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authorGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-05-06 12:01:31 +0000
committerGravatar herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7>2002-05-06 12:01:31 +0000
commite5c7edc338bc31c45b99f305b9d6c068bbd1b269 (patch)
tree0587103dadb23d30a0411c23ab6e1c698e52af05 /theories/Bool/Bool.v
parent866d547fccecf9b07234a5933b3f0a835d179da2 (diff)
Standardisation
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2667 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Bool/Bool.v')
-rwxr-xr-xtheories/Bool/Bool.v12
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Bool/Bool.v b/theories/Bool/Bool.v
index cfd6f656a..9cb4c1bb2 100755
--- a/theories/Bool/Bool.v
+++ b/theories/Bool/Bool.v
@@ -37,14 +37,14 @@ Hints Immediate Is_true_eq_right Is_true_eq_left : bool.
(*******************)
Lemma diff_true_false : ~true=false.
-Goal.
+Proof.
Unfold not; Intro contr; Change (Is_true false).
Elim contr; Simpl; Trivial with bool.
Qed.
Hints Resolve diff_true_false : bool v62.
Lemma diff_false_true : ~false=true.
-Goal.
+Proof.
Red; Intros H; Apply diff_true_false.
Symmetry.
Assumption.
@@ -178,12 +178,12 @@ Definition negb := [b:bool]Cases b of
(**************************)
Lemma negb_intro : (b:bool)b=(negb (negb b)).
-Goal.
+Proof.
Induction b; Reflexivity.
Qed.
Lemma negb_elim : (b:bool)(negb (negb b))=b.
-Goal.
+Proof.
Induction b; Reflexivity.
Qed.
@@ -200,12 +200,12 @@ Proof.
Qed.
Lemma negb_sym : (b,b':bool)(b'=(negb b))->(b=(negb b')).
-Goal.
+Proof.
Induction b; Induction b'; Intros; Simpl; Trivial with bool.
Qed.
Lemma no_fixpoint_negb : (b:bool)~(negb b)=b.
-Goal.
+Proof.
Induction b; Simpl; Unfold not; Intro; Apply diff_true_false; Auto with bool.
Qed.