Cleanups

proof.v

-From iris.program_logic Require Export weakestpre.
-From iris.heap_lang Require Export lang.
-From iris.heap_lang.lib.barrier Require Export barrier.
-From iris.prelude Require Import functions.
-From iris.algebra Require Import upred_big_op.
-From iris.program_logic Require Import saved_prop sts.
-From iris.heap_lang Require Import proofmode.
-From flatcomb Require Import protocol flat.
-
-Class flatG Σ := FlatG {
-  flat_stsG :> stsG Σ sts
-}.
-
-Definition flatΣ : gFunctors := #[stsΣ sts].
-
-Instance subG_flatΣ {Σ} : subG flatΣ Σ → flatG Σ.
-Admitted.
-
-(** Now we come to the Iris part of the proof. *)
-Section proof.
-  Context `{!heapG Σ, !flatG Σ} (N : namespace).
-
-  Coercion state_to_val (s : state) : val :=
-    match s with
-    | Init => #0
-    | Req => #1
-    | Exec => #2
-    | Resp => #3
-    | Ack => #4
-    end.
-
-  Arguments state_to_val !_ / : simpl nomatch.
-  
-  Definition flat_inv (l : loc) (s : state) : iProp Σ :=
-    (l ↦ s)%I.
-
-  Definition flat_ctx (γ: gname) (l : loc) : iProp Σ :=
-  (■ (heapN ⊥ N) ★ heap_ctx ★ sts_ctx γ N (flat_inv l))%I.
-
-  Definition init (l: loc) :=
-    (∃ γ, flat_ctx γ l ★ sts_ownS γ {[ Init ]} ∅)%I.
-
-  Definition req (lo: val) P :=
-    (∃ γ req (l: loc), lo = #l ∧ l ↦ InjLV req ★ P req ★ sts_ownS γ {[ Req ]} {[ White ]})%I.
-
-  Lemma doOp_spec (l f o: val) P:
-    ∀ Φ: val → iProp Σ,
-      (* lock l ★ *)
-      req o P
-      ⊢ WP doOp f o {{ Φ }}.
-
-