diff options
Diffstat (limited to 'theories/NArith/Ndigits.v')
| -rw-r--r-- | theories/NArith/Ndigits.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/NArith/Ndigits.v b/theories/NArith/Ndigits.v index 633f82edb..a3326ccd3 100644 --- a/theories/NArith/Ndigits.v +++ b/theories/NArith/Ndigits.v @@ -511,7 +511,7 @@ Lemma Nless_trans : Nless a a' = true -> Nless a' a'' = true -> Nless a a'' = true. Proof. induction a as [|a IHa|a IHa] using N_ind_double; intros a' a'' H H0. - destruct (Nless N0 a'') in *. trivial. + destruct (Nless N0 a'') as Heqb in *. trivial. rewrite (N0_less_2 a'' Heqb), (Nless_z a') in H0. discriminate H0. induction a' as [|a' _|a' _] using N_ind_double. rewrite (Nless_z (Ndouble a)) in H. discriminate H. @@ -539,10 +539,10 @@ Lemma Nless_total : forall a a', {Nless a a' = true} + {Nless a' a = true} + {a = a'}. Proof. induction a using N_rec_double; intro a'. - destruct (Nless N0 a') in *. left. left. auto. + destruct (Nless N0 a') as Heqb in *. left. left. auto. right. rewrite (N0_less_2 a' Heqb). reflexivity. induction a' as [|a' _|a' _] using N_rec_double. - destruct (Nless N0 (Ndouble a)) in *. left. right. auto. + destruct (Nless N0 (Ndouble a)) as Heqb in *. left. right. auto. right. exact (N0_less_2 _ Heqb). rewrite 2!Nless_def_1. destruct (IHa a') as [ | ->]. left. assumption. |