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Numerical Analysis in Rocq
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Micaela Mayero
Numerical Analysis in Rocq
Commits
75e1dcfb
Project 'mayero/coq-num-analysis' was moved to 'mayero/rocq-num-analysis'. Please update any links and bookmarks that may still have the old path.
Commit
75e1dcfb
authored
3 years ago
by
François Clément
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Add LocallySorted_cons2.
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Lebesgue/sort_compl.v
+15
-3
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Lebesgue/sort_compl.v
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75e1dcfb
...
...
@@ -119,15 +119,15 @@ inversion H1.
now
simpl
.
Qed
.
(
*
Useful
?
Lemma
LocallySorted_0_1_nil
:
forall
P
l
(
a0
:
A
),
l
<>
nil
->
LocallySorted
P
l
->
LocallySorted
P
(
a0
::
l
)
->
P
a0
(
nth
0
l
a0
).
Proof
.
intros
P
;
induction
l
;
intros
.
now
contradict
H
.
inversion
H1
;
now
simpl
.
intros
;
now
apply
LocallySorted_0_1
.
Qed
.
*
)
Lemma
LocallySorted_cons
:
forall
P
(
a
:
A
)
l
,
...
...
@@ -295,6 +295,18 @@ apply Sorted_extends; try assumption.
now
apply
Sorted_LocallySorted_iff
.
Qed
.
Lemma
LocallySorted_cons2
:
forall
(
a
b
:
A
)
l
,
(
forall
x
y
z
,
ord
x
y
->
ord
y
z
->
ord
x
z
)
->
LocallySorted
ord
(
a
::
b
::
l
)
->
LocallySorted
ord
(
a
::
l
).
Proof
.
intros
a
b
l
Ho
Hl
.
inversion
Hl
;
inversion
H1
.
apply
LSorted_cons1
.
apply
LSorted_consn
;
try
easy
.
now
apply
Ho
with
b
.
Qed
.
Lemma
LocallySorted_select
:
forall
P
l
,
(
forall
x
y
z
,
ord
x
y
->
ord
y
z
->
ord
x
z
)
->
...
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