diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-01-03 18:51:13 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-01-03 18:51:13 +0000 |
| commit | 8e2d90a6a9f4480026afd433fc997d9958f76a38 (patch) | |
| tree | 6a92d154766a3a8934b91705acf79cc994a42061 /theories/Numbers/NatInt/NZBase.v | |
| parent | 05662999c9ab0183c0f97fc18579379142ac7b38 (diff) | |
Numbers: some improvements in proofs
- a ltac solve_proper which generalizes solve_predicate_wd and co
- using le_elim is nicer that (apply le_lteq; destruct ...)
- "apply ->" can now be "apply" most of the time.
Benefit: NumPrelude is now almost empty
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13762 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/NatInt/NZBase.v')
| -rw-r--r-- | theories/Numbers/NatInt/NZBase.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Numbers/NatInt/NZBase.v b/theories/Numbers/NatInt/NZBase.v index a86fec3fd..7c7f43de0 100644 --- a/theories/Numbers/NatInt/NZBase.v +++ b/theories/Numbers/NatInt/NZBase.v @@ -48,7 +48,7 @@ Theorem succ_inj_wd : forall n1 n2, S n1 == S n2 <-> n1 == n2. Proof. intros; split. apply succ_inj. -apply succ_wd. +intros. now apply succ_wd. Qed. Theorem succ_inj_wd_neg : forall n m, S n ~= S m <-> n ~= m. @@ -61,7 +61,7 @@ left-inverse to the successor at this point *) Section CentralInduction. -Variable A : predicate t. +Variable A : t -> Prop. Hypothesis A_wd : Proper (eq==>iff) A. Theorem central_induction : @@ -70,7 +70,7 @@ Theorem central_induction : forall n, A n. Proof. intros z Base Step; revert Base; pattern z; apply bi_induction. -solve_predicate_wd. +solve_proper. intro; now apply bi_induction. intro; pose proof (Step n); tauto. Qed. |