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author | filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-02-14 14:39:07 +0000 |
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committer | filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-02-14 14:39:07 +0000 |
commit | 67f72c93f5f364591224a86c52727867e02a8f71 (patch) | |
tree | ecf630daf8346e77e6620233d8f3e6c18a0c9b3c /theories/Arith/Wf_nat.v | |
parent | b239b208eb9a66037b0c629cf7ccb6e4b110636a (diff) |
option -dump-glob pour coqdoc
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2474 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Wf_nat.v')
-rwxr-xr-x | theories/Arith/Wf_nat.v | 21 |
1 files changed, 10 insertions, 11 deletions
diff --git a/theories/Arith/Wf_nat.v b/theories/Arith/Wf_nat.v index f34c97d23..16aa58afa 100755 --- a/theories/Arith/Wf_nat.v +++ b/theories/Arith/Wf_nat.v @@ -8,7 +8,7 @@ (*i $Id$ i*) -(* Well-founded relations and natural numbers *) +(** Well-founded relations and natural numbers *) Require Lt. @@ -37,23 +37,22 @@ Qed. Theorem well_founded_gtof : (well_founded A gtof). Proof well_founded_ltof. -(* It is possible to directly prove the induction principle going +(** It is possible to directly prove the induction principle going back to primitive recursion on natural numbers ([induction_ltof1]) or to use the previous lemmas to extract a program with a fixpoint ([induction_ltof2]) -the ML-like program for [induction_ltof1] is : -\begin{verbatim} + +the ML-like program for [induction_ltof1] is : [[ let induction_ltof1 F a = indrec ((f a)+1) a where rec indrec = function 0 -> (function a -> error) |(S m) -> (function a -> (F a (function y -> indrec y m)));; -\end{verbatim} -the ML-like program for [induction_ltof2] is : -\begin{verbatim} +]] + +the ML-like program for [induction_ltof2] is : [[ let induction_ltof2 F a = indrec a where rec indrec a = F a indrec;; -\end{verbatim} -*) +]] *) Theorem induction_ltof1 : (P:A->Set)((x:A)((y:A)(ltof y x)->(P y))->(P x))->(a:A)(P a). @@ -82,8 +81,8 @@ Theorem induction_gtof2 Proof induction_ltof2. -(* If a relation R is compatible with lt i.e. if x R y => f(x) < f(y) - then R is well-founded. *) +(** If a relation [R] is compatible with [lt] i.e. if [x R y => f(x) < f(y)] + then [R] is well-founded. *) Variable R : A->A->Prop. |