Some box/slice renaming.

base_logic/lib/boxes.v

@@ -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.