aboutsummaryrefslogtreecommitdiffhomepage
path: root/theories
diff options
context:
space:
mode:
authorGravatar Maxime Dénès <mail@maximedenes.fr>2017-03-14 21:12:31 +0100
committerGravatar Maxime Dénès <mail@maximedenes.fr>2017-03-14 21:12:31 +0100
commit229f858e8c37b577bd07a18f3ca1e0ecd0a912fe (patch)
tree1a16db991125ab8c3cad04ebd1c7780919579e78 /theories
parentb54892932959a3b16e31f780f7f1b638062b0a95 (diff)
parent4ccd6436a014d5d1b27d42e9bda40fb381d1bfce (diff)
Merge PR#444: Simplifying a statement in Hurkens.v + a case study for eauto
Diffstat (limited to 'theories')
-rw-r--r--theories/Logic/Hurkens.v13
1 files changed, 4 insertions, 9 deletions
diff --git a/theories/Logic/Hurkens.v b/theories/Logic/Hurkens.v
index 56e03e965..a10c180cc 100644
--- a/theories/Logic/Hurkens.v
+++ b/theories/Logic/Hurkens.v
@@ -360,13 +360,12 @@ Module NoRetractToModalProposition.
Section Paradox.
Variable M : Prop -> Prop.
-Hypothesis unit : forall A:Prop, A -> M A.
-Hypothesis join : forall A:Prop, M (M A) -> M A.
Hypothesis incr : forall A B:Prop, (A->B) -> M A -> M B.
Lemma strength: forall A (P:A->Prop), M(forall x:A,P x) -> forall x:A,M(P x).
Proof.
- eauto.
+ intros A P h x.
+ eapply incr in h; eauto.
Qed.
(** ** The universe of modal propositions *)
@@ -470,7 +469,7 @@ Hypothesis p2p2 : forall A:NProp, El A -> El (b2p (p2b A)).
Theorem paradox : forall B:NProp, El B.
Proof.
intros B.
- unshelve (refine ((fun h => _) (NoRetractToModalProposition.paradox _ _ _ _ _ _ _ _ _ _))).
+ unshelve (refine ((fun h => _) (NoRetractToModalProposition.paradox _ _ _ _ _ _ _ _))).
+ exact (fun P => ~~P).
+ exact bool.
+ exact p2b.
@@ -480,8 +479,6 @@ Proof.
+ cbn. auto.
+ cbn. auto.
+ cbn. auto.
- + auto.
- + auto.
Qed.
End Paradox.
@@ -516,7 +513,7 @@ Hypothesis p2p2 : forall A:NProp, El A -> El (b2p (p2b A)).
Theorem mparadox : forall B:NProp, El B.
Proof.
intros B.
- unshelve (refine ((fun h => _) (NoRetractToModalProposition.paradox _ _ _ _ _ _ _ _ _ _))).
+ unshelve (refine ((fun h => _) (NoRetractToModalProposition.paradox _ _ _ _ _ _ _ _))).
+ exact (fun P => P).
+ exact bool.
+ exact p2b.
@@ -526,8 +523,6 @@ Proof.
+ cbn. auto.
+ cbn. auto.
+ cbn. auto.
- + auto.
- + auto.
Qed.
End MParadox.