qed. ... ...
 ... @@ -41,7 +41,7 @@ Proof. by intros HP HQ; rewrite /vs -HP HQ. Qed. ... @@ -41,7 +41,7 @@ Proof. by intros HP HQ; rewrite /vs -HP HQ. Qed. Global Instance vs_mono' E1 E2 : Global Instance vs_mono' E1 E2 : Proper (flip (⊑) ==> (⊑) ==> (⊑)) (@vs Λ Σ E1 E2). Proper (flip (⊑) ==> (⊑) ==> (⊑)) (@vs Λ Σ E1 E2). Proof. by intros until 2; apply vs_mono. Qed. Proof. solve_proper. Qed. Lemma vs_false_elim E1 E2 P : False ={E1,E2}=> P. Lemma vs_false_elim E1 E2 P : False ={E1,E2}=> P. Proof. apply vs_alt, False_elim. Qed. Proof. apply vs_alt, False_elim. Qed. ... ...
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