Skip to content
GitLab
Explore
Sign in
Primary navigation
Search or go to…
Project
N
Numerical Analysis in Coq
Manage
Activity
Members
Labels
Plan
Issues
Issue boards
Milestones
Wiki
Code
Merge requests
Repository
Branches
Commits
Tags
Repository graph
Compare revisions
Snippets
Build
Pipelines
Jobs
Pipeline schedules
Artifacts
Deploy
Releases
Package Registry
Model registry
Operate
Environments
Terraform modules
Monitor
Incidents
Analyze
Value stream analytics
Contributor analytics
CI/CD analytics
Repository analytics
Model experiments
Help
Help
Support
GitLab documentation
Compare GitLab plans
Community forum
Contribute to GitLab
Provide feedback
Keyboard shortcuts
?
Snippets
Groups
Projects
Show more breadcrumbs
Micaela Mayero
Numerical Analysis in Coq
Commits
9869f119
Commit
9869f119
authored
5 months ago
by
François Clément
Browse files
Options
Downloads
Patches
Plain Diff
Fix {lex,colex}_trans.
Modify {symlex,revlex}_trans.
parent
69dda88a
No related branches found
Branches containing commit
No related tags found
Tags containing commit
No related merge requests found
Pipeline
#8603
waiting for manual action
Stage: test
Changes
1
Pipelines
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
FEM/Compl/Binary_relation.v
+34
-20
34 additions, 20 deletions
FEM/Compl/Binary_relation.v
with
34 additions
and
20 deletions
FEM/Compl/Binary_relation.v
+
34
−
20
View file @
9869f119
...
...
@@ -933,36 +933,50 @@ Lemma revlexT_antisym :
antisymmetric
R
->
forall
n
,
antisymmetric
(
@
revlexT
_
R
n
).
Proof
.
intros
;
apply
antisym_conv
,
colexT_antisym
;
easy
.
Qed
.
(
*
This
seems
wrong
!
Maybe
some
hypotheses
are
missing
...
*
)
Lemma
lex_trans
:
forall
P
,
transitive
R
->
forall
n
,
transitive
(
@
lex
_
R
P
n
).
antisymmetric
R
\
/
asymmetric
R
->
transitive
R
->
forall
P
n
,
transitive
(
@
lex
_
R
P
n
).
Proof
.
intros
P
H1
n
x
y
z
;
induction
n
;
[
easy
|
].
rewrite
!
lex_S
;
intros
[[
H2a
H2b
]
|
[
H2
H3
]]
[[
H4a
H4b
]
|
[
H4
H5
]].
left
;
split
;
[
admit
(
*
WRONG
?
*
)
|
apply
H1
with
(
y
ord0
);
easy
].
rewrite
-
H4
;
left
;
easy
.
rewrite
H2
;
left
;
easy
.
right
;
split
;
[
rewrite
H2
|
apply
IHn
with
(
skipF
y
ord0
)];
easy
.
Admitted
.
intros
H1
H2
P
n
x
y
z
;
induction
n
;
[
easy
|
].
rewrite
!
lex_S
;
intros
[[
H3a
H3b
]
|
[
H3
H4
]]
[[
H5a
H5b
]
|
[
H5
H6
]].
(
*
*
)
left
;
split
;
[
|
apply
H2
with
(
y
ord0
);
easy
].
destruct
(
HT
(
x
ord0
)
(
z
ord0
))
as
[
H4
|
];
[
exfalso
|
easy
].
rewrite
H4
in
H3b
;
destruct
H1
as
[
H1
|
H1
].
contradict
H5a
;
apply
H1
;
easy
.
contradict
H5b
;
apply
H1
;
easy
.
(
*
*
)
rewrite
-
H5
;
left
;
easy
.
rewrite
H3
;
left
;
easy
.
right
;
split
;
[
rewrite
H3
|
apply
IHn
with
(
skipF
y
ord0
)];
easy
.
Qed
.
(
*
This
seems
wrong
!
Maybe
some
hypotheses
are
missing
...
*
)
Lemma
colex_trans
:
forall
P
,
transitive
R
->
forall
n
,
transitive
(
@
colex
_
R
P
n
).
antisymmetric
R
\
/
asymmetric
R
->
transitive
R
->
forall
P
n
,
transitive
(
@
colex
_
R
P
n
).
Proof
.
intros
P
H1
n
x
y
z
;
induction
n
;
[
easy
|
].
rewrite
!
colex_S
;
intros
[[
H2a
H2b
]
|
[
H2
H3
]]
[[
H4a
H4b
]
|
[
H4
H5
]].
left
;
split
;
[
admit
(
*
WRONG
?
*
)
|
apply
H1
with
(
y
ord_max
);
easy
].
rewrite
-
H4
;
left
;
easy
.
rewrite
H2
;
left
;
easy
.
right
;
split
;
[
rewrite
H2
|
apply
IHn
with
(
skipF
y
ord_max
)];
easy
.
Admitted
.
intros
H1
H2
P
n
x
y
z
;
induction
n
;
[
easy
|
].
rewrite
!
colex_S
;
intros
[[
H3a
H3b
]
|
[
H3
H4
]]
[[
H5a
H5b
]
|
[
H5
H6
]].
(
*
*
)
left
;
split
;
[
|
apply
H2
with
(
y
ord_max
);
easy
].
destruct
(
HT
(
x
ord_max
)
(
z
ord_max
))
as
[
H4
|
];
[
exfalso
|
easy
].
rewrite
H4
in
H3b
;
destruct
H1
as
[
H1
|
H1
].
contradict
H5a
;
apply
H1
;
easy
.
contradict
H5b
;
apply
H1
;
easy
.
(
*
*
)
rewrite
-
H5
;
left
;
easy
.
rewrite
H3
;
left
;
easy
.
right
;
split
;
[
rewrite
H3
|
apply
IHn
with
(
skipF
y
ord_max
)];
easy
.
Qed
.
Lemma
symlex_trans
:
forall
P
,
transitive
R
->
forall
n
,
transitive
(
@
symlex
_
R
P
n
).
antisymmetric
R
\
/
asymmetric
R
->
transitive
R
->
forall
P
n
,
transitive
(
@
symlex
_
R
P
n
).
Proof
.
intros
;
apply
trans_conv
,
lex_trans
;
easy
.
Qed
.
Lemma
revlex_trans
:
forall
P
,
transitive
R
->
forall
n
,
transitive
(
@
revlex
_
R
P
n
).
antisymmetric
R
\
/
asymmetric
R
->
transitive
R
->
forall
P
n
,
transitive
(
@
revlex
_
R
P
n
).
Proof
.
intros
;
apply
trans_conv
,
colex_trans
;
easy
.
Qed
.
Lemma
lexF_conn_alt
:
...
...
This diff is collapsed.
Click to expand it.
Preview
0%
Loading
Try again
or
attach a new file
.
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Save comment
Cancel
Please
register
or
sign in
to comment