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Flocq
flocq
Commits
1574e8c2
Commit
1574e8c2
authored
Oct 30, 2009
by
Guillaume Melquiond
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Added theorems about reflexivity of standard predicates.
parent
c8016fa9
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src/Flocq_rnd_prop.v
src/Flocq_rnd_prop.v
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src/Flocq_rnd_prop.v
View file @
1574e8c2
...
...
@@ -201,6 +201,18 @@ rewrite Ropp_involutive.
apply
H1
.
Qed
.
Theorem
Rnd_DN_pt_refl
:
forall
F
:
R
->
Prop
,
forall
x
:
R
,
F
x
->
Rnd_DN_pt
F
x
x
.
Proof
.
intros
F
x
Hx
.
repeat
split
.
exact
Hx
.
apply
Rle_refl
.
now
intros
.
Qed
.
Theorem
Rnd_DN_pt_idempotent
:
forall
F
:
R
->
Prop
,
forall
x
f
:
R
,
...
...
@@ -229,6 +241,18 @@ intros x Hx.
now
apply
Rnd_DN_pt_idempotent
with
(
2
:=
Hx
).
Qed
.
Theorem
Rnd_UP_pt_refl
:
forall
F
:
R
->
Prop
,
forall
x
:
R
,
F
x
->
Rnd_UP_pt
F
x
x
.
Proof
.
intros
F
x
Hx
.
repeat
split
.
exact
Hx
.
apply
Rle_refl
.
now
intros
.
Qed
.
Theorem
Rnd_UP_pt_idempotent
:
forall
F
:
R
->
Prop
,
forall
x
f
:
R
,
...
...
@@ -551,6 +575,20 @@ rewrite Hxy.
apply
Rle_refl
.
Qed
.
Theorem
Rnd_N_pt_refl
:
forall
F
:
R
->
Prop
,
forall
x
:
R
,
F
x
->
Rnd_N_pt
F
x
x
.
Proof
.
intros
F
x
Hx
.
repeat
split
.
exact
Hx
.
intros
g
_.
unfold
Rminus
at
1.
rewrite
Rplus_opp_r
,
Rabs_R0
.
apply
Rabs_pos
.
Qed
.
Theorem
Rnd_N_pt_idempotent
:
forall
F
:
R
->
Prop
,
forall
x
f
:
R
,
...
...
@@ -884,6 +922,20 @@ intros F rnd Hr x y Hxy.
now
apply
Rnd_NA_pt_monotone
with
F
.
Qed
.
Theorem
Rnd_NA_pt_refl
:
forall
F
:
R
->
Prop
,
forall
x
:
R
,
F
x
->
Rnd_NA_pt
F
x
x
.
Proof
.
intros
F
x
Hx
.
split
.
now
apply
Rnd_N_pt_refl
.
intros
f
Hxf
.
apply
Req_le
.
apply
f_equal
.
now
apply
Rnd_N_pt_idempotent
with
(
1
:=
Hxf
).
Qed
.
Theorem
Rnd_NA_pt_idempotent
:
forall
F
:
R
->
Prop
,
forall
x
f
:
R
,
...
...
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