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Marianna Rapoport
iris-coq
Commits
834b2046
Commit
834b2046
authored
Jul 29, 2016
by
Robbert Krebbers
Browse files
Conversion from coPset to gset positive.
parent
daba18d5
Changes
1
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Inline
Side-by-side
prelude/coPset.v
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834b2046
...
...
@@ -315,9 +315,22 @@ Proof.
apply
coPset_finite_spec
;
destruct
X
as
[[
t
?]]
;
apply
of_Pset_raw_finite
.
Qed
.
(** * Conversion from gsets of positives *)
(** * Conversion to and from gsets of positives *)
Lemma
to_gset_wf
(
m
:
Pmap
())
:
gmap_wf
(
K
:
=
positive
)
m
.
Proof
.
done
.
Qed
.
Definition
to_gset
(
X
:
coPset
)
:
gset
positive
:
=
let
'
Mapset
m
:
=
to_Pset
X
in
Mapset
(
GMap
m
(
bool_decide_pack
_
(
to_gset_wf
m
))).
Definition
of_gset
(
X
:
gset
positive
)
:
coPset
:
=
let
'
Mapset
(
GMap
(
PMap
t
Ht
)
_
)
:
=
X
in
of_Pset_raw
t
↾
of_Pset_wf
_
Ht
.
Lemma
elem_of_to_gset
X
i
:
set_finite
X
→
i
∈
to_gset
X
↔
i
∈
X
.
Proof
.
intros
?.
rewrite
<-
elem_of_to_Pset
by
done
.
unfold
to_gset
.
by
destruct
(
to_Pset
X
).
Qed
.
Lemma
elem_of_of_gset
X
i
:
i
∈
of_gset
X
↔
i
∈
X
.
Proof
.
destruct
X
as
[[[
t
?]]]
;
apply
elem_of_of_Pset_raw
.
Qed
.
Lemma
of_gset_finite
X
:
set_finite
(
of_gset
X
).
...
...
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