diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-09-17 20:26:30 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2011-09-17 20:26:30 +0000 |
| commit | 1d68059e265f72e1665cc82b51707d9778103ac1 (patch) | |
| tree | 53d6cf05b6c1f0f1cc680171eb26a6663d4cfcc2 /theories/Arith | |
| parent | 9dc9bd9468cd7bf72715dab4b0a074664667a3ad (diff) | |
Euclid: make the proof transparent (example of extraction in stdlib)
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14477 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith')
| -rw-r--r-- | theories/Arith/Euclid.v | 9 |
1 files changed, 4 insertions, 5 deletions
diff --git a/theories/Arith/Euclid.v b/theories/Arith/Euclid.v index 07fbfe1bf..513fd1108 100644 --- a/theories/Arith/Euclid.v +++ b/theories/Arith/Euclid.v @@ -10,14 +10,13 @@ Require Import Mult. Require Import Compare_dec. Require Import Wf_nat. -Open Local Scope nat_scope. +Local Open Scope nat_scope. Implicit Types a b n q r : nat. Inductive diveucl a b : Set := divex : forall q r, b > r -> a = q * b + r -> diveucl a b. - Lemma eucl_dev : forall n, n > 0 -> forall m:nat, diveucl m n. Proof. intros b H a; pattern a in |- *; apply gt_wf_rec; intros n H0. @@ -30,7 +29,7 @@ Proof. elim e; auto with arith. intros gtbn. apply divex with 0 n; simpl in |- *; auto with arith. -Qed. +Defined. Lemma quotient : forall n, @@ -48,7 +47,7 @@ Proof. elim H1; auto with arith. intros gtbn. exists 0; exists n; simpl in |- *; auto with arith. -Qed. +Defined. Lemma modulo : forall n, @@ -66,4 +65,4 @@ Proof. elim H1; auto with arith. intros gtbn. exists n; exists 0; simpl in |- *; auto with arith. -Qed. +Defined. |