Commit 1f24d020 authored by Robbert Krebbers's avatar Robbert Krebbers

Remove admissable rule for `plainly`.

parent 119fdac5
......@@ -486,8 +486,6 @@ Proof.
intros P QR HP. unseal; split=> n x ? /=. by apply HP, cmra_core_validN.
- (* bi_persistently P ⊢ bi_persistently (bi_persistently P) *)
intros P. unseal; split=> n x ?? /=. by rewrite cmra_core_idemp.
- (* bi_plainly (bi_persistently P) ⊢ bi_plainly P (ADMISSIBLE) *)
intros P. unseal; split=> n x ?? /=. by rewrite -(core_id_core ε).
- (* (∀ a, bi_persistently (Ψ a)) ⊢ bi_persistently (∀ a, Ψ a) *)
by unseal.
- (* bi_persistently (∃ a, Ψ a) ⊢ ∃ a, bi_persistently (Ψ a) *)
......
......@@ -957,8 +957,11 @@ Proof.
Qed.
Lemma plainly_persistently P : bi_plainly (bi_persistently P) bi_plainly P.
Proof.
apply (anti_symm _); first apply plainly_persistently_1.
by rewrite {1}plainly_idemp_2 (plainly_elim_persistently P).
apply (anti_symm _).
- rewrite -{1}(left_id True%I bi_and (bi_plainly _)) (plainly_emp_intro True%I).
rewrite -{2}(persistently_and_emp_elim P).
rewrite !and_alt -plainly_forall_2. by apply forall_mono=> -[].
- by rewrite {1}plainly_idemp_2 (plainly_elim_persistently P).
Qed.
Lemma absorbingly_plainly P : bi_absorbingly (bi_plainly P) bi_plainly P.
......
......@@ -129,8 +129,6 @@ Section bi_mixin.
(* In the ordered RA model: `core` is idempotent *)
bi_mixin_persistently_idemp_2 P :
bi_persistently P bi_persistently (bi_persistently P);
bi_mixin_plainly_persistently_1 P :
bi_plainly (bi_persistently P) bi_plainly P;
(* In the ordered RA model [P ⊢ persisently emp] (which can currently still
be derived from the plainly axioms, which will be removed): `ε ≼ core x` *)
......@@ -453,9 +451,6 @@ Proof. eapply bi_mixin_persistently_mono, bi_bi_mixin. Qed.
Lemma persistently_idemp_2 P :
bi_persistently P bi_persistently (bi_persistently P).
Proof. eapply bi_mixin_persistently_idemp_2, bi_bi_mixin. Qed.
Lemma plainly_persistently_1 P :
bi_plainly (bi_persistently P) bi_plainly P.
Proof. eapply (bi_mixin_plainly_persistently_1 bi_entails), bi_bi_mixin. Qed.
Lemma persistently_forall_2 {A} (Ψ : A PROP) :
( a, bi_persistently (Ψ a)) bi_persistently ( a, Ψ a).
......
......@@ -326,7 +326,6 @@ Proof.
- intros P Q. split=> i. apply bi.sep_elim_l, _.
- intros P Q [?]. split=> i /=. by f_equiv.
- intros P. split=> i. by apply bi.persistently_idemp_2.
- intros P. split=> i /=. by setoid_rewrite bi.plainly_persistently_1.
- intros A Ψ. split=> i. by apply bi.persistently_forall_2.
- intros A Ψ. split=> i. by apply bi.persistently_exist_1.
- intros P Q. split=> i. apply bi.sep_elim_l, _.
......
Markdown is supported
0%
or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment