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Flocq
flocq
Commits
6723f606
Commit
6723f606
authored
Sep 30, 2016
by
Guillaume Melquiond
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Prove pred_lt and succ_lt.
parent
daa79c73
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-19
src/Core/Fcore_ulp.v
src/Core/Fcore_ulp.v
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src/Core/Fcore_ulp.v
View file @
6723f606
...
...
@@ -2004,26 +2004,16 @@ apply error_le_half_ulp.
rewrite
round_DN_opp
;
apply
Ropp_0_gt_lt_contravar
;
apply
Rlt_gt
;
assumption
.
Qed
.
Theorem
pred_le
:
forall
x
y
,
F
x
->
F
y
->
(
x
<=
y
)
%
R
->
(
pred
x
<=
pred
y
)
%
R
.
Theorem
pred_le
:
forall
x
y
,
F
x
->
F
y
->
(
x
<=
y
)
%
R
->
(
pred
x
<=
pred
y
)
%
R
.
Proof
.
intros
x
y
Fx
Fy
Hxy
.
assert
(
V
:
(
((
x
=
0
)
/
\
(
y
=
0
))
\
/
(
x
<>
0
\
/
x
<
y
))
%
R
).
case
(
Req_dec
x
0
);
intros
Zx
.
case
Hxy
;
intros
Zy
.
now
right
;
right
.
left
;
split
;
trivial
;
now
rewrite
<-
Zy
.
now
right
;
left
.
destruct
V
as
[(
V1
,
V2
)
|
V
].
rewrite
V1
,
V2
;
now
right
.
apply
le_pred_lt
;
try
assumption
.
apply
generic_format_pred
;
try
assumption
.
case
V
;
intros
V1
.
apply
Rlt_le_trans
with
(
2
:=
Hxy
).
now
apply
pred_lt_id
.
apply
Rle_lt_trans
with
(
2
:=
V1
).
now
apply
pred_le_id
.
intros
x
y
Fx
Fy
[
Hxy
|
->
].
2
:
apply
Rle_refl
.
apply
le_pred_lt
with
(
2
:=
Fy
).
now
apply
generic_format_pred
.
apply
Rle_lt_trans
with
(
2
:=
Hxy
).
apply
pred_le_id
.
Qed
.
Theorem
succ_le
:
forall
x
y
,
...
...
@@ -2051,6 +2041,28 @@ rewrite <- (pred_succ x), <- (pred_succ y); try assumption.
apply
pred_le
;
trivial
;
now
apply
generic_format_succ
.
Qed
.
Theorem
pred_lt
:
forall
x
y
,
F
x
->
F
y
->
(
x
<
y
)
%
R
->
(
pred
x
<
pred
y
)
%
R
.
Proof
.
intros
x
y
Fx
Fy
Hxy
.
apply
Rnot_le_lt
.
intros
H
.
apply
Rgt_not_le
with
(
1
:=
Hxy
).
now
apply
pred_le_inv
.
Qed
.
Theorem
succ_lt
:
forall
x
y
,
F
x
->
F
y
->
(
x
<
y
)
%
R
->
(
succ
x
<
succ
y
)
%
R
.
Proof
.
intros
x
y
Fx
Fy
Hxy
.
apply
Rnot_le_lt
.
intros
H
.
apply
Rgt_not_le
with
(
1
:=
Hxy
).
now
apply
succ_le_inv
.
Qed
.
(
*
was
lt_UP_le_DN
*
)
Theorem
le_round_DN_lt_UP
:
forall
x
y
,
F
y
->
...
...
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