Commit 249edc6c authored by Robbert Krebbers's avatar Robbert Krebbers

More properties about the relation between wand and impl.

parent 3f768dd2
......@@ -1339,6 +1339,13 @@ Proof.
by rewrite -persistently_and_affinely_sep_l affinely_and_r affinely_and idemp.
Qed.
Lemma wand_impl_affinely_persistently P Q : ( P - Q) (bi_persistently P Q).
Proof.
apply (anti_symm ()).
- apply impl_intro_l. by rewrite persistently_and_affinely_sep_l wand_elim_r.
- apply wand_intro_l. by rewrite -persistently_and_affinely_sep_l impl_elim_r.
Qed.
(* The combined affinely plainly modality *)
Lemma affinely_plainly_elim P : P P.
Proof. apply plainly_and_emp_elim. Qed.
......@@ -1377,6 +1384,9 @@ Proof.
by rewrite -plainly_and_affinely_sep_l affinely_and_r affinely_and idemp.
Qed.
Lemma wand_impl_affinely_plainly P Q : ( P - Q) (bi_plainly P Q).
Proof. by rewrite -(persistently_plainly P) wand_impl_affinely_persistently. Qed.
(* Conditional affinely modality *)
Global Instance affinely_if_ne p : NonExpansive (@bi_affinely_if PROP p).
Proof. solve_proper. Qed.
......
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