Commit e1ef66ef authored by Robbert Krebbers's avatar Robbert Krebbers

Some box/slice renaming.

parent 6923de66
......@@ -89,7 +89,7 @@ Proof.
- by rewrite big_sepM_empty.
Qed.
Lemma box_insert_empty Q E f P :
Lemma slice_insert_empty Q E f P :
box N f P ={E}= γ, f !! γ = None
slice N γ Q box N (<[γ:=false]> f) (Q P).
Proof.
......@@ -108,7 +108,7 @@ Proof.
iFrame; eauto.
Qed.
Lemma box_delete_empty E f P Q γ :
Lemma slice_delete_empty E f P Q γ :
N E
f !! γ = Some false
slice N γ Q - box N f P ={E}= P',
......@@ -128,7 +128,7 @@ Proof.
- iExists Φ; eauto.
Qed.
Lemma box_fill E f γ P Q :
Lemma slice_fill E f γ P Q :
N E
f !! γ = Some false
slice N γ Q - Q - box N f P ={E}= box N (<[γ:=true]> f) P.
......@@ -147,7 +147,7 @@ Proof.
iFrame; eauto.
Qed.
Lemma box_empty E f P Q γ :
Lemma slice_empty E f P Q γ :
N E
f !! γ = Some true
slice N γ Q - box N f P ={E}= Q box N (<[γ:=false]> f) P.
......@@ -167,31 +167,31 @@ Proof.
iFrame; eauto.
Qed.
Lemma box_insert_full Q E f P :
Lemma slice_insert_full Q E f P :
N E
Q - box N f P ={E}= γ, f !! γ = None
slice N γ Q box N (<[γ:=true]> f) (Q P).
Proof.
iIntros (?) "HQ Hbox".
iMod (box_insert_empty with "Hbox") as (γ) "(% & #Hslice & Hbox)".
iExists γ. iFrame "%#". iMod (box_fill with "Hslice HQ Hbox"); first done.
iMod (slice_insert_empty with "Hbox") as (γ) "(% & #Hslice & Hbox)".
iExists γ. iFrame "%#". iMod (slice_fill with "Hslice HQ Hbox"); first done.
by apply lookup_insert. by rewrite insert_insert.
Qed.
Lemma box_delete_full E f P Q γ :
Lemma slice_delete_full E f P Q γ :
N E
f !! γ = Some true
slice N γ Q - box N f P ={E}=
P', Q (P (Q P')) box N (delete γ f) P'.
Proof.
iIntros (??) "#Hslice Hbox".
iMod (box_empty with "Hslice Hbox") as "[$ Hbox]"; try done.
iMod (box_delete_empty with "Hslice Hbox") as (P') "[Heq Hbox]".
done. by apply lookup_insert.
iMod (slice_empty with "Hslice Hbox") as "[$ Hbox]"; try done.
iMod (slice_delete_empty with "Hslice Hbox") as (P') "[Heq Hbox]"; first done.
{ by apply lookup_insert. }
iExists P'. iFrame. rewrite -insert_delete delete_insert ?lookup_delete //.
Qed.
Lemma box_fill_all E f P :
Lemma box_fill E f P :
N E
box N f P - P ={E}= box N (const true <$> f) P.
Proof.
......@@ -208,7 +208,7 @@ Proof.
iApply "Hclose". iNext; iExists true. by iFrame.
Qed.
Lemma box_empty_all E f P :
Lemma box_empty E f P :
N E
map_Forall (λ _, (true =)) f
box N f P ={E}= P box N (const false <$> f) P.
......@@ -230,50 +230,50 @@ Proof.
- iExists Φ; iSplit; by rewrite big_sepM_fmap.
Qed.
Lemma box_split E f P Q1 Q2 γ b :
Lemma slice_split E f P Q1 Q2 γ b :
N E f !! γ = Some b
slice N γ (Q1 Q2) - box N f P ={E}= γ1 γ2,
delete γ f !! γ1 = None delete γ f !! γ2 = None ⌜γ1 γ2
slice N γ1 Q1 slice N γ2 Q2 box N (<[γ2 := b]>(<[γ1 := b]>(delete γ f))) P.
Proof.
iIntros (??) "#Hslice Hbox". destruct b.
- iMod (box_delete_full with "Hslice Hbox") as (P') "([HQ1 HQ2] & Heq & Hbox)"; try done.
iMod (box_insert_full Q1 with "HQ1 Hbox") as (γ1) "(% & #Hslice1 & Hbox)". done.
iMod (box_insert_full Q2 with "HQ2 Hbox") as (γ2) "(% & #Hslice2 & Hbox)". done.
- iMod (slice_delete_full with "Hslice Hbox") as (P') "([HQ1 HQ2] & Heq & Hbox)"; try done.
iMod (slice_insert_full Q1 with "HQ1 Hbox") as (γ1) "(% & #Hslice1 & Hbox)"; first done.
iMod (slice_insert_full Q2 with "HQ2 Hbox") as (γ2) "(% & #Hslice2 & Hbox)"; first done.
iExists γ1, γ2. iFrame "%#". iModIntro. iSplit; last iSplit; try iPureIntro.
{ by eapply lookup_insert_None. }
{ by apply (lookup_insert_None (delete γ f) γ1 γ2 true). }
iNext. eapply internal_eq_rewrite_contractive; [by apply _| |by eauto].
iNext. iRewrite "Heq". iPureIntro. rewrite assoc. f_equiv. by rewrite comm. done.
- iMod (box_delete_empty with "Hslice Hbox") as (P') "[Heq Hbox]"; try done.
iMod (box_insert_empty Q1 with "Hbox") as (γ1) "(% & #Hslice1 & Hbox)".
iMod (box_insert_empty Q2 with "Hbox") as (γ2) "(% & #Hslice2 & Hbox)".
iNext. iRewrite "Heq". iPureIntro. by rewrite assoc (comm _ Q2).
- iMod (slice_delete_empty with "Hslice Hbox") as (P') "[Heq Hbox]"; try done.
iMod (slice_insert_empty Q1 with "Hbox") as (γ1) "(% & #Hslice1 & Hbox)".
iMod (slice_insert_empty Q2 with "Hbox") as (γ2) "(% & #Hslice2 & Hbox)".
iExists γ1, γ2. iFrame "%#". iModIntro. iSplit; last iSplit; try iPureIntro.
{ by eapply lookup_insert_None. }
{ by apply (lookup_insert_None (delete γ f) γ1 γ2 false). }
iNext. eapply internal_eq_rewrite_contractive; [by apply _| |by eauto].
iNext. iRewrite "Heq". iPureIntro. rewrite assoc. f_equiv. by rewrite comm. done.
iNext. iRewrite "Heq". iPureIntro. by rewrite assoc (comm _ Q2).
Qed.
Lemma box_combine E f P Q1 Q2 γ1 γ2 b :
Lemma slice_combine E f P Q1 Q2 γ1 γ2 b :
N E γ1 γ2 f !! γ1 = Some b f !! γ2 = Some b
slice N γ1 Q1 - slice N γ2 Q2 - box N f P ={E}= γ,
delete γ2 (delete γ1 f) !! γ = None slice N γ (Q1 Q2)
box N (<[γ := b]>(delete γ2 (delete γ1 f))) P.
Proof.
iIntros (????) "#Hslice1 #Hslice2 Hbox". destruct b.
- iMod (box_delete_full with "Hslice1 Hbox") as (P1) "(HQ1 & Heq1 & Hbox)"; try done.
iMod (box_delete_full with "Hslice2 Hbox") as (P2) "(HQ2 & Heq2 & Hbox)".
done. by simplify_map_eq.
iMod (box_insert_full (Q1 Q2)%I with "[$HQ1 $HQ2] Hbox")
as (γ) "(% & #Hslice & Hbox)". done.
- iMod (slice_delete_full with "Hslice1 Hbox") as (P1) "(HQ1 & Heq1 & Hbox)"; try done.
iMod (slice_delete_full with "Hslice2 Hbox") as (P2) "(HQ2 & Heq2 & Hbox)"; first done.
{ by simplify_map_eq. }
iMod (slice_insert_full (Q1 Q2)%I with "[$HQ1 $HQ2] Hbox")
as (γ) "(% & #Hslice & Hbox)"; first done.
iExists γ. iFrame "%#". iModIntro. iNext.
eapply internal_eq_rewrite_contractive; [by apply _| |by eauto].
iNext. iRewrite "Heq1". iRewrite "Heq2". by rewrite assoc.
- iMod (box_delete_empty with "Hslice1 Hbox") as (P1) "(Heq1 & Hbox)"; try done.
iMod (box_delete_empty with "Hslice2 Hbox") as (P2) "(Heq2 & Hbox)".
done. by simplify_map_eq.
iMod (box_insert_empty (Q1 Q2)%I with "Hbox") as (γ) "(% & #Hslice & Hbox)".
- iMod (slice_delete_empty with "Hslice1 Hbox") as (P1) "(Heq1 & Hbox)"; try done.
iMod (slice_delete_empty with "Hslice2 Hbox") as (P2) "(Heq2 & Hbox)"; first done.
{ by simplify_map_eq. }
iMod (slice_insert_empty (Q1 Q2)%I with "Hbox") as (γ) "(% & #Hslice & Hbox)".
iExists γ. iFrame "%#". iModIntro. iNext.
eapply internal_eq_rewrite_contractive; [by apply _| |by eauto].
iNext. iRewrite "Heq1". iRewrite "Heq2". by rewrite assoc.
......
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