Commit 5bdf0c21 authored by Robbert Krebbers's avatar Robbert Krebbers

Better `IntoWand` instances for `<affine> ⎡ ... ⎤` as an alternative for ec4ac846.

parent 3ef1bbb5
......@@ -427,10 +427,34 @@ Proof. by rewrite /IntoWand /= intuitionistically_persistently_elim. Qed.
Global Instance into_wand_persistently_false q R P Q :
Absorbing R IntoWand false q R P Q IntoWand false q (<pers> R) P Q.
Proof. intros ?. by rewrite /IntoWand persistently_elim. Qed.
Global Instance into_wand_embed `{BiEmbed PROP PROP'} p q R P Q :
IntoWand p q R P Q IntoWand p q R P Q.
Proof. by rewrite /IntoWand !embed_intuitionistically_if_2 -embed_wand=> ->. Qed.
(* There are two versions for [IntoWand ⎡RR⎤ ...] with the argument being
[<affine> ⎡PP⎤]. When the wand [⎡RR⎤] resides in the intuitionistic context
the result of wand elimination will have the affine modality. Otherwise, it
won't. Note that when the wand [⎡RR⎤] is under an affine modality, the instance
[into_wand_affine] would already have been used. *)
Global Instance into_wand_affine_embed_true `{BiEmbed PROP PROP'} q (PP QQ RR : PROP) :
IntoWand true q RR PP QQ IntoWand true q RR (<affine> PP) (<affine> QQ) | 100.
rewrite /IntoWand /=.
rewrite -(intuitionistically_idemp _ %I) embed_intuitionistically_2=> ->.
apply bi.wand_intro_l. destruct q; simpl.
- rewrite affinely_elim -(intuitionistically_idemp _ %I).
rewrite embed_intuitionistically_2 intuitionistically_sep_2 -embed_sep.
by rewrite wand_elim_r intuitionistically_affinely.
- by rewrite intuitionistically_affinely affinely_sep_2 -embed_sep wand_elim_r.
Global Instance into_wand_affine_embed_false `{BiEmbed PROP PROP'} q (PP QQ RR : PROP) :
IntoWand false q RR (<affine> PP) QQ IntoWand false q RR (<affine> PP) QQ | 100.
rewrite /IntoWand /= => ->.
by rewrite embed_affinely_2 embed_intuitionistically_if_2 embed_wand.
(* FromWand *)
Global Instance from_wand_wand P1 P2 : FromWand (P1 - P2) P1 P2.
Proof. by rewrite /FromWand. Qed.
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