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stdpp
Commits
210bf091
Commit
210bf091
authored
Apr 05, 2018
by
Robbert Krebbers
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Notation `∈@{A}`.
parent
6aba4a3f
Changes
9
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9 changed files
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12 additions
and
10 deletions
+12
-10
theories/base.v
theories/base.v
+3
-0
theories/bset.v
theories/bset.v
+1
-1
theories/coPset.v
theories/coPset.v
+1
-1
theories/collections.v
theories/collections.v
+2
-3
theories/fin_collections.v
theories/fin_collections.v
+1
-1
theories/gmultiset.v
theories/gmultiset.v
+1
-1
theories/infinite.v
theories/infinite.v
+1
-1
theories/list.v
theories/list.v
+1
-1
theories/mapset.v
theories/mapset.v
+1
-1
No files found.
theories/base.v
View file @
210bf091
...
...
@@ -856,6 +856,9 @@ Notation "(∉)" := (λ x X, x ∉ X) (only parsing) : stdpp_scope.
Notation
"( x ∉)"
:
=
(
λ
X
,
x
∉
X
)
(
only
parsing
)
:
stdpp_scope
.
Notation
"(∉ X )"
:
=
(
λ
x
,
x
∉
X
)
(
only
parsing
)
:
stdpp_scope
.
Infix
"∈@{ B }"
:
=
(@
elem_of
_
B
_
)
(
at
level
70
,
only
parsing
)
:
stdpp_scope
.
Notation
"(∈@{ B } )"
:
=
(@
elem_of
_
B
_
)
(
only
parsing
)
:
stdpp_scope
.
Class
Disjoint
A
:
=
disjoint
:
A
→
A
→
Prop
.
Hint
Mode
Disjoint
!
:
typeclass_instances
.
Instance
:
Params
(@
disjoint
)
2
.
...
...
theories/bset.v
View file @
210bf091
...
...
@@ -29,7 +29,7 @@ Proof.
-
intros
X
Y
x
;
unfold
elem_of
,
bset_elem_of
;
simpl
.
destruct
(
bset_car
X
x
),
(
bset_car
Y
x
)
;
simpl
;
tauto
.
Qed
.
Instance
bset_elem_of_dec
{
A
}
:
RelDecision
(
@
elem_of
_
(
bset
A
)
_
).
Instance
bset_elem_of_dec
{
A
}
:
RelDecision
(
∈
@{
bset
A
}
).
Proof
.
refine
(
λ
x
X
,
cast_if
(
decide
(
bset_car
X
x
)))
;
done
.
Defined
.
Typeclasses
Opaque
bset_elem_of
.
...
...
theories/coPset.v
View file @
210bf091
...
...
@@ -190,7 +190,7 @@ Proof.
intros
p
;
apply
eq_bool_prop_intro
,
(
HXY
p
).
Qed
.
Instance
coPset_elem_of_dec
:
RelDecision
(
@
elem_of
_
coPset
_
).
Instance
coPset_elem_of_dec
:
RelDecision
(
∈
@{
coPset
}
).
Proof
.
solve_decision
.
Defined
.
Instance
coPset_equiv_dec
:
RelDecision
(
≡
@{
coPset
}).
Proof
.
refine
(
λ
X
Y
,
cast_if
(
decide
(
X
=
Y
)))
;
abstract
(
by
fold_leibniz
).
Defined
.
...
...
theories/collections.v
View file @
210bf091
...
...
@@ -28,8 +28,7 @@ Section setoids_simple.
Qed
.
Global
Instance
singleton_proper
:
Proper
((=)
==>
(
≡
@{
C
}))
singleton
.
Proof
.
apply
_
.
Qed
.
Global
Instance
elem_of_proper
:
Proper
((=)
==>
(
≡
)
==>
iff
)
(@
elem_of
A
C
_
)
|
5
.
Global
Instance
elem_of_proper
:
Proper
((=)
==>
(
≡
)
==>
iff
)
(
∈
@{
C
})
|
5
.
Proof
.
by
intros
x
?
<-
X
Y
.
Qed
.
Global
Instance
disjoint_proper
:
Proper
((
≡
)
==>
(
≡
)
==>
iff
)
(@
disjoint
C
_
).
Proof
.
...
...
@@ -695,7 +694,7 @@ Section collection.
End
leibniz
.
Section
dec
.
Context
`
{!
RelDecision
(
@
elem_of
A
C
_
)}.
Context
`
{!
RelDecision
(
∈
@{
C
}
)}.
Lemma
not_elem_of_intersection
x
X
Y
:
x
∉
X
∩
Y
↔
x
∉
X
∨
x
∉
Y
.
Proof
.
rewrite
elem_of_intersection
.
destruct
(
decide
(
x
∈
X
))
;
tauto
.
Qed
.
Lemma
not_elem_of_difference
x
X
Y
:
x
∉
X
∖
Y
↔
x
∉
X
∨
x
∈
Y
.
...
...
theories/fin_collections.v
View file @
210bf091
...
...
@@ -23,7 +23,7 @@ Implicit Types X Y : C.
Lemma
fin_collection_finite
X
:
set_finite
X
.
Proof
.
by
exists
(
elements
X
)
;
intros
;
rewrite
elem_of_elements
.
Qed
.
Instance
elem_of_dec_slow
:
RelDecision
(
@
elem_of
A
C
_
)
|
100
.
Instance
elem_of_dec_slow
:
RelDecision
(
∈
@{
C
}
)
|
100
.
Proof
.
refine
(
λ
x
X
,
cast_if
(
decide_rel
(
∈
)
x
(
elements
X
)))
;
by
rewrite
<-(
elem_of_elements
_
).
...
...
theories/gmultiset.v
View file @
210bf091
...
...
@@ -98,7 +98,7 @@ Proof.
by
split
;
auto
with
lia
.
-
intros
X
Y
x
.
rewrite
!
elem_of_multiplicity
,
multiplicity_union
.
omega
.
Qed
.
Global
Instance
gmultiset_elem_of_dec
:
RelDecision
(
@
elem_of
_
(
gmultiset
A
)
_
).
Global
Instance
gmultiset_elem_of_dec
:
RelDecision
(
∈
@{
gmultiset
A
}
).
Proof
.
refine
(
λ
x
X
,
cast_if
(
decide
(
0
<
multiplicity
x
X
)))
;
done
.
Defined
.
(* Algebraic laws *)
...
...
theories/infinite.v
View file @
210bf091
...
...
@@ -26,7 +26,7 @@ Qed.
(** * Fresh elements *)
Section
Fresh
.
Context
`
{
FinCollection
A
C
,
Infinite
A
,
!
RelDecision
(
@
elem_of
A
C
_
)}.
Context
`
{
FinCollection
A
C
,
Infinite
A
,
!
RelDecision
(
∈
@{
C
}
)}.
Definition
fresh_generic_body
(
s
:
C
)
(
rec
:
∀
s'
,
s'
⊂
s
→
nat
→
A
)
(
n
:
nat
)
:
A
:
=
let
cand
:
=
inject
n
in
...
...
theories/list.v
View file @
210bf091
...
...
@@ -311,7 +311,7 @@ Instance list_subseteq {A} : SubsetEq (list A) := λ l1 l2, ∀ x, x ∈ l1 →
Section list_set.
Context `{dec : EqDecision A}.
Global Instance elem_of_list_dec : RelDecision (
@elem_of A (list A) _
).
Global Instance elem_of_list_dec : RelDecision (
∈@{list A}
).
Proof.
refine (
fix go x l :=
...
...
theories/mapset.v
View file @
210bf091
...
...
@@ -78,7 +78,7 @@ Section deciders.
Defined
.
Global
Instance
mapset_equiv_dec
:
RelDecision
(
≡
@{
mapset
M
})
|
1
.
Proof
.
refine
(
λ
X1
X2
,
cast_if
(
decide
(
X1
=
X2
)))
;
abstract
(
by
fold_leibniz
).
Defined
.
Global
Instance
mapset_elem_of_dec
:
RelDecision
(
@
elem_of
_
(
mapset
M
)
_
)
|
1
.
Global
Instance
mapset_elem_of_dec
:
RelDecision
(
∈
@{
mapset
M
}
)
|
1
.
Proof
.
refine
(
λ
x
X
,
cast_if
(
decide
(
mapset_car
X
!!
x
=
Some
())))
;
done
.
Defined
.
Global
Instance
mapset_disjoint_dec
:
RelDecision
(@
disjoint
(
mapset
M
)
_
).
Proof
.
...
...
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