From 7d220f8b61649646692983872626d6a8042446a9 Mon Sep 17 00:00:00 2001
From: letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7>
Date: Fri, 20 Mar 2009 01:22:58 +0000
Subject: Directory 'contrib' renamed into 'plugins', to end confusion with
 archive of user contribs

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11996 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 plugins/funind/Recdef.v | 48 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 plugins/funind/Recdef.v

(limited to 'plugins/funind/Recdef.v')

diff --git a/plugins/funind/Recdef.v b/plugins/funind/Recdef.v
new file mode 100644
index 000000000..2d206220e
--- /dev/null
+++ b/plugins/funind/Recdef.v
@@ -0,0 +1,48 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+Require Compare_dec.
+Require Wf_nat.
+
+Section Iter.
+Variable A : Type.
+
+Fixpoint iter (n : nat) : (A -> A) -> A -> A :=
+  fun (fl : A -> A) (def : A) =>
+  match n with
+  | O => def
+  | S m => fl (iter m fl def)
+  end.
+End Iter.
+
+Theorem SSplus_lt : forall p p' : nat, p < S (S (p + p')).
+  intro p; intro p'; change (S p <= S (S (p + p'))); 
+    apply le_S; apply Gt.gt_le_S; change (p < S (p + p')); 
+    apply Lt.le_lt_n_Sm; apply Plus.le_plus_l.
+Qed.
+ 
+
+Theorem Splus_lt : forall p p' : nat, p' < S (p + p').
+  intro p; intro p'; change (S p' <= S (p + p')); 
+    apply Gt.gt_le_S; change (p' < S (p + p')); apply Lt.le_lt_n_Sm;
+       apply Plus.le_plus_r.
+Qed.
+
+Theorem le_lt_SS : forall x y, x <= y -> x < S (S y).
+intro x; intro y; intro H; change (S x <= S (S y)); 
+    apply le_S; apply Gt.gt_le_S; change (x < S y); 
+    apply Lt.le_lt_n_Sm; exact H.
+Qed.
+
+Inductive max_type (m n:nat) : Set :=
+  cmt : forall v, m <= v -> n <= v -> max_type m n.
+
+Definition max : forall m n:nat, max_type m n.
+intros m n; case (Compare_dec.le_gt_dec m n).
+intros h; exists n; [exact h | apply le_n].
+intros h; exists m; [apply le_n | apply Lt.lt_le_weak; exact h].
+Defined.
-- 
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