Commit 135f1298 authored by Robbert Krebbers's avatar Robbert Krebbers

Describe `plainly` in terms of equality.

parent 3e1b5787
......@@ -1916,7 +1916,17 @@ Proof.
rewrite -(internal_eq_refl True%I a) plainly_pure; auto.
Qed.
Lemma plainly_alt P `{!Absorbing P} : bi_plainly P P True.
Lemma plainly_alt P : bi_plainly P bi_affinely P emp.
Proof.
rewrite -plainly_affinely. apply (anti_symm ()).
- rewrite -prop_ext. apply plainly_mono, and_intro; apply wand_intro_l.
+ by rewrite affinely_elim_emp left_id.
+ by rewrite left_id.
- rewrite internal_eq_sym (internal_eq_rewrite _ _ bi_plainly).
by rewrite -plainly_True_emp plainly_pure True_impl.
Qed.
Lemma plainly_alt_absorbing P `{!Absorbing P} : bi_plainly P P True.
Proof.
apply (anti_symm ()).
- rewrite -prop_ext. apply plainly_mono, and_intro; apply wand_intro_l; auto.
......
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