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David Swasey
coq-stdpp
Commits
e5fe972d
Commit
e5fe972d
authored
Mar 04, 2016
by
Robbert Krebbers
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List inclusion in terms of list membership.
parent
c81c8218
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theories/collections.v
theories/collections.v
+4
-0
theories/list.v
theories/list.v
+9
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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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