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-rwxr-xr-xtheories/Arith/Wf_nat.v21
1 files changed, 10 insertions, 11 deletions
diff --git a/theories/Arith/Wf_nat.v b/theories/Arith/Wf_nat.v
index f34c97d23f..16aa58afac 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.