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stdpp
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3eec2de1
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Commit
3eec2de1
authored
8 years ago
by
Robbert Krebbers
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Tweak some proofs.
parent
adc95f1c
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theories/base.v
+8
-14
8 additions, 14 deletions
theories/base.v
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14 deletions
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3eec2de1
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@@ -933,28 +933,22 @@ Inductive elem_of_list {A} : ElemOf A (list A) :=
|
elem_of_list_further
(
x
y
:
A
)
l
:
x
∈
l
→
x
∈
y
::
l
.
Existing
Instance
elem_of_list
.
Lemma
elem_of_list_In
{
A
}
(
l
:
list
A
)
x
:
x
∈
l
↔
In
x
l
.
Lemma
elem_of_list_In
{
A
}
(
l
:
list
A
)
x
:
x
∈
l
↔
In
x
l
.
Proof
.
induction
l
.
-
split
;
inversion
1
.
-
split
;
inversion
1
;
subst
;
(
left
+
(
right
;
apply
IHl
));
now
auto
.
split
.
-
induction
1
;
simpl
;
auto
.
-
induction
l
;
intros
[];
subst
;
constructor
;
auto
.
Qed
.
Inductive
NoDup
{
A
}
:
list
A
→
Prop
:=
|
NoDup_nil_2
:
NoDup
[]
|
NoDup_cons_2
x
l
:
x
∉
l
→
NoDup
l
→
NoDup
(
x
::
l
)
.
Lemma
NoDup_ListNoDup
{
A
}
(
l
:
list
A
)
:
NoDup
l
↔
List
.
NoDup
l
.
Lemma
NoDup_ListNoDup
{
A
}
(
l
:
list
A
)
:
NoDup
l
↔
List
.
NoDup
l
.
Proof
.
induction
l
.
-
split
;
intros
_;
now
constructor
.
-
split
;
inversion
1
;
subst
.
+
constructor
;
[
now
rewrite
<-
elem_of_list_In
|]
.
now
apply
IHl
.
+
constructor
;
[
now
rewrite
elem_of_list_In
|]
.
now
apply
IHl
.
split
.
-
induction
1
;
constructor
;
rewrite
<-
?elem_of_list_In
;
auto
.
-
induction
1
;
constructor
;
rewrite
?elem_of_list_In
;
auto
.
Qed
.
(** Decidability of equality of the carrier set is admissible, but we add it
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