improve

misc.v

@@ -4,7 +4,7 @@ From iris.heap_lang Require Export lang.
 From iris.heap_lang Require Import proofmode notation.
 From iris.heap_lang.lib Require Import spin_lock.
 From iris.tests Require Import atomic.
-From iris.algebra Require Import dec_agree frac.
+From iris.algebra Require Import dec_agree frac gmap upred_big_op.
 From iris.program_logic Require Import auth.
 Import uPred.
 
@@ -32,5 +32,54 @@ Section lemmas.
   Lemma pair_l_frac_op_1' (g g': val):
      (1%Qp, DecAgree g') ~~> (((1/2)%Qp, DecAgree g') ⋅ ((1/2)%Qp, DecAgree g')).
   Proof. by rewrite pair_op dec_agree_idemp frac_op' Qp_div_2. Qed.
-  
+
+  Lemma split_mapk
+        {Σ} {K: Type} `{Countable K} {V: cmraT}
+        (m: gmapUR K V) (k: K) (v: V) (R: K → iProp Σ) :
+    m !! k = Some v → ([★ map] k ↦ v ∈ m, R k) ⊢ R k ★ ([★ map] k ↦ v ∈ delete k m, R k).
+  Proof. iIntros (?) "HRm". by iApply (big_sepM_delete (fun k _ => R k)). Qed.
+
+  Lemma split_mapv
+        {Σ} {K: Type} `{Countable K} {V: cmraT}
+        (m: gmapUR K V) (k: K) (v: V) (R: V → iProp Σ) :
+    m !! k = Some v → ([★ map] k ↦ v ∈ m, R v) ⊢ R v ★ ([★ map] k ↦ v ∈ delete k m, R v).
+  Proof. iIntros (?) "HRm". by iApply (big_sepM_delete (fun _ v => R v)). Qed.
+
+  Lemma map_agree {A: cmraT} m m' (hd: loc) (p q: A) x y:
+    m !! hd = Some (p, DecAgree y) →
+    x ≠ y → m = {[hd := (q, DecAgree x)]} ⋅ m' → False.
+  Proof.
+    intros H1 H2 H3.
+    subst. rewrite lookup_op lookup_singleton in H1.
+    destruct (m' !! hd) as [[b [c|]]|] eqn:Heqn; rewrite Heqn in H1; inversion H1=>//.
+    destruct (decide (x = c)) as [->|Hneq3]=>//.
+    - rewrite dec_agree_idemp in H3. by inversion H3.        
+    - rewrite dec_agree_ne in H3=>//.
+  Qed.
+
+  Lemma map_agree_none {A: cmraT} m m' (hd: loc) (q: A) x:
+    m !! hd = None → m = {[hd := (q, DecAgree x)]} ⋅ m' → False.
+  Proof.
+    intros H1 H2. subst. rewrite lookup_op lookup_singleton in H1.
+    destruct (m' !! hd)=>//.
+  Qed.
+
 End lemmas.
+
+
+Section heap_extra.
+  Context `{heapG Σ}.
+
+  Lemma bogus_heap p (q1 q2: Qp) a b:
+    ~((q1 + q2)%Qp ≤ 1%Qp)%Qc →
+    heap_ctx ★ p ↦{q1} a ★ p ↦{q2} b ⊢ False.
+  Proof.
+    iIntros (?) "(#Hh & Hp1 & Hp2)".
+    iCombine "Hp1" "Hp2" as "Hp".
+    iDestruct (heap_mapsto_op_1 with "Hp") as "[_ Hp]".
+    rewrite heap_mapsto_eq. iDestruct (auth_own_valid with "Hp") as %H'.
+    apply singleton_valid in H'. destruct H' as [H' _].
+    auto.
+  Qed.
+  
+End heap_extra.