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Flocq
flocq
Commits
7773d1aa
Commit
7773d1aa
authored
Oct 30, 2009
by
Guillaume Melquiond
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Added reflexivity for Rnd_gNE.
parent
e9dfd4d4
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src/Flocq_rnd_ne.v
src/Flocq_rnd_ne.v
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src/Flocq_rnd_ne.v
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7773d1aa
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@@ -159,14 +159,24 @@ apply Rnd_gNE_pt_unicity_prop.
Qed
.
Theorem
Rnd_gNE_pt_monotone
:
forall
x
y
f
g
:
R
,
Rnd_gNE_pt
x
f
->
Rnd_gNE_pt
y
g
->
(
x
<=
y
)
%
R
->
(
f
<=
g
)
%
R
.
rounding_pred_monotone
Rnd_gNE_pt
.
Proof
.
apply
Rnd_NG_pt_monotone
.
apply
Rnd_gNE_pt_unicity_prop
.
Qed
.
Theorem
Rnd_gNE_pt_refl
:
forall
x
:
R
,
format
x
->
Rnd_gNE_pt
x
x
.
Proof
.
intros
x
Hx
.
split
.
now
apply
Rnd_N_pt_refl
.
right
.
intros
f
Hf
.
now
apply
Rnd_N_pt_idempotent
with
format
.
Qed
.
Theorem
Rnd_gNE_pt_idempotent
:
forall
x
f
:
R
,
Rnd_gNE_pt
x
f
->
format
x
->
...
...
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