diff options
Diffstat (limited to 'theories/Reals/Rfunctions.v')
| -rw-r--r-- | theories/Reals/Rfunctions.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Reals/Rfunctions.v b/theories/Reals/Rfunctions.v index 62eff1d1f..188699e6d 100644 --- a/theories/Reals/Rfunctions.v +++ b/theories/Reals/Rfunctions.v @@ -226,10 +226,10 @@ Lemma Pow_x_infinity : forall x:R, Rabs x > 1 -> forall b:R, - exists N : nat | (forall n:nat, (n >= N)%nat -> Rabs (x ^ n) >= b). + exists N : nat, (forall n:nat, (n >= N)%nat -> Rabs (x ^ n) >= b). Proof. intros; elim (archimed (b * / (Rabs x - 1))); intros; clear H1; - cut ( exists N : nat | INR N >= b * / (Rabs x - 1)). + cut (exists N : nat, INR N >= b * / (Rabs x - 1)). intro; elim H1; clear H1; intros; exists x0; intros; apply (Rge_trans (Rabs (x ^ n)) (Rabs (x ^ x0)) b). apply Rle_ge; apply Power_monotonic; assumption. @@ -289,7 +289,7 @@ Lemma pow_lt_1_zero : Rabs x < 1 -> forall y:R, 0 < y -> - exists N : nat | (forall n:nat, (n >= N)%nat -> Rabs (x ^ n) < y). + exists N : nat, (forall n:nat, (n >= N)%nat -> Rabs (x ^ n) < y). Proof. intros; elim (Req_dec x 0); intro. exists 1%nat; rewrite H1; intros n GE; rewrite pow_ne_zero. @@ -789,5 +789,5 @@ Qed. Definition infinit_sum (s:nat -> R) (l:R) : Prop := forall eps:R, eps > 0 -> - exists N : nat - | (forall n:nat, (n >= N)%nat -> R_dist (sum_f_R0 s n) l < eps).
\ No newline at end of file + exists N : nat, + (forall n:nat, (n >= N)%nat -> R_dist (sum_f_R0 s n) l < eps). |