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Flocq
flocq
Commits
39cf7e2e
Commit
39cf7e2e
authored
May 17, 2010
by
Guillaume Melquiond
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Moved opposites to goals.
parent
e37bc5ec
Changes
2
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2 changed files
with
19 additions
and
19 deletions
+19
-19
src/Core/Fcore_generic_fmt.v
src/Core/Fcore_generic_fmt.v
+2
-1
src/Core/Fcore_rnd.v
src/Core/Fcore_rnd.v
+17
-18
No files found.
src/Core/Fcore_generic_fmt.v
View file @
39cf7e2e
...
...
@@ -711,9 +711,10 @@ Theorem generic_UP_pt :
Rnd_UP_pt
generic_format
x
(
rounding
ZrndUP
x
).
Proof
.
intros
x
.
rewrite
<-
(
Ropp_involutive
x
).
rewrite
rounding_UP_opp
.
apply
Rnd_DN_UP_pt_sym
.
apply
generic_format_satisfies_any
.
rewrite
<-
rounding_DN_opp
.
apply
generic_DN_pt
.
Qed
.
...
...
src/Core/Fcore_rnd.v
View file @
39cf7e2e
...
...
@@ -143,44 +143,42 @@ Theorem Rnd_DN_UP_pt_sym :
forall
F
:
R
->
Prop
,
(
forall
x
,
F
x
->
F
(
-
x
)
)
->
forall
x
f
:
R
,
Rnd_DN_pt
F
(
-
x
)
(
-
f
)
->
Rnd_UP_pt
F
x
f
.
Rnd_DN_pt
F
x
f
->
Rnd_UP_pt
F
(
-
x
)
(
-
f
)
.
Proof
.
intros
F
HF
x
f
H
.
rewrite
<-
(
Ropp_involutive
f
).
repeat
split
.
apply
HF
.
apply
H
.
apply
Ropp_le_cancel
.
rewrite
Ropp_involutive
.
apply
Ropp_le_contravar
.
apply
H
.
intros
.
apply
Ropp_le_cancel
.
rewrite
Ropp_involutive
.
intros
g
Hg
.
rewrite
<-
(
Ropp_involutive
g
).
intros
Hxg
.
apply
Ropp_le_contravar
.
apply
H
.
now
apply
HF
.
now
apply
Ropp_le_c
ontravar
.
now
apply
Ropp_le_c
ancel
.
Qed
.
Theorem
Rnd_UP_DN_pt_sym
:
forall
F
:
R
->
Prop
,
(
forall
x
,
F
x
->
F
(
-
x
)
)
->
forall
x
f
:
R
,
Rnd_UP_pt
F
(
-
x
)
(
-
f
)
->
Rnd_DN_pt
F
x
f
.
Rnd_UP_pt
F
x
f
->
Rnd_DN_pt
F
(
-
x
)
(
-
f
)
.
Proof
.
intros
F
HF
x
f
H
.
rewrite
<-
(
Ropp_involutive
f
).
repeat
split
.
apply
HF
.
apply
H
.
apply
Ropp_le_cancel
.
rewrite
Ropp_involutive
.
apply
Ropp_le_contravar
.
apply
H
.
intros
.
apply
Ropp_le_cancel
.
rewrite
Ropp_involutive
.
intros
g
Hg
.
rewrite
<-
(
Ropp_involutive
g
).
intros
Hxg
.
apply
Ropp_le_contravar
.
apply
H
.
now
apply
HF
.
now
apply
Ropp_le_c
ontravar
.
now
apply
Ropp_le_c
ancel
.
Qed
.
Theorem
Rnd_DN_UP_sym
:
...
...
@@ -195,9 +193,9 @@ rewrite <- (Ropp_involutive (rnd1 (-x))).
apply
f_equal
.
apply
(
Rnd_UP_unicity
F
(
fun
x
=>
-
rnd1
(
-
x
)))
;
trivial
.
intros
y
.
pattern
y
at
1
;
rewrite
<-
Ropp_involutive
.
apply
Rnd_DN_UP_pt_sym
.
apply
HF
.
rewrite
Ropp_involutive
.
apply
H1
.
Qed
.
...
...
@@ -1293,9 +1291,10 @@ split.
intros
x
.
destruct
(
proj1
(
satisfies_any_imp_DN
F
Hany
)
(
-
x
))
as
(
f
,
Hf
).
exists
(
-
f
).
rewrite
<-
(
Ropp_involutive
x
).
apply
Rnd_DN_UP_pt_sym
.
apply
Hany
.
now
rewrite
Ropp_involutive
.
exact
Hf
.
apply
Rnd_UP_pt_monotone
.
Qed
.
...
...
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