diff options
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. |