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Mathlib
.
Data
.
Finite
.
Prod
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Imports
Init
Mathlib.Data.Fintype.Prod
Mathlib.Data.Fintype.Vector
Imported by
Finite
.
instProd
Finite
.
instPProd
Finite
.
prod_left
Finite
.
prod_right
Pi
.
finite
instFiniteSym
Finiteness of products
#
source
instance
Finite
.
instProd
{α :
Type
u_1}
{β :
Type
u_2}
[
Finite
α
]
[
Finite
β
]
:
Finite
(
α
×
β
)
Equations
⋯
=
⋯
source
instance
Finite
.
instPProd
{α :
Sort
u_3}
{β :
Sort
u_4}
[
Finite
α
]
[
Finite
β
]
:
Finite
(
α
×'
β
)
Equations
⋯
=
⋯
source
theorem
Finite
.
prod_left
{α :
Type
u_1}
(β :
Type
u_3)
[
Finite
(
α
×
β
)
]
[
Nonempty
β
]
:
Finite
α
source
theorem
Finite
.
prod_right
{β :
Type
u_2}
(α :
Type
u_3)
[
Finite
(
α
×
β
)
]
[
Nonempty
α
]
:
Finite
β
source
instance
Pi
.
finite
{α :
Sort
u_3}
{β :
α
→
Sort
u_4
}
[
Finite
α
]
[
∀ (
a
:
α
),
Finite
(
β
a
)
]
:
Finite
((
a
:
α
) →
β
a
)
Equations
⋯
=
⋯
source
instance
instFiniteSym
{α :
Type
u_1}
[
Finite
α
]
{n :
ℕ
}
:
Finite
(
Sym
α
n
)
Equations
⋯
=
⋯