diff options
Diffstat (limited to 'theories/Arith/Wf_nat.v')
| -rwxr-xr-x | theories/Arith/Wf_nat.v | 12 |
1 files changed, 8 insertions, 4 deletions
diff --git a/theories/Arith/Wf_nat.v b/theories/Arith/Wf_nat.v index 3e8d174c88..041d243495 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). |