Commit 75cc5c91 authored by Filip Sieczkowski's avatar Filip Sieczkowski

Finished the proof of Ralf's statement of soundness.

parent f95ee313
......@@ -1175,13 +1175,14 @@ Qed.
(HV : is_value e') :
φ (exist _ e' HV).
Proof.
edestruct (soundness _ _ _ _ _ 0 _ _ _ _ fdEmpty (ex_own _ σ, pcm_unit _) 1 HT HSN) as [w' [r' [s' [H_wle [H_phi _] ] ] ] ].
- simpl. hnf. exists (pcm_unit _).
rewrite pcm_op_unit by intuition. reflexivity.
- rewrite Plus.plus_comm. simpl. split.
+ admit. (* TODO: rewrite comm. does not work though?? *)
+ exists (fdEmpty (V:=res)). simpl. split; [reflexivity|].
intros i _. split; [tauto|].
edestruct (soundness _ _ _ _ _ 0 _ _ _ _ fdEmpty (ex_own _ σ, pcm_unit _) 1 HT HSN) as [w [r [s [H_wle [H_phi _] ] ] ] ].
- exists (pcm_unit _); now rewrite pcm_op_unit by apply _.
- rewrite Plus.plus_comm; split.
+ assert (HS : Some (ex_own _ σ, pcm_unit _) · 1 = Some (ex_own _ σ, pcm_unit _));
[| now setoid_rewrite HS].
eapply ores_equiv_eq; now erewrite comm, pcm_op_unit by apply _.
+ exists (fdEmpty (V:=res)); split; [reflexivity|].
intros i _; split; [reflexivity |].
intros _ _ [].
- exact H_phi.
Qed.
......
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