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-rw-r--r--theories/Logic/Berardi.v16
1 files changed, 7 insertions, 9 deletions
diff --git a/theories/Logic/Berardi.v b/theories/Logic/Berardi.v
index d954f40c..38377573 100644
--- a/theories/Logic/Berardi.v
+++ b/theories/Logic/Berardi.v
@@ -1,13 +1,11 @@
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2011 *)
+(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
-(*i $Id: Berardi.v 14641 2011-11-06 11:59:10Z herbelin $ i*)
-
(** This file formalizes Berardi's paradox which says that in
the calculus of constructions, excluded middle (EM) and axiom of
choice (AC) imply proof irrelevance (PI).
@@ -47,7 +45,7 @@ Lemma AC_IF :
(B -> Q e1) -> (~ B -> Q e2) -> Q (IFProp B e1 e2).
Proof.
intros P B e1 e2 Q p1 p2.
-unfold IFProp in |- *.
+unfold IFProp.
case (EM B); assumption.
Qed.
@@ -78,7 +76,7 @@ Record retract_cond : Prop :=
Lemma AC : forall r:retract_cond, retract -> forall a:A, j2 r (i2 r a) = a.
Proof.
intros r.
-case r; simpl in |- *.
+case r; simpl.
trivial.
Qed.
@@ -115,7 +113,7 @@ Lemma retract_pow_U_U : retract (pow U) U.
Proof.
exists g f.
intro a.
-unfold f, g in |- *; simpl in |- *.
+unfold f, g; simpl.
apply AC.
exists (fun x:pow U => x) (fun x:pow U => x).
trivial.
@@ -132,8 +130,8 @@ Definition R : U := g (fun u:U => Not_b (u U u)).
Lemma not_has_fixpoint : R R = Not_b (R R).
Proof.
-unfold R at 1 in |- *.
-unfold g in |- *.
+unfold R at 1.
+unfold g.
rewrite AC with (r := L1 U U) (a := fun u:U => Not_b (u U u)).
trivial.
exists (fun x:pow U => x) (fun x:pow U => x); trivial.
@@ -143,7 +141,7 @@ Qed.
Theorem classical_proof_irrelevence : T = F.
Proof.
generalize not_has_fixpoint.
-unfold Not_b in |- *.
+unfold Not_b.
apply AC_IF.
intros is_true is_false.
elim is_true; elim is_false; trivial.