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Init
.
Data
.
Array
.
OfFn
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Imports
Init.Data.Array.Lemmas
Init.Data.List.OfFn
Imported by
Array
.
ofFn_zero
Array
.
ofFn_succ
Array
.
toList_ofFn
Array
.
ofFn_eq_empty_iff
Array
.
mem_ofFn
Theorems about
Array.ofFn
#
source
@[simp]
theorem
Array
.
ofFn_zero
{
α
:
Type
u_1}
(
f
:
Fin
0
→
α
)
:
ofFn
f
=
#[
]
source
theorem
Array
.
ofFn_succ
{
n
:
Nat
}
{
α
:
Type
u_1}
(
f
:
Fin
(
n
+
1
)
→
α
)
:
ofFn
f
=
(
ofFn
fun (
i
:
Fin
n
) =>
f
i
.
castSucc
)
.
push
(
f
⟨
n
,
⋯
⟩
)
source
@[simp]
theorem
Array
.
toList_ofFn
{
n
:
Nat
}
{
α
:
Type
u_1}
(
f
:
Fin
n
→
α
)
:
(
ofFn
f
)
.
toList
=
List.ofFn
f
source
@[simp]
theorem
Array
.
ofFn_eq_empty_iff
{
n
:
Nat
}
{
α
:
Type
u_1}
{
f
:
Fin
n
→
α
}
:
ofFn
f
=
#[
]
↔
n
=
0
source
@[simp]
theorem
Array
.
mem_ofFn
{
α
:
Type
u_1}
{
n
:
Nat
}
(
f
:
Fin
n
→
α
)
(
a
:
α
)
:
a
∈
ofFn
f
↔
∃
(
i
:
Fin
n
)
,
f
i
=
a