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AVA
FloVer
Commits
5c7b0225
Commit
5c7b0225
authored
Feb 06, 2017
by
Heiko Becker
Browse files
Move some lemmas
parent
2e3aaa7d
Changes
2
Hide whitespace changes
Inline
Sidebyside
coq/Infra/RealRationalProps.v
View file @
5c7b0225
...
...
@@ 165,31 +165,6 @@ Proof.
unfold
Qle_bool
;
auto
.
Qed
.
Lemma
minAbs_positive_iv_is_lo
a
b
:
(
0
<
a
)
%
R
>
(
a
<=
b
)
%
R
>
RminAbsFun
(
a
,
b
)
=
a
.
Proof
.
intros
;
unfold
RminAbsFun
;
simpl
.
assert
(
0
<
b
)
%
R
by
lra
.
assert
(
Rabs
a
=
a
)
%
R
as
Rabs_pos_a
by
(
apply
Rabs_right
;
lra
).
assert
(
Rabs
b
=
b
)
%
R
as
Rabs_pos_b
by
(
apply
Rabs_right
;
lra
).
rewrite
Rabs_pos_a
,
Rabs_pos_b
.
rewrite
Rmin_left
;
lra
.
Qed
.
Lemma
minAbs_negative_iv_is_hi
a
b
:
(
b
<
0
)
%
R
>
(
a
<=
b
)
%
R
>
(
RminAbsFun
(
a
,
b
)
=

b
)
%
R
.
Proof
.
intros
;
unfold
RminAbsFun
;
simpl
.
assert
(
Rabs
a
=

a
)
%
R
as
Rabs_neg_a
by
(
apply
Rabs_left
;
lra
).
assert
(
Rabs
b
=

b
)
%
R
as
Rabs_neg_b
by
(
apply
Rabs_left
;
lra
).
rewrite
Rabs_neg_a
,
Rabs_neg_b
.
rewrite
Rmin_right
;
lra
.
Qed
.
Lemma
Q_case_div_to_R_case_div
a
b
:
(
b
<
0
\
/
0
<
a
)
%
Q
>
(
Q2R
b
<
0
\
/
0
<
Q2R
a
)
%
R
.
...
...
coq/IntervalArith.v
View file @
5c7b0225
...
...
@@ 347,4 +347,30 @@ Proof.
rewrite
Rabs_minus_sym
in
abs_le
.
unfold
Rabs
in
abs_le
.
destruct
Rcase_abs
in
abs_le
;
try
lra
.
Qed
.
Lemma
minAbs_positive_iv_is_lo
a
b
:
(
0
<
a
)
%
R
>
(
a
<=
b
)
%
R
>
RminAbsFun
(
a
,
b
)
=
a
.
Proof
.
intros
;
unfold
RminAbsFun
;
simpl
.
assert
(
0
<
b
)
%
R
by
lra
.
assert
(
Rabs
a
=
a
)
%
R
as
Rabs_pos_a
by
(
apply
Rabs_right
;
lra
).
assert
(
Rabs
b
=
b
)
%
R
as
Rabs_pos_b
by
(
apply
Rabs_right
;
lra
).
rewrite
Rabs_pos_a
,
Rabs_pos_b
.
rewrite
Rmin_left
;
lra
.
Qed
.
Lemma
minAbs_negative_iv_is_hi
a
b
:
(
b
<
0
)
%
R
>
(
a
<=
b
)
%
R
>
(
RminAbsFun
(
a
,
b
)
=

b
)
%
R
.
Proof
.
intros
;
unfold
RminAbsFun
;
simpl
.
assert
(
Rabs
a
=

a
)
%
R
as
Rabs_neg_a
by
(
apply
Rabs_left
;
lra
).
assert
(
Rabs
b
=

b
)
%
R
as
Rabs_neg_b
by
(
apply
Rabs_left
;
lra
).
rewrite
Rabs_neg_a
,
Rabs_neg_b
.
rewrite
Rmin_right
;
lra
.
Qed
.
\ No newline at end of file
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