diff options
| author |  coq <coq@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2001-04-20 16:00:43 +0000 |
|---|---|---|
| committer | coq <coq@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2001-04-20 16:00:43 +0000 |
| commit | d857c99c6c985eb36ce8a4b2667dc0b5ccca115c (patch) | |
| tree | 2ea53c80dd3319b24c38b15cb5be5a582c9b302a /theories/Arith/Wf_nat.v | |
| parent | 4837b599b4f158decc91f615a25e3a636c6ced5d (diff) | |
Library doc adjustments (until page 140)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1655 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Wf_nat.v')
| -rwxr-xr-x | theories/Arith/Wf_nat.v | 11 |
1 files changed, 7 insertions, 4 deletions
diff --git a/theories/Arith/Wf_nat.v b/theories/Arith/Wf_nat.v index 2f100ebc5..ff502af94 100755 --- a/theories/Arith/Wf_nat.v +++ b/theories/Arith/Wf_nat.v @@ -55,7 +55,8 @@ the ML-like program for [induction_ltof2] is : \end{verbatim} *) -Theorem induction_ltof1 : (P:A->Set)((x:A)((y:A)(ltof y x)->(P y))->(P x))->(a:A)(P a). +Theorem induction_ltof1 + : (P:A->Set)((x:A)((y:A)(ltof y x)->(P y))->(P x))->(a:A)(P a). 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. @@ -68,14 +69,16 @@ Apply Hm. Apply lt_le_trans with (f a); Auto with arith. Qed. -Theorem induction_gtof1 : (P:A->Set)((x:A)((y:A)(gtof y x)->(P y))->(P x))->(a:A)(P a). +Theorem induction_gtof1 + : (P:A->Set)((x:A)((y:A)(gtof y x)->(P y))->(P x))->(a:A)(P a). Proof induction_ltof1. Theorem induction_ltof2 - : (P:A->Set)((x:A)((y:A)(ltof y x)->(P y))->(P x))->(a:A)(P a). + : (P:A->Set)((x:A)((y:A)(ltof y x)->(P y))->(P x))->(a:A)(P a). Proof (well_founded_induction A ltof well_founded_ltof). -Theorem induction_gtof2 : (P:A->Set)((x:A)((y:A)(gtof y x)->(P y))->(P x))->(a:A)(P a). +Theorem induction_gtof2 + : (P:A->Set)((x:A)((y:A)(gtof y x)->(P y))->(P x))->(a:A)(P a). Proof induction_ltof2. |