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authorGravatar filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7>2001-04-11 12:41:41 +0000
committerGravatar filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7>2001-04-11 12:41:41 +0000
commit4ac0580306ea9e45da1863316936d700969465ad (patch)
treebf7595cd76895f3a349e7e75ca9d64231b01dcf8 /theories/Arith/Wf_nat.v
parent8a7452976731275212f0c464385b380e2d590f5e (diff)
documentation automatique de la bibliothèque standard
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1578 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Wf_nat.v')
-rwxr-xr-xtheories/Arith/Wf_nat.v12
1 files changed, 8 insertions, 4 deletions
diff --git a/theories/Arith/Wf_nat.v b/theories/Arith/Wf_nat.v
index 3e8d174c8..041d24349 100755
--- a/theories/Arith/Wf_nat.v
+++ b/theories/Arith/Wf_nat.v
@@ -38,17 +38,21 @@ Theorem well_founded_gtof : (well_founded A gtof).
Proof well_founded_ltof.
(* It is possible to directly prove the induction principle going
- back to primitive recursion on natural numbers (induction_ltof1)
+ 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 :
+ ([induction_ltof2])
+the ML-like program for [induction_ltof1] is :
+\begin{verbatim}
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)));;
-the ML-like program for induction_ltof2 is :
+\end{verbatim}
+the ML-like program for [induction_ltof2] is :
+\begin{verbatim}
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).