Commit 36159b49 authored by Robbert Krebbers's avatar Robbert Krebbers

Prove variants of CMRA facts for CMRAs with = ≡.

parent e49f34cf
......@@ -520,6 +520,64 @@ Section ucmra.
End ucmra.
Hint Immediate cmra_unit_total.
(** * Properties about CMRAs with Leibniz equality *)
Section cmra_leibniz.
Context {A : cmraT} `{!LeibnizEquiv A}.
Implicit Types x y : A.
Global Instance cmra_assoc_L : Assoc (=) (@op A _).
Proof. intros x y z. unfold_leibniz. by rewrite assoc. Qed.
Global Instance cmra_comm_L : Comm (=) (@op A _).
Proof. intros x y. unfold_leibniz. by rewrite comm. Qed.
Lemma cmra_pcore_l_L x cx : pcore x = Some cx cx x = x.
Proof. unfold_leibniz. apply cmra_pcore_l'. Qed.
Lemma cmra_pcore_idemp_L x cx : pcore x = Some cx pcore cx = Some cx.
Proof. unfold_leibniz. apply cmra_pcore_idemp'. Qed.
Lemma cmra_opM_assoc_L x y mz : (x y) ? mz = x (y ? mz).
Proof. unfold_leibniz. apply cmra_opM_assoc. Qed.
(** ** Core *)
Lemma cmra_pcore_r_L x cx : pcore x = Some cx x cx = x.
Proof. unfold_leibniz. apply cmra_pcore_r'. Qed.
Lemma cmra_pcore_dup_L x cx : pcore x = Some cx cx = cx cx.
Proof. unfold_leibniz. apply cmra_pcore_dup'. Qed.
(** ** Persistent elements *)
Lemma persistent_dup_L x `{!Persistent x} : x x x.
Proof. unfold_leibniz. by apply persistent_dup. Qed.
(** ** Total core *)
Section total_core.
Context `{CMRATotal A}.
Lemma cmra_core_r_L x : x core x = x.
Proof. unfold_leibniz. apply cmra_core_r. Qed.
Lemma cmra_core_l_L x : core x x = x.
Proof. unfold_leibniz. apply cmra_core_l. Qed.
Lemma cmra_core_idemp_L x : core (core x) = core x.
Proof. unfold_leibniz. apply cmra_core_idemp. Qed.
Lemma cmra_core_dup_L x : core x = core x core x.
Proof. unfold_leibniz. apply cmra_core_dup. Qed.
Lemma persistent_total_L x : Persistent x core x = x.
Proof. unfold_leibniz. apply persistent_total. Qed.
Lemma persistent_core_L x `{!Persistent x} : core x = x.
Proof. by apply persistent_total_L. Qed.
End total_core.
End cmra_leibniz.
Section ucmra_leibniz.
Context {A : ucmraT} `{!LeibnizEquiv A}.
Implicit Types x y z : A.
Global Instance ucmra_unit_left_id_L : LeftId (=) (@op A _).
Proof. intros x. unfold_leibniz. by rewrite left_id. Qed.
Global Instance ucmra_unit_right_id_L : RightId (=) (@op A _).
Proof. intros x. unfold_leibniz. by rewrite right_id. Qed.
End ucmra_leibniz.
(** * Constructing a CMRA with total core *)
Section cmra_total.
Context A `{Dist A, Equiv A, PCore A, Op A, Valid A, ValidN A}.
......
......@@ -142,7 +142,7 @@ Section heap.
iIntros (<-%of_to_val ?) "[#Hinv HΦ]". rewrite /heap_ctx.
iVs (auth_empty heap_name) as "Hh".
iVs (auth_open with "[Hh]") as (h) "[Hv [Hh Hclose]]"; eauto.
rewrite left_id /heap_inv. iDestruct "Hv" as %?.
rewrite left_id_L /heap_inv. iDestruct "Hv" as %?.
iApply wp_alloc_pst. iFrame "Hh". iNext.
iIntros (l) "[% Hh] !==>".
iVs ("Hclose" $! {[ l := (1%Qp, DecAgree v) ]} with "[Hh]").
......
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