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Flocq
flocq
Commits
f94725d7
Commit
f94725d7
authored
Dec 21, 2010
by
Guillaume Melquiond
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Added digits_gt_0.
parent
2a3675a5
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-7
src/Calc/Fcalc_digits.v
src/Calc/Fcalc_digits.v
+14
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src/Calc/Fcalc_digits.v
View file @
f94725d7
...
...
@@ -191,16 +191,13 @@ now apply Zpower_NR0.
apply
Zmult_1_r
.
Qed
.
Theorem
digits_g
e
_0
:
forall
n
,
(
0
<
=
digits
n
)
%
Z
.
Theorem
digits_g
t
_0
:
forall
n
,
(
n
<>
0
)
%
Z
->
(
0
<
digits
n
)
%
Z
.
Proof
.
intros
n
.
destruct
(
Z_eq_dec
n
0
)
as
[
H
|
H
].
now
rewrite
H
.
intros
n
H
.
rewrite
digits_ln_beta
with
(
1
:=
H
).
destruct
ln_beta
as
(
e
,
He
).
simpl
.
apply
(
le_bpow
beta
).
apply
Rlt_le
.
apply
(
lt_bpow
beta
).
apply
Rle_lt_trans
with
(
Rabs
(
Z2R
n
)).
simpl
.
rewrite
<-
Z2R_abs
.
...
...
@@ -214,6 +211,16 @@ apply He.
now
apply
(
Z2R_neq
_
0
).
Qed
.
Theorem
digits_ge_0
:
forall
n
,
(
0
<=
digits
n
)
%
Z
.
Proof
.
intros
n
.
destruct
(
Z_eq_dec
n
0
)
as
[
H
|
H
].
now
rewrite
H
.
apply
Zlt_le_weak
.
now
apply
digits_gt_0
.
Qed
.
Theorem
ln_beta_F2R_digits
:
forall
m
e
,
m
<>
Z0
->
(
ln_beta
beta
(
F2R
(
Float
beta
m
e
))
=
digits
m
+
e
:>
Z
)
%
Z
.
...
...
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