diff options
Diffstat (limited to 'theories/Reals/RIneq.v')
| -rw-r--r-- | theories/Reals/RIneq.v | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index ad67223ad..346938735 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -1306,7 +1306,7 @@ Hint Resolve not_1_INR: real. (**********) -Lemma IZN : forall n:Z, (0 <= n)%Z -> exists m : nat | n = Z_of_nat m. +Lemma IZN : forall n:Z, (0 <= n)%Z -> exists m : nat, n = Z_of_nat m. intros z; idtac; apply Z_of_nat_complete; assumption. Qed. @@ -1483,7 +1483,7 @@ Lemma tech_single_z_r_R1 : forall r (n:Z), r < IZR n -> IZR n <= r + 1 -> - ( exists s : Z | s <> n /\ r < IZR s /\ IZR s <= r + 1) -> False. + (exists s : Z, s <> n /\ r < IZR s /\ IZR s <= r + 1) -> False. intros r z H1 H2 [s [H3 [H4 H5]]]. apply H3; apply single_z_r_R1 with r; trivial. Qed. @@ -1626,6 +1626,6 @@ Qed. (**********) Lemma completeness_weak : forall E:R -> Prop, - bound E -> ( exists x : R | E x) -> exists m : R | is_lub E m. + bound E -> (exists x : R, E x) -> exists m : R, is_lub E m. intros; elim (completeness E H H0); intros; split with x; assumption. Qed. |