diff options
Diffstat (limited to 'theories/Reals/Ranalysis1.v')
| -rw-r--r-- | theories/Reals/Ranalysis1.v | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/theories/Reals/Ranalysis1.v b/theories/Reals/Ranalysis1.v index f60c609a07..b7d4902254 100644 --- a/theories/Reals/Ranalysis1.v +++ b/theories/Reals/Ranalysis1.v @@ -234,8 +234,8 @@ Qed. Definition derivable_pt_lim f (x l:R) : Prop := forall eps:R, 0 < eps -> - exists delta : posreal - | (forall h:R, + exists delta : posreal, + (forall h:R, h <> 0 -> Rabs h < delta -> Rabs ((f (x + h) - f x) / h - l) < eps). Definition derivable_pt_abs f (x l:R) : Prop := derivable_pt_lim f x l. @@ -255,7 +255,7 @@ Arguments Scope derive [Rfun_scope _]. Definition antiderivative f (g:R -> R) (a b:R) : Prop := (forall x:R, - a <= x <= b -> exists pr : derivable_pt g x | f x = derive_pt g x pr) /\ + a <= x <= b -> exists pr : derivable_pt g x, f x = derive_pt g x pr) /\ a <= b. (************************************) (** Class of differential functions *) @@ -446,7 +446,7 @@ Qed. (***********************************) (**********) Lemma derivable_derive : - forall f (x:R) (pr:derivable_pt f x), exists l : R | derive_pt f x pr = l. + forall f (x:R) (pr:derivable_pt f x), exists l : R, derive_pt f x pr = l. intros; exists (projT1 pr). unfold derive_pt in |- *; reflexivity. Qed. @@ -1476,4 +1476,4 @@ unfold Rdiv in |- *; rewrite <- Ropp_mult_distr_l_reverse; apply Rplus_lt_reg_r with l. unfold Rminus in |- *; rewrite Rplus_opp_r; rewrite Rplus_0_r; assumption. apply Rinv_0_lt_compat; prove_sup0. -Qed.
\ No newline at end of file +Qed. |