diff options
Diffstat (limited to 'theories/Arith/Euclid.v')
| -rw-r--r-- | theories/Arith/Euclid.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Arith/Euclid.v b/theories/Arith/Euclid.v index fdd149e01a..d5f715d843 100644 --- a/theories/Arith/Euclid.v +++ b/theories/Arith/Euclid.v @@ -21,7 +21,7 @@ Inductive diveucl a b : Set := Lemma eucl_dev : forall n, n > 0 -> forall m:nat, diveucl m n. Proof. - induction m as (m,H0) using gt_wf_rec. + intros n H m; induction m as (m,H0) using gt_wf_rec. destruct (le_gt_dec n m) as [Hlebn|Hgtbn]. destruct (H0 (m - n)) as (q,r,Hge0,Heq); auto with arith. apply divex with (S q) r; trivial. @@ -34,7 +34,7 @@ Lemma quotient : n > 0 -> forall m:nat, {q : nat | exists r : nat, m = q * n + r /\ n > r}. Proof. - induction m as (m,H0) using gt_wf_rec. + intros n H m; induction m as (m,H0) using gt_wf_rec. destruct (le_gt_dec n m) as [Hlebn|Hgtbn]. destruct (H0 (m - n)) as (q & Hq); auto with arith; exists (S q). destruct Hq as (r & Heq & Hgt); exists r; split; trivial. @@ -47,7 +47,7 @@ Lemma modulo : n > 0 -> forall m:nat, {r : nat | exists q : nat, m = q * n + r /\ n > r}. Proof. - induction m as (m,H0) using gt_wf_rec. + intros n H m; induction m as (m,H0) using gt_wf_rec. destruct (le_gt_dec n m) as [Hlebn|Hgtbn]. destruct (H0 (m - n)) as (r & Hr); auto with arith; exists r. destruct Hr as (q & Heq & Hgt); exists (S q); split; trivial. |