Commit 7b5cf8fe authored by Ralf Jung's avatar Ralf Jung

show that even \later^n False is inconsistent (for any fixed n); properly use...

show that even \later^n False is inconsistent (for any fixed n); properly use pvs in counter_examples
parent d999d538
Pipeline #2558 passed with stage
in 3 minutes and 56 seconds
......@@ -346,10 +346,18 @@ Qed.
Global Instance: AntiSymm () (@uPred_entails M).
Proof. intros P Q HPQ HQP; split=> x n; by split; [apply HPQ|apply HQP]. Qed.
Lemma sound : ¬ (True False).
Proof.
unseal. intros [H]. apply (H 0 ); last done. apply ucmra_unit_validN.
Qed.
Lemma soundness_later n : ¬ (True ^n False).
Proof.
unseal. intros [H].
assert ((^n @uPred_pure_def M False) n )%I as Hn.
(* So Coq still has no nice way to say "make this precondition of that lemma a goal"?!? *)
{ apply H; by auto using ucmra_unit_validN. }
clear H. induction n.
- done.
- move: Hn. simpl. unseal. done.
Qed.
Theorem soundness : ¬ (True False).
Proof. exact (soundness_later 0). Qed.
Lemma equiv_spec P Q : (P Q) (P Q) (Q P).
Proof.
......
......@@ -9,11 +9,12 @@ Section savedprop.
Notation iProp := (uPred M).
Notation "¬ P" := ((P False))%I : uPred_scope.
(* Saved Propositions. *)
Context (sprop : Type) (saved : sprop iProp iProp).
(* Saved Propositions and view shifts. *)
Context (sprop : Type) (saved : sprop iProp iProp) (pvs : iProp iProp).
Hypothesis pvs_mono : forall P Q, (P Q) pvs P pvs Q.
Hypothesis sprop_persistent : forall i P, PersistentP (saved i P).
Hypothesis sprop_alloc_dep :
forall (P : sprop iProp), True i, saved i (P i).
forall (P : sprop iProp), True pvs ( i, saved i (P i)).
Hypothesis sprop_agree :
forall i P Q, saved i P saved i Q P Q.
......@@ -50,16 +51,17 @@ Section savedprop.
(* We can obtain such a [Q i]. *)
Lemma make_Q :
True i, Q i.
True pvs ( i, Q i).
Proof.
apply sprop_alloc_dep.
Qed.
(* Put together all the pieces to derive a contradiction. *)
Lemma contradiction : False.
(* TODO: Have a lemma in upred.v that says that we cannot view shift to False. *)
Lemma contradiction : True pvs False.
Proof.
apply (@uPred.sound M). iIntros "".
iPoseProof make_Q as "HQ". iDestruct "HQ" as (i) "HQ".
rewrite make_Q. apply pvs_mono.
iIntros "HQ". iDestruct "HQ" as (i) "HQ".
iApply (@no_self_contradiction (A i) _).
by iApply Q_self_contradiction.
Qed.
......
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