Commit 6b6381fe authored by Robbert Krebbers's avatar Robbert Krebbers

Use rvs in counter_example and integrate with adequacy to obtain False.

parent bd660383
......@@ -2,8 +2,7 @@ From iris.algebra Require Import upred.
From iris.proofmode Require Import tactics.
(** This proves that we need the ▷ in a "Saved Proposition" construction with
name-dependend allocation. *)
(** We fork in [uPred M] for any M, but the proof would work in any BI. *)
name-dependend allocation. *)
Section savedprop.
Context (M : ucmraT).
Notation iProp := (uPred M).
......@@ -11,11 +10,10 @@ Section savedprop.
Implicit Types P : iProp.
(* Saved Propositions and view shifts. *)
Context (sprop : Type) (saved : sprop iProp iProp) (pvs : iProp iProp).
Hypothesis pvs_mono : P Q, (P Q) pvs P pvs Q.
Context (sprop : Type) (saved : sprop iProp iProp).
Hypothesis sprop_persistent : i P, PersistentP (saved i P).
Hypothesis sprop_alloc_dep :
(P : sprop iProp), True pvs ( i, saved i (P i)).
(P : sprop iProp), True =r=> ( i, saved i (P i)).
Hypothesis sprop_agree : i P Q, saved i P saved i Q P Q.
(* Self-contradicting assertions are inconsistent *)
......@@ -44,14 +42,19 @@ Section savedprop.
Proof. iIntros "#HQ !". by iApply (saved_is_A i (¬A i)). Qed.
(* We can obtain such a [Q i]. *)
Lemma make_Q : True pvs ( i, Q i).
Lemma make_Q : True =r=> i, Q i.
Proof. apply sprop_alloc_dep. Qed.
(* Put together all the pieces to derive a contradiction. *)
(* TODO: Have a lemma in upred.v that says that we cannot view shift to False. *)
Lemma contradiction : True pvs False.
Lemma rvs_false : (True : uPred M) =r=> False.
Proof.
rewrite make_Q. apply pvs_mono. iDestruct 1 as (i) "HQ".
rewrite make_Q. apply uPred.rvs_mono. iDestruct 1 as (i) "HQ".
iApply (no_self_contradiction (A i)). by iApply Q_self_contradiction.
Qed.
Lemma contradiction : False.
Proof.
apply (@uPred.adequacy M False 1); simpl.
rewrite -uPred.later_intro. apply rvs_false.
Qed.
End savedprop.
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