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stdpp
Commits
e5fe972d
Commit
e5fe972d
authored
Mar 04, 2016
by
Robbert Krebbers
Browse files
List inclusion in terms of list membership.
parent
c81c8218
Changes
2
Hide whitespace changes
Inline
Side-by-side
theories/collections.v
View file @
e5fe972d
...
...
@@ -324,6 +324,10 @@ Section list_unfold.
intros
??
;
constructor
.
by
rewrite
elem_of_app
,
(
set_unfold
(
x
∈
l
)
P
),
(
set_unfold
(
x
∈
k
)
Q
).
Qed
.
Global
Instance
set_unfold_included
l
k
(
P
Q
:
A
→
Prop
)
:
(
∀
x
,
SetUnfold
(
x
∈
l
)
(
P
x
))
→
(
∀
x
,
SetUnfold
(
x
∈
k
)
(
Q
x
))
→
SetUnfold
(
l
`
included
`
k
)
(
∀
x
,
P
x
→
Q
x
).
Proof
.
by
constructor
;
unfold
included
;
set_unfold
.
Qed
.
End
list_unfold
.
(** * Guard *)
...
...
theories/list.v
View file @
e5fe972d
...
...
@@ -282,6 +282,9 @@ Inductive Forall3 {A B C} (P : A → B → C → Prop) :
P
x
y
z
→
Forall3
P
l
k
k'
→
Forall3
P
(
x
::
l
)
(
y
::
k
)
(
z
::
k'
).
(** Set operations on lists *)
Definition
included
{
A
}
(
l1
l2
:
list
A
)
:
=
∀
x
,
x
∈
l1
→
x
∈
l2
.
Infix
"`included`"
:
=
included
(
at
level
70
)
:
C_scope
.
Section
list_set
.
Context
{
A
}
{
dec
:
∀
x
y
:
A
,
Decision
(
x
=
y
)}.
Global
Instance
elem_of_list_dec
{
dec
:
∀
x
y
:
A
,
Decision
(
x
=
y
)}
...
...
@@ -2017,6 +2020,12 @@ Section contains_dec.
abstract
(
rewrite
Permutation_alt
;
tauto
).
Defined
.
End
contains_dec
.
(** ** Properties of [included] *)
Global
Instance
included_preorder
:
PreOrder
(@
included
A
).
Proof
.
split
;
firstorder
.
Qed
.
Lemma
included_nil
l
:
[]
`
included
`
l
.
Proof
.
intros
x
.
by
rewrite
elem_of_nil
.
Qed
.
End
more_general_properties
.
(** ** Properties of the [Forall] and [Exists] predicate *)
...
...
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