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d6c38891
Commit
d6c38891
authored
Nov 22, 2016
by
Robbert Krebbers
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Function to convert a multiset into a gset.
parent
49e3e00f
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gmultiset.v
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prelude/gmultiset.v
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d6c38891
...
...
@@ -39,11 +39,15 @@ Section definitions.
let
(
X
)
:=
X
in
let
(
Y
)
:=
Y
in
GMultiSet
$
difference_with
(
λ
x
y
,
let
z
:=
x
-
y
in
guard
(
0
<
z
);
Some
(
pred
z
))
X
Y
.
Instance
gmultiset_dom
:
Dom
(
gmultiset
A
)
(
gset
A
)
:=
λ
X
,
let
(
X
)
:=
X
in
dom
_
X
.
End
definitions
.
Typeclasses
Opaque
gmultiset_elem_of
gmultiset_subseteq
.
Typeclasses
Opaque
gmultiset_elements
gmultiset_size
gmultiset_empty
.
Typeclasses
Opaque
gmultiset_singleton
gmultiset_union
gmultiset_difference
.
Typeclasses
Opaque
gmultiset_dom
.
(** These instances are declared using [Hint Extern] to avoid too
eager type class search. *)
...
...
@@ -63,6 +67,8 @@ Hint Extern 1 (Elements _ (gmultiset _)) =>
eapply
@
gmultiset_elements
:
typeclass_instances
.
Hint
Extern
1
(
Size
(
gmultiset
_))
=>
eapply
@
gmultiset_size
:
typeclass_instances
.
Hint
Extern
1
(
Dom
(
gmultiset
_)
_)
=>
eapply
@
gmultiset_dom
:
typeclass_instances
.
Section
lemmas
.
Context
`
{
Countable
A
}.
...
...
@@ -196,6 +202,12 @@ Proof.
exists
(
x
,
n
);
split
;
[|
by
apply
elem_of_map_to_list
].
apply
elem_of_replicate
;
auto
with
omega
.
Qed
.
Lemma
gmultiset_elem_of_dom
x
X
:
x
∈
dom
(
gset
A
)
X
↔
x
∈
X
.
Proof
.
unfold
dom
,
gmultiset_dom
,
elem_of
at
2
,
gmultiset_elem_of
,
multiplicity
.
destruct
X
as
[
X
];
simpl
;
rewrite
elem_of_dom
,
<-
not_eq_None_Some
.
destruct
(
X
!!
x
);
naive_solver
omega
.
Qed
.
(* Properties of the size operation *)
Lemma
gmultiset_size_empty
:
size
(
∅
:
gmultiset
A
)
=
0
.
...
...
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