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| author |  herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2005-04-26 16:42:06 +0000 |
|---|---|---|
| committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2005-04-26 16:42:06 +0000 |
| commit | fde155742bf2dabc08dff82ef3a1bbbb676c8c4b (patch) | |
| tree | 8d6ab563c5c432ff4c568ba98c673afff4a895e8 /theories/ZArith/Wf_Z.v | |
| parent | 2d5be7b772820099c057b153b29d4d1554c895e1 (diff) | |
Fixed hypotheses of Z_lt_induction (see #957)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@6962 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith/Wf_Z.v')
| -rw-r--r-- | theories/ZArith/Wf_Z.v | 5 |
1 files changed, 3 insertions, 2 deletions
diff --git a/theories/ZArith/Wf_Z.v b/theories/ZArith/Wf_Z.v index 17c530ed7..b8113b2e0 100644 --- a/theories/ZArith/Wf_Z.v +++ b/theories/ZArith/Wf_Z.v @@ -180,7 +180,7 @@ Qed. Lemma Z_lt_rec : forall P:Z -> Type, - (forall x:Z, (forall y:Z, 0 <= y < x -> P y) -> P x) -> + (forall x:Z, (forall y:Z, 0 <= y < x -> P y) -> 0 <= x -> P x) -> forall x:Z, 0 <= x -> P x. Proof. intros P Hrec z; pattern z in |- *; apply (well_founded_induction_type R_wf). @@ -189,13 +189,14 @@ apply Hrec; intros. assert (H2 : 0 < 0). apply Zle_lt_trans with y; intuition. inversion H2. +assumption. firstorder. unfold Zle, Zcompare in H; elim H; auto. Defined. Lemma Z_lt_induction : forall P:Z -> Prop, - (forall x:Z, (forall y:Z, 0 <= y < x -> P y) -> P x) -> + (forall x:Z, (forall y:Z, 0 <= y < x -> P y) -> 0 <= x -> P x) -> forall x:Z, 0 <= x -> P x. Proof. exact Z_lt_rec. |