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8b9a96ad
Commit
8b9a96ad
authored
Sep 23, 2016
by
Robbert Krebbers
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Relate "elements" of a finite set to nil.
parent
65171af2
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prelude/fin_collections.v
View file @
8b9a96ad
...
...
@@ -38,6 +38,17 @@ Proof.
apply
elem_of_nil_inv
;
intros
x
.
rewrite
elem_of_elements
,
elem_of_empty
;
tauto
.
Qed
.
Lemma
elements_empty_inv
X
:
elements
X
=
[]
→
X
≡
∅
.
Proof
.
intros
HX
;
apply
elem_of_equiv_empty
;
intros
x
.
rewrite
<-
elem_of_elements
,
HX
,
elem_of_nil
.
tauto
.
Qed
.
Lemma
elements_empty'
X
:
elements
X
=
[]
↔
X
≡
∅
.
Proof
.
split
;
intros
HX
;
[
by
apply
elements_empty_inv
|].
by
rewrite
<-
Permutation_nil
,
HX
,
elements_empty
.
Qed
.
Lemma
elements_union_singleton
(
X
:
C
)
x
:
x
∉
X
→
elements
({[
x
]}
∪
X
)
≡
ₚ
x
::
elements
X
.
Proof
.
...
...
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