Documentation
Mathlib
.
Algebra
.
BigOperators
.
Sym
Search
return to top
source
Imports
Init
Mathlib.Data.Finset.Sym
Mathlib.Data.Sym.Sym2.Order
Mathlib.Algebra.BigOperators.Group.Finset.Basic
Imported by
Finset
.
sum_sym2_filter_not_isDiag
Lemmas on
Finset.sum
and
Finset.prod
involving
Finset.sym2
#
source
theorem
Finset
.
sum_sym2_filter_not_isDiag
{ι :
Type
u_1}
{α :
Type
u_2}
[
LinearOrder
ι
]
[
AddCommMonoid
α
]
(s :
Finset
ι
)
(p :
Sym2
ι
→
α
)
:
∑
i
∈
filter
(fun (
i
:
Sym2
ι
) =>
¬
i
.IsDiag
)
s
.sym2
,
p
i
=
∑
i
∈
filter
(fun (
i
:
ι
×
ι
) =>
i
.1
<
i
.2
)
s
.offDiag
,
p
s(
i
.1
,
i
.2
)