Commit 4ac87063 authored by Robbert Krebbers's avatar Robbert Krebbers

Reorganize algebra/gset a bit.

parent f8e40d51
Pipeline #2547 passed with stage
in 4 minutes and 5 seconds
......@@ -55,8 +55,6 @@ Section gset.
discreteUR (gset_disj K) gset_disj_ra_mixin gset_disj_ucmra_mixin.
Arguments op _ _ _ _ : simpl never.
Section fpu.
Context `{Fresh K (gset K), !FreshSpec K (gset K)}.
Lemma gset_alloc_updateP_strong P (Q : gset_disj K Prop) X :
( Y, X Y j, j Y P j)
......@@ -69,18 +67,10 @@ Section gset.
- apply HQ; set_solver by eauto.
- apply gset_disj_valid_op. set_solver by eauto.
Qed.
Lemma gset_alloc_updateP (Q : gset_disj K Prop) X :
( i, i X Q (GSet ({[i]} X))) GSet X ~~>: Q.
Proof.
intro; eapply gset_alloc_updateP_strong with (λ _, True); eauto.
intros Y ?; exists (fresh Y); eauto using is_fresh.
Qed.
Lemma gset_alloc_updateP_strong' P X :
( Y, X Y j, j Y P j)
GSet X ~~>: λ Y, i, Y = GSet ({[ i ]} X) i X P i.
Proof. eauto using gset_alloc_updateP_strong. Qed.
Lemma gset_alloc_updateP' X : GSet X ~~>: λ Y, i, Y = GSet ({[ i ]} X) i X.
Proof. eauto using gset_alloc_updateP. Qed.
Lemma gset_alloc_empty_updateP_strong P (Q : gset_disj K Prop) :
( Y : gset K, j, j Y P j)
......@@ -89,17 +79,29 @@ Section gset.
intros. apply (gset_alloc_updateP_strong P); eauto.
intros i; rewrite right_id_L; auto.
Qed.
Lemma gset_alloc_empty_updateP (Q : gset_disj K Prop) :
( i, Q (GSet {[i]})) GSet ~~>: Q.
Proof. intro. apply gset_alloc_updateP. intros i; rewrite right_id_L; auto. Qed.
Lemma gset_alloc_empty_updateP_strong' P :
( Y : gset K, j, j Y P j)
GSet ~~>: λ Y, i, Y = GSet {[ i ]} P i.
Proof. eauto using gset_alloc_empty_updateP_strong. Qed.
Lemma gset_alloc_empty_updateP' : GSet ~~>: λ Y, i, Y = GSet {[ i ]}.
Proof. eauto using gset_alloc_empty_updateP. Qed.
End fpu.
Section fresh_updates.
Context `{Fresh K (gset K), !FreshSpec K (gset K)}.
Lemma gset_alloc_updateP (Q : gset_disj K Prop) X :
( i, i X Q (GSet ({[i]} X))) GSet X ~~>: Q.
Proof.
intro; eapply gset_alloc_updateP_strong with (λ _, True); eauto.
intros Y ?; exists (fresh Y); eauto using is_fresh.
Qed.
Lemma gset_alloc_updateP' X : GSet X ~~>: λ Y, i, Y = GSet ({[ i ]} X) i X.
Proof. eauto using gset_alloc_updateP. Qed.
Lemma gset_alloc_empty_updateP (Q : gset_disj K Prop) :
( i, Q (GSet {[i]})) GSet ~~>: Q.
Proof. intro. apply gset_alloc_updateP. intros i; rewrite right_id_L; auto. Qed.
Lemma gset_alloc_empty_updateP' : GSet ~~>: λ Y, i, Y = GSet {[ i ]}.
Proof. eauto using gset_alloc_empty_updateP. Qed.
End fresh_updates.
Lemma gset_alloc_local_update X i Xf :
i X i Xf GSet X ~l~> GSet ({[i]} X) @ Some (GSet Xf).
......
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