### The types of propositions for monPred lemma need to be [monPred I PROP] and...

`The types of propositions for monPred lemma need to be [monPred I PROP] and not [bi_car (monPredI I PROP)], otherwise iIntoValid fails in a very weird way. Seems to be related to a Coq bug.`
parent c78c8b7a
 ... ... @@ -395,11 +395,12 @@ End canonical_sbi. Section bi_facts. Context {I : biIndex} {PROP : bi}. Local Notation monPred := (monPred I PROP). Local Notation monPredI := (monPredI I PROP). Local Notation monPred_at := (@monPred_at I PROP). Local Notation BiIndexBottom := (@BiIndexBottom I). Implicit Types i : I. Implicit Types P Q : monPredI. Implicit Types P Q : monPred. (** Instances *) ... ... @@ -565,9 +566,9 @@ Lemma monPred_at_or i P Q : (P ∨ Q) i ⊣⊢ P i ∨ Q i. Proof. by unseal. Qed. Lemma monPred_at_impl i P Q : (P → Q) i ⊣⊢ ∀ j, ⌜i ⊑ j⌝ → P j → Q j. Proof. by unseal. Qed. Lemma monPred_at_forall {A} i (Φ : A → monPredI) : (∀ x, Φ x) i ⊣⊢ ∀ x, Φ x i. Lemma monPred_at_forall {A} i (Φ : A → monPred) : (∀ x, Φ x) i ⊣⊢ ∀ x, Φ x i. Proof. by unseal. Qed. Lemma monPred_at_exist {A} i (Φ : A → monPredI) : (∃ x, Φ x) i ⊣⊢ ∃ x, Φ x i. Lemma monPred_at_exist {A} i (Φ : A → monPred) : (∃ x, Φ x) i ⊣⊢ ∃ x, Φ x i. Proof. by unseal. Qed. Lemma monPred_at_sep i P Q : (P ∗ Q) i ⊣⊢ P i ∗ Q i. Proof. by unseal. Qed. ... ... @@ -743,9 +744,10 @@ End bi_facts. Section sbi_facts. Context {I : biIndex} {PROP : sbi}. Local Notation monPred := (monPred I PROP). Local Notation monPredSI := (monPredSI I PROP). Implicit Types i : I. Implicit Types P Q : monPredSI. Implicit Types P Q : monPred. Global Instance monPred_at_timeless P i : Timeless P → Timeless (P i). Proof. move => [] /(_ i). unfold Timeless. by unseal. Qed. ... ... @@ -810,7 +812,7 @@ Lemma monPred_at_except_0 i P : (◇ P) i ⊣⊢ ◇ P i. Proof. by unseal. Qed. Lemma monPred_fupd_embed `{FUpdFacts PROP} E1 E2 (P : PROP) : ⎡|={E1,E2}=> P⎤ ⊣⊢ fupd E1 E2 (PROP:=monPred I PROP) ⎡P⎤. ⎡|={E1,E2}=> P⎤ ⊣⊢ fupd E1 E2 (PROP:=monPred) ⎡P⎤. Proof. unseal. split=>i /=. setoid_rewrite bi.pure_impl_forall. apply bi.equiv_spec; split. - by do 2 apply bi.forall_intro=>?. ... ...
 ... ... @@ -50,4 +50,9 @@ Section tests. iStartProof PROP. iIntros (i) "HW". iIntros (j ->) "HP". iSpecialize ("HW" with "HP"). done. Qed. Lemma test_apply_in_elim (P : monPredI) (i : I) : monPred_in i ∧ ⎡ P i ⎤ -∗ P. Proof. iIntros. by iApply monPred_in_elim. Qed. End tests.
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