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Flocq
flocq
Commits
6c0480f2
Commit
6c0480f2
authored
Jun 21, 2012
by
Jacques-Henri Jourdan
Committed by
Guillaume Melquiond
Jul 09, 2012
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Move cond_Zopp to Fcore_Zaux.
parent
2e32d89f
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2
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29 additions
and
24 deletions
+29
-24
src/Core/Fcore_Raux.v
src/Core/Fcore_Raux.v
+2
-24
src/Core/Fcore_Zaux.v
src/Core/Fcore_Zaux.v
+27
-0
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src/Core/Fcore_Raux.v
View file @
6c0480f2
...
...
@@ -1897,9 +1897,8 @@ Qed.
End
Bool
.
Section
cond_opp
.
Section
cond_
R
opp
.
Definition
cond_Zopp
(
b
:
bool
)
m
:=
if
b
then
Zopp
m
else
m
.
Definition
cond_Ropp
(
b
:
bool
)
m
:=
if
b
then
Ropp
m
else
m
.
Theorem
Z2R_cond_Zopp
:
...
...
@@ -1911,15 +1910,6 @@ apply Z2R_opp.
apply
refl_equal
.
Qed
.
Theorem
abs_cond_Zopp
:
forall
b
m
,
Zabs
(
cond_Zopp
b
m
)
=
Zabs
m
.
Proof
.
intros
[
|
]
m
.
apply
Zabs_Zopp
.
apply
refl_equal
.
Qed
.
Theorem
abs_cond_Ropp
:
forall
b
m
,
Rabs
(
cond_Ropp
b
m
)
=
Rabs
m
.
...
...
@@ -1929,18 +1919,6 @@ apply Rabs_Ropp.
apply
refl_equal
.
Qed
.
Theorem
cond_Zopp_Zlt_bool
:
forall
m
,
cond_Zopp
(
Zlt_bool
m
0
)
m
=
Zabs
m
.
Proof
.
intros
m
.
apply
sym_eq
.
case
Zlt_bool_spec
;
intros
Hm
.
apply
Zabs_non_eq
.
now
apply
Zlt_le_weak
.
now
apply
Zabs_eq
.
Qed
.
Theorem
cond_Ropp_Rlt_bool
:
forall
m
,
cond_Ropp
(
Rlt_bool
m
0
)
m
=
Rabs
m
.
...
...
@@ -2015,4 +1993,4 @@ apply Ropp_plus_distr.
apply
refl_equal
.
Qed
.
End
cond_opp
.
End
cond_
R
opp
.
src/Core/Fcore_Zaux.v
View file @
6c0480f2
...
...
@@ -745,3 +745,30 @@ apply Zlt_gt.
Qed
.
End
Zcompare
.
Section
cond_Zopp
.
Definition
cond_Zopp
(
b
:
bool
)
m
:=
if
b
then
Zopp
m
else
m
.
Theorem
abs_cond_Zopp
:
forall
b
m
,
Zabs
(
cond_Zopp
b
m
)
=
Zabs
m
.
Proof
.
intros
[
|
]
m
.
apply
Zabs_Zopp
.
apply
refl_equal
.
Qed
.
Theorem
cond_Zopp_Zlt_bool
:
forall
m
,
cond_Zopp
(
Zlt_bool
m
0
)
m
=
Zabs
m
.
Proof
.
intros
m
.
apply
sym_eq
.
case
Zlt_bool_spec
;
intros
Hm
.
apply
Zabs_non_eq
.
now
apply
Zlt_le_weak
.
now
apply
Zabs_eq
.
Qed
.
End
cond_Zopp
.
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