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Flocq
flocq
Commits
d8ce723c
Commit
d8ce723c
authored
7 years ago
by
Guillaume Melquiond
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Remove pred_eq_opp_succ_opp and succ_eq_opp_pred_opp.
parent
87c28ab4
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src/Core/Round_NE.v
+1
-0
1 addition, 0 deletions
src/Core/Round_NE.v
src/Core/Ulp.v
+18
-28
18 additions, 28 deletions
src/Core/Ulp.v
with
19 additions
and
28 deletions
src/Core/Round_NE.v
+
1
−
0
View file @
d8ce723c
...
...
@@ -327,6 +327,7 @@ Qed.
Theorem
Rnd_NE_pt_round
:
round_pred
Rnd_NE_pt
.
Proof
.
split
.
apply
Rnd_NE_pt_total
.
apply
Rnd_NE_pt_monotone
.
...
...
This diff is collapsed.
Click to expand it.
src/Core/Ulp.v
+
18
−
28
View file @
d8ce723c
...
...
@@ -175,8 +175,6 @@ now apply Rabs_pos_lt.
now
apply
generic_format_abs
.
Qed
.
(
*
was
ulp_DN_UP
*
)
Theorem
round_UP_DN_ulp
:
forall
x
,
~
F
x
->
round
beta
fexp
Zceil
x
=
(
round
beta
fexp
Zfloor
x
+
ulp
x
)
%
R
.
...
...
@@ -320,7 +318,7 @@ rewrite <- ulp_bpow.
apply
H
.
Qed
.
Theorem
ulp_le_pos
:
Lemma
ulp_le_pos
:
forall
{
Hm
:
Monotone_exp
fexp
}
,
forall
x
y
:
R
,
(
0
<=
x
)
%
R
->
(
x
<=
y
)
%
R
->
...
...
@@ -395,30 +393,18 @@ intros x Hx; unfold succ.
now
rewrite
Rle_bool_true
.
Qed
.
Lemma
pred_eq_opp_succ_opp
:
forall
x
,
pred
x
=
(
-
succ
(
-
x
))
%
R
.
Proof
.
reflexivity
.
Qed
.
Lemma
succ_eq_opp_pred_opp
:
forall
x
,
succ
x
=
(
-
pred
(
-
x
))
%
R
.
Proof
.
intros
x
;
unfold
pred
.
now
rewrite
2
!
Ropp_involutive
.
Qed
.
Lemma
succ_opp
:
Theorem
succ_opp
:
forall
x
,
succ
(
-
x
)
=
(
-
pred
x
)
%
R
.
Proof
.
intros
x
;
rewrite
succ_eq_opp_pred_opp
.
now
rewrite
Ropp_involutive
.
intros
x
.
now
apply
sym_eq
,
Ropp_involutive
.
Qed
.
Lemma
pred_opp
:
Theorem
pred_opp
:
forall
x
,
pred
(
-
x
)
=
(
-
succ
x
)
%
R
.
Proof
.
intros
x
;
rewrite
pred_eq_opp_succ_opp
.
intros
x
.
unfold
pred
.
now
rewrite
Ropp_involutive
.
Qed
.
...
...
@@ -1540,7 +1526,7 @@ rewrite <- Ropp_0 at 1.
apply
pred_opp
.
Qed
.
Theorem
pred_succ_aux
:
Lemma
pred_succ_aux
:
forall
x
,
F
x
->
(
0
<
x
)
%
R
->
pred
(
succ
x
)
=
x
.
Proof
.
...
...
@@ -1572,8 +1558,8 @@ now apply succ_pred_aux.
rewrite
<-
Hx
.
rewrite
pred_0
,
succ_opp
,
pred_ulp_0
.
apply
Ropp_0
.
rewrite
pred_eq_opp_succ_opp
,
succ_opp
.
rewrite
pred_succ_aux
.
unfold
pred
.
rewrite
succ_opp
,
pred_succ_aux
.
apply
Ropp_involutive
.
now
apply
generic_format_opp
.
now
apply
Ropp_0_gt_lt_contravar
.
...
...
@@ -2003,12 +1989,16 @@ apply Rle_lt_trans with (2 := Hxy).
apply
pred_le_id
.
Qed
.
Theorem
succ_le
:
forall
x
y
,
F
x
->
F
y
->
(
x
<=
y
)
%
R
->
(
succ
x
<=
succ
y
)
%
R
.
Theorem
succ_le
:
forall
x
y
,
F
x
->
F
y
->
(
x
<=
y
)
%
R
->
(
succ
x
<=
succ
y
)
%
R
.
Proof
.
intros
x
y
Fx
Fy
Hxy
.
rewrite
2
!
succ_eq_opp_pred_opp
.
apply
Ropp_le_contravar
,
pred_le
;
try
apply
generic_format_opp
;
try
assumption
.
apply
Ropp_le_cancel
.
rewrite
<-
2
!
pred_opp
.
apply
pred_le
.
now
apply
generic_format_opp
.
now
apply
generic_format_opp
.
now
apply
Ropp_le_contravar
.
Qed
.
...
...
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