Commit fdc94f14 authored by Jacques-Henri Jourdan's avatar Jacques-Henri Jourdan

Simplify core.

parent 74cba44e
......@@ -5,7 +5,7 @@ Import uPred.
(** The "core" of an assertion is its maximal persistent part. *)
Definition coreP {M : ucmraT} (P : uPred M) : uPred M :=
( Q, (Q Q) (P Q) Q)%I.
( Q, (P Q) Q)%I.
Instance: Params (@coreP) 1.
Typeclasses Opaque coreP.
......@@ -14,15 +14,10 @@ Section core.
Implicit Types P Q : uPred M.
Lemma coreP_intro P : P - coreP P.
Proof. rewrite /coreP. iIntros "HP" (Q) "_ HPQ". by iApply "HPQ". Qed.
Proof. rewrite /coreP. iIntros "HP" (Q) "HPQ". by iApply "HPQ". Qed.
Global Instance coreP_persistent P : Persistent (coreP P).
Proof.
rewrite /coreP /Persistent. iIntros "HC" (Q). rewrite !affine_affinely.
iApply persistently_impl_plainly. iIntros "#HQ".
iApply persistently_impl_plainly. iIntros "#HPQ".
iApply "HQ". by iApply "HC"; rewrite !affine_affinely.
Qed.
Proof. rewrite /coreP /Persistent. iIntros "#HC" (Q) "!#". iApply "HC". Qed.
Global Instance coreP_ne : NonExpansive (@coreP M).
Proof. solve_proper. Qed.
......@@ -30,13 +25,12 @@ Section core.
Proof. solve_proper. Qed.
Global Instance coreP_mono : Proper (() ==> ()) (@coreP M).
Proof.
rewrite /coreP. iIntros (P P' HP) "H"; iIntros (Q) "#HQ #HPQ".
iApply ("H" $! Q with "[]"); first done. by rewrite HP.
Qed.
Proof. solve_proper. Qed.
Lemma coreP_elim P : Persistent P coreP P - P.
Proof. rewrite /coreP. iIntros (?) "HCP". iApply ("HCP" $! P); auto. Qed.
Proof.
rewrite /coreP. iIntros (?) "HCP". iApply ("HCP" $! P with "[]"). auto.
Qed.
Lemma coreP_wand P Q : (coreP P Q) (P Q).
Proof.
......@@ -44,6 +38,6 @@ Section core.
- iIntros (HP) "HP". iDestruct (coreP_intro with "HP") as "#HcP".
iAlways. by iApply HP.
- iIntros (HPQ) "HcP". iDestruct (coreP_mono _ _ HPQ with "HcP") as "HcQ".
iDestruct (coreP_elim with "HcQ") as "#HQ". done.
by iDestruct (coreP_elim with "HcQ") as "#HQ".
Qed.
End core.
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