Commit 42cf780a authored by Jacques-Henri Jourdan's avatar Jacques-Henri Jourdan

Stronger splitting rule for boxes.

parent 26ae0c67
Pipeline #3125 passed with stage
in 10 minutes and 34 seconds
......@@ -233,22 +233,24 @@ Qed.
Lemma box_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
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.
iExists γ1, γ2. iFrame "%#". iModIntro. iSplit.
{ iPureIntro. by eapply lookup_insert_None. }
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)".
iExists γ1, γ2. iFrame "%#". iModIntro. iSplit.
{ iPureIntro. by eapply lookup_insert_None. }
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.
Qed.
......
Markdown is supported
0%
or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment