diff --git a/theories/proofmode/class_instances_bi.v b/theories/proofmode/class_instances_bi.v index fd6b4d4d530ac5c1a7f65d6f757068fce9fffc11..3edfef488945525fd1c36916a1aa44dcca62e9ae 100644 --- a/theories/proofmode/class_instances_bi.v +++ b/theories/proofmode/class_instances_bi.v @@ -698,7 +698,8 @@ Qed. Global Instance into_and_sep `{BiPositive PROP} P Q : IntoAnd true (P ∗ Q) P Q. Proof. - rewrite /IntoAnd /= intuitionistically_sep -and_sep_intuitionistically intuitionistically_and //. + rewrite /IntoAnd /= intuitionistically_sep + -and_sep_intuitionistically intuitionistically_and //. Qed. Global Instance into_and_sep_affine P Q : TCOr (Affine P) (Absorbing Q) → TCOr (Absorbing P) (Affine Q) → @@ -990,29 +991,31 @@ Global Instance into_forall_wand P Q : Proof. rewrite /IntoForall. apply forall_intro=><-. rewrite emp_wand //. Qed. Global Instance into_forall_impl `{!BiAffine PROP} P Q : IntoForall (P → Q) (λ _ : ⊢ P, Q) | 10. -Proof. rewrite /IntoForall. apply forall_intro=><-. rewrite -True_emp True_impl //. Qed. +Proof. + rewrite /IntoForall. apply forall_intro=><-. rewrite -True_emp True_impl //. +Qed. (** FromForall *) Global Instance from_forall_forall {A} (Φ : A → PROP) : - FromForall (∀ x, Φ x)%I Φ. + FromForall (∀ x, Φ x) Φ. Proof. by rewrite /FromForall. Qed. Global Instance from_forall_tforall {A} (Φ : tele_arg A → PROP) : FromForall (∀.. x, Φ x)%I Φ. Proof. by rewrite /FromForall bi_tforall_forall. Qed. Global Instance from_forall_pure {A} (φ : A → Prop) : - @FromForall PROP A (⌜∀ a : A, φ aâŒ)%I (λ a, ⌜ φ a âŒ)%I. + @FromForall PROP A ⌜∀ a : A, φ a⌠(λ a, ⌜ φ a âŒ)%I. Proof. by rewrite /FromForall pure_forall. Qed. Global Instance from_forall_pure_not (φ : Prop) : - @FromForall PROP φ (⌜¬ φâŒ)%I (λ a : φ, False)%I. + @FromForall PROP φ ⌜¬ φ⌠(λ a : φ, False)%I. Proof. by rewrite /FromForall pure_forall. Qed. Global Instance from_forall_impl_pure P Q φ : - IntoPureT P φ → FromForall (P → Q)%I (λ _ : φ, Q)%I. + IntoPureT P φ → FromForall (P → Q) (λ _ : φ, Q). Proof. intros (φ'&->&?). by rewrite /FromForall -pure_impl_forall (into_pure P). Qed. Global Instance from_forall_wand_pure P Q φ : IntoPureT P φ → TCOr (Affine P) (Absorbing Q) → - FromForall (P -∗ Q)%I (λ _ : φ, Q)%I. + FromForall (P -∗ Q) (λ _ : φ, Q)%I. Proof. intros (φ'&->&?) [|]; rewrite /FromForall; apply wand_intro_r. - rewrite -(affine_affinely P) (into_pure P) -persistent_and_affinely_sep_r. @@ -1027,10 +1030,10 @@ Proof. by rewrite persistently_forall. Qed. Global Instance from_forall_persistently {A} P (Φ : A → PROP) : - FromForall P Φ → FromForall (<pers> P)%I (λ a, <pers> (Φ a))%I. + FromForall P Φ → FromForall (<pers> P) (λ a, <pers> (Φ a))%I. Proof. rewrite /FromForall=> <-. by rewrite persistently_forall. Qed. Global Instance from_forall_embed `{BiEmbed PROP PROP'} {A} P (Φ : A → PROP) : - FromForall P Φ → FromForall ⎡P⎤%I (λ a, ⎡Φ a⎤%I). + FromForall P Φ → FromForall ⎡P⎤ (λ a, ⎡Φ a⎤%I). Proof. by rewrite /FromForall -embed_forall => <-. Qed. (** IntoInv *)