Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
C
coqstdpp
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
0
Issues
0
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Incidents
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
David Swasey
coqstdpp
Commits
8a43c1bb
Commit
8a43c1bb
authored
Mar 02, 2015
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Remove duplicate mem_allocable notion.
parent
8734dd1c
Changes
2
Hide whitespace changes
Inline
Sidebyside
Showing
2 changed files
with
41 additions
and
12 deletions
+41
12
theories/collections.v
theories/collections.v
+35
12
theories/fin_map_dom.v
theories/fin_map_dom.v
+6
0
No files found.
theories/collections.v
View file @
8a43c1bb
...
...
@@ 430,16 +430,19 @@ End more_quantifiers.
(** * Fresh elements *)
(** We collect some properties on the [fresh] operation. In particular we
generalize [fresh] to generate lists of fresh elements. *)
Section
fresh
.
Context
`
{
FreshSpec
A
C
}
.
Fixpoint
fresh_list
`
{
Fresh
A
C
,
Union
C
,
Singleton
A
C
}
(
n
:
nat
)
(
X
:
C
)
:
list
A
:
=
match
n
with

0
=>
[]

S
n
=>
let
x
:
=
fresh
X
in
x
::
fresh_list
n
({[
x
]}
∪
X
)
end
.
Inductive
Forall_fresh
`
{
ElemOf
A
C
}
(
X
:
C
)
:
list
A
→
Prop
:
=

Forall_fresh_nil
:
Forall_fresh
X
[]

Forall_fresh_cons
x
xs
:
x
∉
xs
→
x
∉
X
→
Forall_fresh
X
xs
→
Forall_fresh
X
(
x
::
xs
).
Definition
fresh_sig
(
X
:
C
)
:
{
x
:
A

x
∉
X
}
:
=
exist
(
∉
X
)
(
fresh
X
)
(
is_fresh
X
).
Fixpoint
fresh_list
(
n
:
nat
)
(
X
:
C
)
:
list
A
:
=
match
n
with

0
=>
[]

S
n
=>
let
x
:
=
fresh
X
in
x
::
fresh_list
n
({[
x
]}
∪
X
)
end
.
Section
fresh
.
Context
`
{
FreshSpec
A
C
}.
Global
Instance
fresh_proper
:
Proper
((
≡
)
==>
(=))
fresh
.
Proof
.
intros
???.
by
apply
fresh_proper_alt
,
elem_of_equiv
.
Qed
.
...
...
@@ 448,18 +451,38 @@ Section fresh.
intros
?
n
>.
induction
n
as
[
n
IH
]
;
intros
??
E
;
f_equal'
;
[
by
rewrite
E
].
apply
IH
.
by
rewrite
E
.
Qed
.
Lemma
Forall_fresh_NoDup
X
xs
:
Forall_fresh
X
xs
→
NoDup
xs
.
Proof
.
induction
1
;
by
constructor
.
Qed
.
Lemma
Forall_fresh_elem_of
X
xs
x
:
Forall_fresh
X
xs
→
x
∈
xs
→
x
∉
X
.
Proof
.
intros
HX
;
revert
x
;
rewrite
<
Forall_forall
.
by
induction
HX
;
constructor
.
Qed
.
Lemma
Forall_fresh_alt
X
xs
:
Forall_fresh
X
xs
↔
NoDup
xs
∧
∀
x
,
x
∈
xs
→
x
∉
X
.
Proof
.
split
;
eauto
using
Forall_fresh_NoDup
,
Forall_fresh_elem_of
.
rewrite
<
Forall_forall
.
intros
[
Hxs
Hxs'
].
induction
Hxs
;
decompose_Forall_hyps
;
constructor
;
auto
.
Qed
.
Lemma
fresh_list_length
n
X
:
length
(
fresh_list
n
X
)
=
n
.
Proof
.
revert
X
.
induction
n
;
simpl
;
auto
.
Qed
.
Lemma
fresh_list_is_fresh
n
X
x
:
x
∈
fresh_list
n
X
→
x
∉
X
.
Proof
.
revert
X
.
induction
n
as
[
n
IH
]
;
intros
X
;
simpl
;
[
by
rewrite
elem_of_nil
].
revert
X
.
induction
n
as
[
n
IH
]
;
intros
X
;
simpl
;
[
by
rewrite
elem_of_nil
].
rewrite
elem_of_cons
;
intros
[>
Hin
]
;
[
apply
is_fresh
].
apply
IH
in
Hin
;
solve_elem_of
.
Qed
.
Lemma
fresh_list_nodup
n
X
:
NoDup
(
fresh_list
n
X
).
Lemma
NoDup_fresh_list
n
X
:
NoDup
(
fresh_list
n
X
).
Proof
.
revert
X
.
induction
n
;
simpl
;
constructor
;
auto
.
intros
Hin
.
apply
fresh_list_is_fresh
in
Hin
.
solve_elem_of
.
intros
Hin
;
apply
fresh_list_is_fresh
in
Hin
;
solve_elem_of
.
Qed
.
Lemma
Forall_fresh_list
X
n
:
Forall_fresh
X
(
fresh_list
n
X
).
Proof
.
rewrite
Forall_fresh_alt
;
eauto
using
NoDup_fresh_list
,
fresh_list_is_fresh
.
Qed
.
End
fresh
.
...
...
theories/fin_map_dom.v
View file @
8a43c1bb
...
...
@@ 44,6 +44,12 @@ Proof.
intros
E
.
apply
map_empty
.
intros
.
apply
not_elem_of_dom
.
rewrite
E
.
solve_elem_of
.
Qed
.
Lemma
dom_alter
{
A
}
f
(
m
:
M
A
)
i
:
dom
D
(
alter
f
i
m
)
≡
dom
D
m
.
Proof
.
apply
elem_of_equiv
;
intros
j
;
rewrite
!
elem_of_dom
;
unfold
is_Some
.
destruct
(
decide
(
i
=
j
))
;
simplify_map_equality'
;
eauto
.
destruct
(
m
!!
j
)
;
naive_solver
.
Qed
.
Lemma
dom_insert
{
A
}
(
m
:
M
A
)
i
x
:
dom
D
(<[
i
:
=
x
]>
m
)
≡
{[
i
]}
∪
dom
D
m
.
Proof
.
apply
elem_of_equiv
.
intros
j
.
rewrite
elem_of_union
,
!
elem_of_dom
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment