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| author |  emakarov <emakarov@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2007-07-13 17:52:22 +0000 |
|---|---|---|
| committer | emakarov <emakarov@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2007-07-13 17:52:22 +0000 |
| commit | e8f786b4ef55aae4fc40c46f1b73c185ee0e5819 (patch) | |
| tree | 6c6f65c85a1476572ebca39c975e59c38d2e10d3 /theories/Numbers/NumPrelude.v | |
| parent | 72cd18d711b3e9ea2ecb0d657187dc5febfbc8e3 (diff) | |
An update on axiomatization of number classes.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10002 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/NumPrelude.v')
| -rw-r--r-- | theories/Numbers/NumPrelude.v | 9 |
1 files changed, 8 insertions, 1 deletions
diff --git a/theories/Numbers/NumPrelude.v b/theories/Numbers/NumPrelude.v index 2fe547681..a23fb0bc0 100644 --- a/theories/Numbers/NumPrelude.v +++ b/theories/Numbers/NumPrelude.v @@ -18,7 +18,14 @@ Definition eq_bool := (@eq bool). Inductive eq_true : bool -> Prop := is_eq_true : eq_true true. Coercion eq_true : bool >-> Sortclass. -Theorem neg_eq_true : forall x : bool, ~ x -> x = false. +Theorem eq_true_unfold : forall b : bool, b <-> b = true. +Proof. +intro b; split; intro H. +now inversion H. +now rewrite H. +Qed. + +Theorem eq_true_neg : forall x : bool, ~ x -> x = false. Proof. intros x H; destruct x; [elim (H is_eq_true) | reflexivity]. Qed. |