diff --git a/theories/proofmode/monpred.v b/theories/proofmode/monpred.v index b65eddfa72652c6578a8d327246109b493ffd1fe..0dabf37cd9a737f7a5161f08ae8d5b8eac127311 100644 --- a/theories/proofmode/monpred.v +++ b/theories/proofmode/monpred.v @@ -81,32 +81,32 @@ Proof. Qed. Global Instance as_valid_monPred_car φ P (Φ : I → PROP) : - AsValid φ P → (∀ i, MakeMonPredCar i P (Φ i)) → AsValid φ (∀ i, Φ i) | 100. + AsValid φ P → (∀ i, MakeMonPredCar i P (Φ i)) → AsValid' φ (∀ i, Φ i) | 100. Proof. - rewrite /MakeMonPredCar /AsValid /bi_valid=> -> EQ. setoid_rewrite <-EQ. - unseal; split. + rewrite /MakeMonPredCar /AsValid' /AsValid /bi_valid=> -> EQ. + setoid_rewrite <-EQ. unseal; split. - move=>[/= /bi.forall_intro //]. - - move=>H. split=>i. rewrite /= H bi.forall_elim //. + - move=>HP. split=>i. rewrite /= HP bi.forall_elim //. Qed. Global Instance as_valid_monPred_car_wand φ P Q (Φ Ψ : I → PROP) : AsValid φ (P -∗ Q) → (∀ i, MakeMonPredCar i P (Φ i)) → (∀ i, MakeMonPredCar i Q (Ψ i)) → - AsValid φ (∀ i, Φ i -∗ Ψ i). + AsValid' φ (∀ i, Φ i -∗ Ψ i). Proof. - rewrite /AsValid /MakeMonPredCar. intros -> EQ1 EQ2. + rewrite /AsValid' /AsValid /MakeMonPredCar. intros -> EQ1 EQ2. setoid_rewrite <-EQ1. setoid_rewrite <-EQ2. split. - - move=>/bi.wand_entails H. setoid_rewrite H. by iIntros (i) "$". - - move=>H. apply bi.entails_wand. split=>i. iIntros "H". by iApply H. + - move=>/bi.wand_entails HP. setoid_rewrite HP. by iIntros (i) "$". + - move=>HP. apply bi.entails_wand. split=>i. iIntros "H". by iApply HP. Qed. Global Instance as_valid_monPred_car_equiv φ P Q (Φ Ψ : I → PROP) : AsValid φ (P ∗-∗ Q) → (∀ i, MakeMonPredCar i P (Φ i)) → (∀ i, MakeMonPredCar i Q (Ψ i)) → - AsValid φ (∀ i, Φ i ∗-∗ Ψ i). + AsValid' φ (∀ i, Φ i ∗-∗ Ψ i). Proof. - rewrite /AsValid /MakeMonPredCar. intros -> EQ1 EQ2. + rewrite /AsValid' /AsValid /MakeMonPredCar. intros -> EQ1 EQ2. setoid_rewrite <-EQ1. setoid_rewrite <-EQ2. split. - - move=>/bi.wand_iff_equiv H. setoid_rewrite H. iIntros. iSplit; iIntros "$". - - move=>H. apply bi.equiv_wand_iff. split=>i. by iSplit; iIntros; iApply H. + - move=>/bi.wand_iff_equiv HP. setoid_rewrite HP. iIntros. iSplit; iIntros "$". + - move=>HP. apply bi.equiv_wand_iff. split=>i. by iSplit; iIntros; iApply HP. Qed. Global Instance into_pure_monPred_car P φ i : diff --git a/theories/proofmode/tactics.v b/theories/proofmode/tactics.v index 9c002eaf9ca8ed761e317a85ac27b790442e4091..64b281c788206403ce2d102c5cf489cefb3737fb 100644 --- a/theories/proofmode/tactics.v +++ b/theories/proofmode/tactics.v @@ -71,9 +71,13 @@ Proof. split. apply bi.entails_wand. apply bi.wand_entails. Qed. Instance as_valid_equiv {PROP : bi} (P Q : PROP) : AsValid (P ≡ Q) (P ∗-∗ Q) | 0. Proof. split. apply bi.equiv_wand_iff. apply bi.wand_iff_equiv. Qed. +Class AsValid' {PROP : bi} (φ : Prop) (P : PROP) := as_valid' :> AsValid φ P. +Arguments AsValid' {_} _%type _%I. +Hint Mode AsValid' ! ! - : typeclass_instances. + Instance as_valid_embed `{BiEmbedding PROP PROP'} (φ : Prop) (P : PROP) : - AsValid φ P → AsValid φ ⎡P⎤. -Proof. rewrite /AsValid=> ->. rewrite bi_embed_valid //. Qed. + AsValid φ P → AsValid' φ ⎡P⎤. +Proof. rewrite /AsValid' /AsValid=> ->. rewrite bi_embed_valid //. Qed. (** * Start a proof *) Tactic Notation "iStartProof" uconstr(PROP) :=