Commit 7dcb3217 authored by Robbert Krebbers's avatar Robbert Krebbers

Support `AIEnvId` for the spatial context.

parent 74cf33ae
......@@ -134,7 +134,7 @@ Record always_modality_mixin {PROP : bi} (M : PROP → PROP)
| AIEnvForall C => P, C P P M P
| AIEnvTransform C => ( P Q, C P Q P M Q)
| AIEnvClear => P, Absorbing (M P)
| AIEnvId => False
| AIEnvId => P, P M P
end;
always_modality_mixin_emp : emp M emp;
always_modality_mixin_mono P Q : (P Q) M P M Q;
......@@ -175,8 +175,8 @@ Section always_modality.
Lemma always_modality_spatial_clear P :
always_modality_spatial_spec M = AIEnvClear Absorbing (M P).
Proof. destruct M as [??? []]; naive_solver. Qed.
Lemma always_modality_spatial_id :
always_modality_spatial_spec M AIEnvId.
Lemma always_modality_spatial_id P :
always_modality_spatial_spec M = AIEnvId P M P.
Proof. destruct M as [??? []]; naive_solver. Qed.
Lemma always_modality_emp : emp M emp.
......
......@@ -720,7 +720,8 @@ Proof.
eauto using always_modality_spatial_transform.
+ rewrite -HQ' /= right_id comm -{2}(always_modality_spatial_clear M) //.
by rewrite (True_intro ([] Γs)%I).
+ by destruct (always_modality_spatial_id M).
+ rewrite -HQ' {1}(always_modality_spatial_id M ([] Γs')%I) //.
by rewrite -always_modality_sep.
Qed.
Lemma tac_persistent Δ Δ' i p P P' Q :
......
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