Commit bd15a981 authored by Robbert Krebbers's avatar Robbert Krebbers

Prove Timelessness of pure in the logic.

parent 0e49878b
......@@ -731,6 +731,12 @@ Lemma pure_elim_r φ Q R : (φ → Q ⊢ R) → Q ∧ ■ φ ⊢ R.
Proof. intros; apply pure_elim with φ; eauto. Qed.
Lemma pure_equiv (φ : Prop) : φ φ True.
Proof. intros; apply (anti_symm _); auto using pure_intro. Qed.
Lemma pure_alt φ : φ _ : φ, True.
Proof.
apply (anti_symm _).
- eapply pure_elim; eauto=> H. rewrite -(exist_intro H); auto.
- by apply exist_elim, pure_intro.
Qed.
Lemma eq_refl' {A : cofeT} (a : A) P : P a a.
Proof. rewrite (True_intro P). apply eq_refl. Qed.
......@@ -1014,8 +1020,6 @@ Proof.
unseal; split=> n x ? HP; induction n as [|n IH]; [by apply HP|].
apply HP, IH, uPred_closed with (S n); eauto using cmra_validN_S.
Qed.
Lemma later_pure φ : φ False φ.
Proof. unseal; split=> -[|n] x ?? /=; auto. Qed.
Lemma later_and P Q : (P Q) P Q.
Proof. unseal; split=> -[|n] x; by split. Qed.
Lemma later_or P Q : (P Q) P Q.
......@@ -1254,7 +1258,9 @@ Proof. uPred.unseal. by destruct mx. Qed.
(* Timeless instances *)
Global Instance pure_timeless φ : TimelessP ( φ : uPred M)%I.
Proof. by rewrite /TimelessP later_pure. Qed.
Proof.
rewrite /TimelessP pure_alt later_exist_false. by setoid_rewrite later_True.
Qed.
Global Instance valid_timeless {A : cmraT} `{CMRADiscrete A} (a : A) :
TimelessP ( a : uPred M)%I.
Proof. rewrite /TimelessP !discrete_valid. apply (timelessP _). Qed.
......
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