diff options
| author |  herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2001-08-05 19:04:16 +0000 |
|---|---|---|
| committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2001-08-05 19:04:16 +0000 |
| commit | 83c56744d7e232abeb5f23e6d0f23cd0abc14a9c (patch) | |
| tree | 6d7d4c2ce3bb159b8f81a4193abde1e3573c28d4 /theories/Arith/Wf_nat.v | |
| parent | f7351ff222bad0cc906dbee3c06b20babf920100 (diff) | |
Expérimentation de NewDestruct et parfois NewInduction
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1880 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Wf_nat.v')
| -rwxr-xr-x | theories/Arith/Wf_nat.v | 18 |
1 files changed, 9 insertions, 9 deletions
diff --git a/theories/Arith/Wf_nat.v b/theories/Arith/Wf_nat.v index ff502af94..f34c97d23 100755 --- a/theories/Arith/Wf_nat.v +++ b/theories/Arith/Wf_nat.v @@ -25,12 +25,12 @@ Proof. Red. Cut (n:nat)(a:A)(lt (f a) n)->(Acc A ltof a). Intros H a; Apply (H (S (f a))); Auto with arith. -Induction n. +NewInduction n. Intros; Absurd (lt (f a) O); Auto with arith. -Intros m Hm a ltSma. +Intros a ltSma. Apply Acc_intro. Unfold ltof; Intros b ltfafb. -Apply Hm. +Apply IHn. Apply lt_le_trans with (f a); Auto with arith. Qed. @@ -60,12 +60,12 @@ Theorem induction_ltof1 Proof. Intros P F; Cut (n:nat)(a:A)(lt (f a) n)->(P a). Intros H a; Apply (H (S (f a))); Auto with arith. -Induction n. +NewInduction n. Intros; Absurd (lt (f a) O); Auto with arith. -Intros m Hm a ltSma. +Intros a ltSma. Apply F. Unfold ltof; Intros b ltfafb. -Apply Hm. +Apply IHn. Apply lt_le_trans with (f a); Auto with arith. Qed. @@ -94,12 +94,12 @@ Proof. Red. Cut (n:nat)(a:A)(lt (f a) n)->(Acc A R a). Intros H a; Apply (H (S (f a))); Auto with arith. -Induction n. +NewInduction n. Intros; Absurd (lt (f a) O); Auto with arith. -Intros m Hm a ltSma. +Intros a ltSma. Apply Acc_intro. Intros b ltfafb. -Apply Hm. +Apply IHn. Apply lt_le_trans with (f a); Auto with arith. Save. |