Commit daaabf41 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Use implication in core so that we can test it.

parent 72ac1ee1
Pipeline #7333 passed with stage
in 12 minutes and 5 seconds
......@@ -7,7 +7,7 @@ Import bi.
i.e. the conjunction of all persistent assertions that are weaker
than P (as in, implied by P). *)
Definition coreP `{!BiPlainly PROP} (P : PROP) : PROP :=
( Q : PROP, <affine> (Q - <pers> Q) - <affine> (P - Q) - Q)%I.
( Q : PROP, (Q - <pers> Q) (P - Q) Q)%I.
Instance: Params (@coreP) 1.
Typeclasses Opaque coreP.
......@@ -16,19 +16,14 @@ Section core.
Implicit Types P Q : PROP.
Lemma coreP_intro P : P - coreP P.
rewrite /coreP. iIntros "HP" (Q) "_ HPQ".
(* FIXME: Cannot apply HPQ directly. *)
iDestruct (affinely_plainly_elim with "HPQ") as "HPQ".
by iApply "HPQ".
Proof. rewrite /coreP. iIntros "HP" (Q) "_ #HPQ". by iApply "HPQ". Qed.
Global Instance coreP_persistent P : Persistent (coreP P).
rewrite /coreP /Persistent. iIntros "HC" (Q).
iApply persistently_wand_affinely_plainly. iIntros "#HQ".
iApply persistently_wand_affinely_plainly. iIntros "#HPQ".
iApply "HQ". iApply "HC"; auto.
iApply persistently_impl_plainly. iIntros "#HQ".
iApply persistently_impl_plainly. iIntros "#HPQ".
iApply "HQ". by iApply ("HC" with "[#] [#]").
Global Instance coreP_ne : NonExpansive (coreP (PROP:=PROP)).
......@@ -40,7 +35,7 @@ Section core.
Proof. solve_proper. Qed.
Lemma coreP_elim P : Persistent P coreP P - P.
Proof. rewrite /coreP. iIntros (?) "HCP". iApply "HCP"; auto. Qed.
Proof. rewrite /coreP. iIntros (?) "HCP". iApply ("HCP" with "[#] [#]"); auto. Qed.
(* TODO: Can we generalize this to non-affine BIs? *)
Lemma coreP_wand `{!BiAffine PROP} P Q : (coreP P Q) (P <pers> Q).
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