Documentation Verification Report

Fin

📁 Source: Mathlib/Algebra/BigOperators/Fin.lean

Statistics

MetricCount
DefinitionspartialProd, partialSum, finFunctionFinEquiv, finPiFinEquiv, finSigmaFinEquiv
5
Theoremsadd_sum_removeNth, inv_partialProd_mul_eq_contractNth, mul_prod_removeNth, neg_partialSum_add_eq_contractNth, partialProd_contractNth, partialProd_init, partialProd_left_inv, partialProd_right_inv, partialProd_succ, partialProd_succ', partialProd_zero, partialSum_contractNth, partialSum_init, partialSum_left_neg, partialSum_right_neg, partialSum_succ, partialSum_succ', partialSum_zero, prod_Icc_cast, prod_Icc_castAdd, prod_Icc_castLE, prod_Icc_castSucc, prod_Icc_succ, prod_Ici_cast, prod_Ici_succ, prod_Ico_cast, prod_Ico_castAdd, prod_Ico_castLE, prod_Ico_castSucc, prod_Ico_succ, prod_Iic_cast, prod_Iic_castAdd, prod_Iic_castLE, prod_Iic_castSucc, prod_Iio_cast, prod_Iio_castAdd, prod_Iio_castLE, prod_Iio_castSucc, prod_Ioc_cast, prod_Ioc_castAdd, prod_Ioc_castLE, prod_Ioc_castSucc, prod_Ioc_succ, prod_Ioi_cast, prod_Ioi_succ, prod_Ioi_zero, prod_Ioo_cast, prod_Ioo_castAdd, prod_Ioo_castLE, prod_Ioo_castSucc, prod_Ioo_succ, prod_congr', prod_cons, prod_const, prod_insertNth, prod_ofFn, prod_prod_eq_prod_triangle_mul, prod_snoc, prod_trunc, prod_uIcc_cast, prod_uIcc_castAdd, prod_uIcc_castLE, prod_uIcc_castSucc, prod_uIcc_succ, prod_univ_add, prod_univ_castSucc, prod_univ_def, prod_univ_eight, prod_univ_five, prod_univ_four, prod_univ_fun_getElem, prod_univ_getElem, prod_univ_one, prod_univ_seven, prod_univ_six, prod_univ_succ, prod_univ_succAbove, prod_univ_three, prod_univ_two, prod_univ_two', prod_univ_zero, sum_Icc_cast, sum_Icc_castAdd, sum_Icc_castLE, sum_Icc_castSucc, sum_Icc_succ, sum_Ici_cast, sum_Ici_succ, sum_Ico_cast, sum_Ico_castAdd, sum_Ico_castLE, sum_Ico_castSucc, sum_Ico_succ, sum_Iic_cast, sum_Iic_castAdd, sum_Iic_castLE, sum_Iic_castSucc, sum_Iio_cast, sum_Iio_castAdd, sum_Iio_castLE, sum_Iio_castSucc, sum_Ioc_cast, sum_Ioc_castAdd, sum_Ioc_castLE, sum_Ioc_castSucc, sum_Ioc_succ, sum_Ioi_cast, sum_Ioi_succ, sum_Ioi_zero, sum_Ioo_cast, sum_Ioo_castAdd, sum_Ioo_castLE, sum_Ioo_castSucc, sum_Ioo_succ, sum_congr', sum_cons, sum_const, sum_insertNth, sum_neg_one_pow, sum_ofFn, sum_pow_mul_eq_add_pow, sum_snoc, sum_sum_eq_sum_triangle_add, sum_trunc, sum_uIcc_cast, sum_uIcc_castAdd, sum_uIcc_castLE, sum_uIcc_castSucc, sum_uIcc_succ, sum_univ_add, sum_univ_castSucc, sum_univ_def, sum_univ_eight, sum_univ_five, sum_univ_four, sum_univ_fun_getElem, sum_univ_getElem, sum_univ_one, sum_univ_seven, sum_univ_six, sum_univ_succ, sum_univ_succAbove, sum_univ_three, sum_univ_two, sum_univ_two', sum_univ_zero, prod_range, sum_range, alternatingProd_eq_finset_prod, alternatingSum_eq_finset_sum, prod_ofFn, prod_take_ofFn, sum_ofFn, sum_take_ofFn, finFunctionFinEquiv_apply, finFunctionFinEquiv_apply_val, finFunctionFinEquiv_single, finFunctionFinEquiv_symm_apply_val, finPiFinEquiv_apply, finPiFinEquiv_single, finSigmaFinEquiv_apply, finSigmaFinEquiv_one
162
Total167

Fin

Definitions

NameCategoryTheorems
partialProd 📖CompOp
15 mathmath: partialProd_contractNth, Rep.diagonalSuccIsoFree_inv_hom_single, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_left, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_right, Rep.diagonalSuccIsoTensorTrivial_inv_hom_single_single, Rep.diagonalSuccIsoFree_inv_hom_single_single, Action.diagonalSuccIsoTensorTrivial_inv_hom_apply, partialProd_left_inv, partialProd_init, partialProd_succ, inv_partialProd_mul_eq_contractNth, partialProd_succ', partialProd_zero, Rep.diagonalHomEquiv_apply, partialProd_right_inv
partialSum 📖CompOp
9 mathmath: Representation.apply_sub_id_partialSum_eq, partialSum_zero, partialSum_left_neg, partialSum_init, partialSum_succ', partialSum_right_neg, neg_partialSum_add_eq_contractNth, partialSum_succ, partialSum_contractNth

Theorems

NameKindAssumesProvesValidatesDepends On
add_sum_removeNth 📖mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum
Finset.univ
fintype
removeNth
sum_insertNth
insertNth_self_removeNth
inv_partialProd_mul_eq_contractNth 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
partialProd
succAbove
contractNth
lt_trichotomy
succAbove_of_castSucc_lt
le_iff_val_le_val
le_of_lt
partialProd_right_inv
contractNth_apply_of_lt
le_of_eq
succAbove_of_le_castSucc
partialProd_succ
mul_assoc
contractNth_apply_of_eq
inv_mul_cancel_left
contractNth_apply_of_gt
mul_prod_removeNth 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod
Finset.univ
fintype
removeNth
prod_insertNth
insertNth_self_removeNth
neg_partialSum_add_eq_contractNth 📖mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
partialSum
succAbove
contractNth
lt_trichotomy
succAbove_of_castSucc_lt
le_iff_val_le_val
le_of_lt
partialSum_right_neg
contractNth_apply_of_lt
le_of_eq
succAbove_of_le_castSucc
le_refl
partialSum_succ
add_assoc
contractNth_apply_of_eq
neg_add_cancel_left
contractNth_apply_of_gt
partialProd_contractNth 📖mathematicalpartialProd
contractNth
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
succAbove
partialProd_zero
succ_succAbove_zero
succ_succAbove_succ
partialProd_succ
lt_trichotomy
succAbove_of_castSucc_lt
contractNth_apply_of_lt
contractNth_apply_of_eq
succAbove_of_le_castSucc
mul_assoc
contractNth_apply_of_gt
partialProd_init 📖mathematicalpartialProd
init
partialProd_zero
partialProd_succ
partialProd_left_inv 📖mathematicalFunction.hasSMul
SemigroupAction.toSMul
Monoid.toSemigroup
DivInvMonoid.toMonoid
Group.toDivInvMonoid
MulAction.toSemigroupAction
Monoid.toMulAction
partialProd
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
partialProd_zero
mul_one
partialProd_succ
mul_assoc
mul_inv_cancel_left
partialProd_right_inv 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
partialProd
partialProd_succ
inv_mul_cancel_left
partialProd_succ 📖mathematicalpartialProd
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Semigroup.to_isLawfulIdentity
Semigroup.to_isAssociative
mul_one
partialProd_succ' 📖mathematicalpartialProd
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
tail
partialProd_zero 📖mathematicalpartialProd
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
partialSum_contractNth 📖mathematicalpartialSum
contractNth
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
succAbove
partialSum_zero
succ_succAbove_zero
succ_succAbove_succ
partialSum_succ
lt_trichotomy
succAbove_of_castSucc_lt
contractNth_apply_of_lt
castSucc_lt_succ_iff
contractNth_apply_of_eq
succAbove_of_le_castSucc
add_assoc
contractNth_apply_of_gt
partialSum_init 📖mathematicalpartialSum
init
partialSum_zero
partialSum_succ
partialSum_left_neg 📖mathematicalHVAdd.hVAdd
instHVAdd
Function.hasVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddAction.toAddSemigroupAction
AddMonoid.toAddAction
partialSum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
partialSum_zero
add_zero
partialSum_succ
add_assoc
add_neg_cancel_left
partialSum_right_neg 📖mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
partialSum
partialSum_succ
neg_add_cancel_left
partialSum_succ 📖mathematicalpartialSum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddSemigroup.to_isLawfulIdentity
AddSemigroup.to_isAssociative
add_zero
partialSum_succ' 📖mathematicalpartialSum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
tail
partialSum_zero 📖mathematicalpartialSum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
prod_Icc_cast 📖mathematicalFinset.prod
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Icc_castAdd 📖mathematicalFinset.prod
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Icc_castLE 📖mathematicalFinset.prod
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Icc_castSucc 📖mathematicalFinset.prod
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Icc_succ 📖mathematicalFinset.prod
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ici_cast 📖mathematicalFinset.prod
Finset.Ici
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.prod_congr
Finset.prod_map
prod_Ici_succ 📖mathematicalFinset.prod
Finset.Ici
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.prod_congr
Finset.prod_map
prod_Ico_cast 📖mathematicalFinset.prod
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ico_castAdd 📖mathematicalFinset.prod
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ico_castLE 📖mathematicalFinset.prod
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ico_castSucc 📖mathematicalFinset.prod
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ico_succ 📖mathematicalFinset.prod
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Iic_cast 📖mathematicalFinset.prod
Finset.Iic
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.prod_congr
Finset.prod_map
prod_Iic_castAdd 📖mathematicalFinset.prod
Finset.Iic
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.prod_congr
Finset.prod_map
prod_Iic_castLE 📖mathematicalFinset.prod
Finset.Iic
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.prod_congr
Finset.prod_map
prod_Iic_castSucc 📖mathematicalFinset.prod
Finset.Iic
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.prod_congr
Finset.prod_map
prod_Iio_cast 📖mathematicalFinset.prod
Finset.Iio
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.prod_congr
Finset.prod_map
prod_Iio_castAdd 📖mathematicalFinset.prod
Finset.Iio
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.prod_congr
Finset.prod_map
prod_Iio_castLE 📖mathematicalFinset.prod
Finset.Iio
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.prod_congr
Finset.prod_map
prod_Iio_castSucc 📖mathematicalFinset.prod
Finset.Iio
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.prod_congr
Finset.prod_map
prod_Ioc_cast 📖mathematicalFinset.prod
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioc_castAdd 📖mathematicalFinset.prod
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioc_castLE 📖mathematicalFinset.prod
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioc_castSucc 📖mathematicalFinset.prod
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioc_succ 📖mathematicalFinset.prod
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioi_cast 📖mathematicalFinset.prod
Finset.Ioi
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.prod_congr
Finset.prod_map
prod_Ioi_succ 📖mathematicalFinset.prod
Finset.Ioi
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.prod_congr
Finset.prod_map
prod_Ioi_zero 📖mathematicalFinset.prod
Finset.Ioi
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.univ
fintype
Finset.prod_congr
Ioi_zero_eq_map
Finset.prod_map
prod_Ioo_cast 📖mathematicalFinset.prod
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioo_castAdd 📖mathematicalFinset.prod
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioo_castLE 📖mathematicalFinset.prod
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioo_castSucc 📖mathematicalFinset.prod
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_Ioo_succ 📖mathematicalFinset.prod
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_congr' 📖mathematicalFinset.prod
Finset.univ
fintype
prod_cons 📖mathematicalFinset.prod
Finset.univ
fintype
cons
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_succ
cons_zero
Finset.prod_congr
cons_succ
prod_const 📖mathematicalFinset.prod
Finset.univ
fintype
Monoid.toNatPow
CommMonoid.toMonoid
Finset.prod_const
Fintype.card_fin
prod_insertNth 📖mathematicalFinset.prod
Finset.univ
fintype
insertNth
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_ofFn 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
Finset.prod
Finset.univ
fintype
univ_val_map
prod_prod_eq_prod_triangle_mul 📖mathematicalFinset.prod
Finset.univ
fintype
Finset.Ici
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod_congr
Finset.filter.congr_simp
Finset.prod_filter_mul_prod_filter_not
prod_univ_castSucc
prod_univ_succ
Finset.filter_le_eq_Ici
Finset.filter_false
mul_one
Finset.filter_ge_eq_Iic
one_mul
Finset.prod_comm'
Finset.prod_mul_distrib
prod_snoc 📖mathematicalFinset.prod
Finset.univ
fintype
snoc
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod_congr
prod_univ_castSucc
snoc_castSucc
snoc_last
prod_trunc 📖mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod
Finset.univ
fintype
prod_univ_add
Fintype.prod_eq_one
mul_one
prod_uIcc_cast 📖mathematicalFinset.prod
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_uIcc_castAdd 📖mathematicalFinset.prod
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_uIcc_castLE 📖mathematicalFinset.prod
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_uIcc_castSucc 📖mathematicalFinset.prod
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_uIcc_succ 📖mathematicalFinset.prod
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.prod_congr
Finset.prod_map
prod_univ_add 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Fintype.prod_equiv
Equiv.apply_symm_apply
Fintype.prod_sum_type
prod_univ_castSucc 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
mul_comm
Finset.prod_congr
succAbove_last
prod_univ_succAbove
prod_univ_def 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
List.ofFn_eq_map
prod_ofFn
prod_univ_eight 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_castSucc
prod_univ_seven
prod_univ_five 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_castSucc
prod_univ_four
prod_univ_four 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_castSucc
prod_univ_three
prod_univ_fun_getElem 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
univ_val_map
List.ofFn_getElem_eq_map
prod_univ_getElem 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
univ_val_map
List.ofFn_getElem
prod_univ_one 📖mathematicalFinset.prod
Finset.univ
fintype
Finset.prod_congr
Finset.univ_unique
Finset.prod_singleton
prod_univ_seven 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_castSucc
prod_univ_six
prod_univ_six 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_castSucc
prod_univ_five
prod_univ_succ 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_succAbove
prod_univ_succAbove 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
succAbove
univ_succAbove
Finset.prod_cons
Finset.prod_map
coe_succAboveEmb
prod_univ_three 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_castSucc
prod_univ_two
prod_univ_two 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_succ
Finset.prod_congr
Finset.univ_unique
Finset.prod_singleton
prod_univ_two' 📖mathematicalFinset.prod
Finset.univ
fintype
Matrix.vecCons
Matrix.vecEmpty
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod_univ_two
prod_univ_zero 📖mathematicalFinset.prod
Finset.univ
fintype
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
sum_Icc_cast 📖mathematicalFinset.sum
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_finCongr_Icc
Finset.sum_map
sum_Icc_castAdd 📖mathematicalFinset.sum
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castAddEmb_Icc
Finset.sum_map
sum_Icc_castLE 📖mathematicalFinset.sum
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castLEEmb_Icc
Finset.sum_map
sum_Icc_castSucc 📖mathematicalFinset.sum
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castSuccEmb_Icc
Finset.sum_map
sum_Icc_succ 📖mathematicalFinset.sum
Finset.Icc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_succEmb_Icc
Finset.sum_map
sum_Ici_cast 📖mathematicalFinset.sum
Finset.Ici
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.sum_congr
map_finCongr_Ici
Finset.sum_map
sum_Ici_succ 📖mathematicalFinset.sum
Finset.Ici
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.sum_congr
map_succEmb_Ici
Finset.sum_map
sum_Ico_cast 📖mathematicalFinset.sum
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_finCongr_Ico
Finset.sum_map
sum_Ico_castAdd 📖mathematicalFinset.sum
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castAddEmb_Ico
Finset.sum_map
sum_Ico_castLE 📖mathematicalFinset.sum
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castLEEmb_Ico
Finset.sum_map
sum_Ico_castSucc 📖mathematicalFinset.sum
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castSuccEmb_Ico
Finset.sum_map
sum_Ico_succ 📖mathematicalFinset.sum
Finset.Ico
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_succEmb_Ico
Finset.sum_map
sum_Iic_cast 📖mathematicalFinset.sum
Finset.Iic
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.sum_congr
map_finCongr_Iic
Finset.sum_map
sum_Iic_castAdd 📖mathematicalFinset.sum
Finset.Iic
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.sum_congr
map_castAddEmb_Iic
Finset.sum_map
sum_Iic_castLE 📖mathematicalFinset.sum
Finset.Iic
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.sum_congr
map_castLEEmb_Iic
Finset.sum_map
sum_Iic_castSucc 📖mathematicalFinset.sum
Finset.Iic
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.sum_congr
map_castSuccEmb_Iic
Finset.sum_map
sum_Iio_cast 📖mathematicalFinset.sum
Finset.Iio
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.sum_congr
map_finCongr_Iio
Finset.sum_map
sum_Iio_castAdd 📖mathematicalFinset.sum
Finset.Iio
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.sum_congr
map_castAddEmb_Iio
Finset.sum_map
sum_Iio_castLE 📖mathematicalFinset.sum
Finset.Iio
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.sum_congr
map_castLEEmb_Iio
Finset.sum_map
sum_Iio_castSucc 📖mathematicalFinset.sum
Finset.Iio
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderBot
Finset.sum_congr
map_castSuccEmb_Iio
Finset.sum_map
sum_Ioc_cast 📖mathematicalFinset.sum
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_finCongr_Ioc
Finset.sum_map
sum_Ioc_castAdd 📖mathematicalFinset.sum
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castAddEmb_Ioc
Finset.sum_map
sum_Ioc_castLE 📖mathematicalFinset.sum
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castLEEmb_Ioc
Finset.sum_map
sum_Ioc_castSucc 📖mathematicalFinset.sum
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castSuccEmb_Ioc
Finset.sum_map
sum_Ioc_succ 📖mathematicalFinset.sum
Finset.Ioc
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_succEmb_Ioc
Finset.sum_map
sum_Ioi_cast 📖mathematicalFinset.sum
Finset.Ioi
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.sum_congr
map_finCongr_Ioi
Finset.sum_map
sum_Ioi_succ 📖mathematicalFinset.sum
Finset.Ioi
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.sum_congr
map_succEmb_Ioi
Finset.sum_map
sum_Ioi_zero 📖mathematicalFinset.sum
Finset.Ioi
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
Finset.univ
fintype
Finset.sum_congr
Ioi_zero_eq_map
Finset.sum_map
sum_Ioo_cast 📖mathematicalFinset.sum
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_finCongr_Ioo
Finset.sum_map
sum_Ioo_castAdd 📖mathematicalFinset.sum
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castAddEmb_Ioo
Finset.sum_map
sum_Ioo_castLE 📖mathematicalFinset.sum
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castLEEmb_Ioo
Finset.sum_map
sum_Ioo_castSucc 📖mathematicalFinset.sum
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_castSuccEmb_Ioo
Finset.sum_map
sum_Ioo_succ 📖mathematicalFinset.sum
Finset.Ioo
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrder
Finset.sum_congr
map_succEmb_Ioo
Finset.sum_map
sum_congr' 📖mathematicalFinset.sum
Finset.univ
fintype
sum_cons 📖mathematicalFinset.sum
Finset.univ
fintype
cons
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_succ
cons_zero
Finset.sum_congr
cons_succ
sum_const 📖mathematicalFinset.sum
Finset.univ
fintype
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
Finset.sum_const
Fintype.card_fin
sum_insertNth 📖mathematicalFinset.sum
Finset.univ
fintype
insertNth
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_neg_one_pow 📖mathematicalFinset.sum
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Finset.univ
fintype
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Even
Nat.instDecidablePredEven
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Finset.sum_congr
Finset.univ_eq_empty
isEmpty'
sum_univ_castSucc
Even.neg_pow
one_pow
zero_add
Odd.neg_pow
Nat.not_even_iff_odd
add_neg_cancel
sum_ofFn 📖mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
Finset.sum
Finset.univ
fintype
univ_val_map
sum_pow_mul_eq_add_pow 📖mathematicalFinset.sum
Finset
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
Finset.univ
Finset.fintype
fintype
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Finset.card
Distrib.toAdd
Finset.sum_congr
Fintype.card_fin
Fintype.sum_pow_mul_eq_add_pow
sum_snoc 📖mathematicalFinset.sum
Finset.univ
fintype
snoc
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum_congr
sum_univ_castSucc
snoc_castSucc
snoc_last
sum_sum_eq_sum_triangle_add 📖mathematicalFinset.sum
Finset.univ
fintype
Finset.Ici
PartialOrder.toPreorder
instPartialOrder
instLocallyFiniteOrderTop
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum_congr
Finset.filter.congr_simp
not_le
Finset.sum_add_distrib
Finset.sum_filter_add_sum_filter_not
sum_univ_castSucc
sum_univ_succ
castSucc_le_castSucc_iff
Finset.filter_le_eq_Ici
castSucc_ne_last
Finset.filter_false
add_zero
castSucc_lt_succ_iff
Finset.filter_ge_eq_Iic
zero_add
Finset.sum_comm'
Finset.mem_univ
Finset.mem_Iic
Finset.mem_Ici
sum_trunc 📖mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum
Finset.univ
fintype
sum_univ_add
Fintype.sum_eq_zero
add_zero
sum_uIcc_cast 📖mathematicalFinset.sum
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.sum_congr
map_finCongr_uIcc
Finset.sum_map
sum_uIcc_castAdd 📖mathematicalFinset.sum
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.sum_congr
map_castAddEmb_uIcc
Finset.sum_map
sum_uIcc_castLE 📖mathematicalFinset.sum
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.sum_congr
map_castLEEmb_uIcc
Finset.sum_map
sum_uIcc_castSucc 📖mathematicalFinset.sum
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.sum_congr
map_castSuccEmb_uIcc
Finset.sum_map
sum_uIcc_succ 📖mathematicalFinset.sum
Finset.uIcc
instLattice
instLocallyFiniteOrder
Finset.sum_congr
map_succEmb_uIcc
Finset.sum_map
sum_univ_add 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Fintype.sum_equiv
Equiv.apply_symm_apply
Fintype.sum_sum_type
sum_univ_castSucc 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
add_comm
Finset.sum_congr
succAbove_last
sum_univ_succAbove
sum_univ_def 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
List.ofFn_eq_map
sum_ofFn
sum_univ_eight 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_castSucc
sum_univ_seven
sum_univ_five 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_castSucc
sum_univ_four
sum_univ_four 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_castSucc
sum_univ_three
sum_univ_fun_getElem 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
univ_val_map
List.ofFn_getElem_eq_map
sum_univ_getElem 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
univ_val_map
List.ofFn_getElem
sum_univ_one 📖mathematicalFinset.sum
Finset.univ
fintype
Finset.sum_congr
Finset.univ_unique
Finset.sum_singleton
sum_univ_seven 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_castSucc
sum_univ_six
sum_univ_six 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_castSucc
sum_univ_five
sum_univ_succ 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_succAbove
sum_univ_succAbove 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
succAbove
univ_succAbove
Finset.sum_cons
Finset.sum_map
coe_succAboveEmb
sum_univ_three 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_castSucc
sum_univ_two
sum_univ_two 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_succ
Finset.sum_congr
Finset.univ_unique
Finset.sum_singleton
sum_univ_two' 📖mathematicalFinset.sum
Finset.univ
fintype
Matrix.vecCons
Matrix.vecEmpty
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum_univ_two
sum_univ_zero 📖mathematicalFinset.sum
Finset.univ
fintype
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid

Finset

Theorems

NameKindAssumesProvesValidatesDepends On
prod_range 📖mathematicalprod
range
univ
Fin.fintype
Fin.prod_univ_eq_prod_range
sum_range 📖mathematicalsum
range
univ
Fin.fintype
Fin.sum_univ_eq_sum_range

List

Theorems

NameKindAssumesProvesValidatesDepends On
alternatingProd_eq_finset_prod 📖mathematicalalternatingProd
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
DivisionMonoid.toDivInvMonoid
InvOneClass.toInv
Finset.prod
DivisionCommMonoid.toCommMonoid
Finset.univ
Fin.fintype
DivInvMonoid.toZPow
Monoid.toNatPow
Int.instMonoid
alternatingProd.eq_1
Finset.prod_eq_one
le_refl
Fin.prod_univ_succ
pow_zero
zpow_one
Finset.prod_congr
Finset.univ_eq_empty
Fin.isEmpty'
Finset.prod_const
mul_one
mul_assoc
pow_one
zpow_neg
pow_add
mul_neg
neg_neg
alternatingSum_eq_finset_sum 📖mathematicalalternatingSum
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
SubtractionMonoid.toSubNegMonoid
NegZeroClass.toNeg
Finset.sum
SubtractionCommMonoid.toAddCommMonoid
Finset.univ
Fin.fintype
SubNegMonoid.toZSMul
Monoid.toNatPow
Int.instMonoid
alternatingSum.eq_1
Finset.sum_eq_zero
le_refl
Fin.sum_univ_succ
pow_zero
one_zsmul
Finset.sum_congr
Finset.univ_eq_empty
Fin.isEmpty'
Finset.sum_const
zero_nsmul
add_zero
add_assoc
pow_one
neg_zsmul
pow_add
mul_neg
mul_one
neg_neg
prod_ofFn 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
Finset.prod
Finset.univ
Fin.fintype
Fin.prod_ofFn
prod_take_ofFn 📖mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
Finset.prod
Finset.filter
Finset.univ
Fin.fintype
Finset.prod_congr
Finset.filter.congr_simp
Finset.filter_false
prod_take_succ
Finset.ext
Finset.prod_insert
mul_comm
not_lt
le_trans
lt_of_lt_of_le
lt_trans
sum_ofFn 📖mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
Finset.sum
Finset.univ
Fin.fintype
Fin.sum_ofFn
sum_take_ofFn 📖mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
Finset.sum
Finset.filter
Finset.univ
Fin.fintype
Finset.sum_congr
Finset.filter.congr_simp
Finset.filter_false
sum_take_succ
Finset.ext
Finset.mem_filter
Finset.mem_univ
Finset.mem_insert
Finset.sum_insert
lt_self_iff_false
add_comm
not_lt
le_trans
lt_of_lt_of_le
lt_trans

(root)

Definitions

NameCategoryTheorems
finFunctionFinEquiv 📖CompOp
4 mathmath: finFunctionFinEquiv_apply_val, finFunctionFinEquiv_apply, finFunctionFinEquiv_single, finFunctionFinEquiv_symm_apply_val
finPiFinEquiv 📖CompOp
2 mathmath: finPiFinEquiv_apply, finPiFinEquiv_single
finSigmaFinEquiv 📖CompOp
2 mathmath: finSigmaFinEquiv_apply, finSigmaFinEquiv_one

Theorems

NameKindAssumesProvesValidatesDepends On
finFunctionFinEquiv_apply 📖mathematicalMonoid.toNatPow
Nat.instMonoid
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
finFunctionFinEquiv
Finset.sum
Nat.instAddCommMonoid
Finset.univ
Fin.fintype
finFunctionFinEquiv_apply_val 📖mathematicalMonoid.toNatPow
Nat.instMonoid
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
finFunctionFinEquiv
Finset.sum
Nat.instAddCommMonoid
Finset.univ
Fin.fintype
finFunctionFinEquiv_single 📖mathematicalMonoid.toNatPow
Nat.instMonoid
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
finFunctionFinEquiv
Pi.single
finFunctionFinEquiv_apply
Fintype.sum_eq_single
Pi.single_eq_of_ne
MulZeroClass.zero_mul
Pi.single_eq_same
finFunctionFinEquiv_symm_apply_val 📖mathematicalDFunLike.coe
Equiv
Monoid.toNatPow
Nat.instMonoid
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
finFunctionFinEquiv
finPiFinEquiv_apply 📖mathematicalFinset.prod
Nat.instCommMonoid
Finset.univ
Fin.fintype
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
finPiFinEquiv
Finset.sum
Nat.instAddCommMonoid
LT.lt.le
Nat.instPreorder
finPiFinEquiv_single 📖mathematicalMulZeroClass.toZero
Nat.instMulZeroClass
Finset.prod
Nat.instCommMonoid
Finset.univ
Fin.fintype
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
finPiFinEquiv
Pi.single
LT.lt.le
Nat.instPreorder
LT.lt.le
finPiFinEquiv_apply
Fintype.sum_eq_single
Pi.single_eq_of_ne
MulZeroClass.zero_mul
Pi.single_eq_same
finSigmaFinEquiv_apply 📖mathematicalFinset.sum
Nat.instAddCommMonoid
Finset.univ
Fin.fintype
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
finSigmaFinEquiv
LT.lt.le
Nat.instPreorder
LT.lt.le
finSigmaFinEquiv.eq_2
Finset.sum_congr
finSigmaFinEquiv_one 📖mathematicalFinset.sum
Nat.instAddCommMonoid
Finset.univ
Fin.fintype
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
finSigmaFinEquiv
LT.lt.le
finSigmaFinEquiv_apply
add_eq_right
AddRightCancelSemigroup.toIsRightCancelAdd
Finset.sum_of_isEmpty
Fin.isEmpty'

---

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