Documentation Verification Report

Odd

📁 Source: Mathlib/Order/Monotone/Odd.lean

Statistics

MetricCount
DefinitionsOdd, Odd, Odd
3
Theoremsantitone_of_odd_of_monotoneOn_nonneg, monotone_of_odd_of_monotoneOn_nonneg, strictAnti_of_odd_strictAntiOn_nonneg, strictMono_of_odd_strictMonoOn_nonneg
4
Total7

DirichletCharacter

Definitions

NameCategoryTheorems
Odd 📖MathDef
3 mathmath: even_or_odd, Even.not_odd, not_even_and_odd

Function

Definitions

NameCategoryTheorems
Odd 📖MathDef
10 mathmath: Even.mul_odd, DirichletCharacter.Odd.to_fun, Odd.comp_odd, Odd.zero, Odd.mul_even, Even.smul_odd, Odd.smul_even, Odd.add, ZMod.dft_odd_iff, Odd.const_smul

(root)

Definitions

NameCategoryTheorems
Odd 📖MathDef
145 mathmath: odd_add_one_self', odd_add_one_self, Nat.odd_fermatNumber, Odd.neg, pow_eq_neg_pow_iff, even_sub_one, ZMod.isCyclic_units_iff_of_odd, Even.one_add, Int.odd_mul, Int.isCoprime_two_right, neg_one_pow_eq_neg_one_iff_odd, Even.add_one, Int.odd_sign_iff, Nat.four_dvd_or_exists_odd_prime_and_dvd_of_two_lt, Int.odd_pow', Int.even_xor'_odd, Odd.natAbs, Polynomial.Chebyshev.eval_T_real_eq_neg_one_iff, Fin.not_odd_iff_even_of_even, Nat.odd_add_one, Int.negOnePow_eq_neg_one_iff, Finset.even_sum_iff_even_card_odd, Nat.odd_totient_iff, ZMod.natCast_eq_one_iff_odd, Set.odd_ncard_compl_iff, Nat.odd_sub', Fin.odd_of_val, SimpleGraph.odd_card_odd_degree_vertices_ne, ZMod.isCyclic_units_iff, zpow_eq_neg_zpow_iff₀, Nat.infinite_odd_deficient, geom_sum_pos_iff, Set.odd_card_insert_iff, Int.odd_add, ZMod.natCast_ne_zero_iff_odd, Nat.infinite_odd_abundant, Equiv.Perm.sign_of_cycleType_eq_replicate, Nat.odd_totient_iff_eq_one, odd_add_self_one', AlternatingGroup.card_of_cycleType_singleton, ComplexShape.down_nat_odd_add, Int.odd_coe_nat, Even.sub_odd, odd_neg_one, Nat.not_odd_iff_even, SimpleGraph.even_card_odd_degree_vertices, Nat.Even.sub_odd, Int.isCompl_even_odd, Int.odd_sub, Odd.mod_even, Nat.Prime.odd_of_ne_two, Even.add_odd, Set.even_card_insert_iff, Odd.intCast, Nat.not_even_iff_odd, Fin.odd_iff_of_even, Nat.frequently_odd, Odd.map, Fin.even_add_one_iff_odd, Nat.coprime_two_left, Nat.coprime_two_right, Int.even_or_odd, odd_add_two, Odd.of_dvd_nat, Fin.even_iff, Equiv.Perm.centralizer_le_alternating_iff, odd_neg, Nat.Odd.sub_even, Nat.odd_pow_iff, MonoidHom.FixedPointFree.odd_orderOf_of_involutive, Int.odd_iff, Nat.Odd.of_mul_right, Int.odd_sub', Finset.odd_sum_iff_odd_card_odd, Int.not_even_iff_odd, even_add_one, Nat.odd_mul, Odd.natCast, Odd.sub_even, Nat.even_sub', Fin.odd_iff_imp, Int.not_odd_zero, ComplexShape.up_nat_odd_add, ZMod.intCast_eq_one_iff_odd, Int.even_add', Fin.even_succAbove_add_predAbove, Nat.even_xor_odd, odd_sub_two, Int.isCoprime_two_left, Int.odd_add', Odd.add_even, odd_add_one, Fin.odd_iff, Nat.Prime.eq_two_or_odd', Int.natAbs_odd, odd_one, Nat.not_odd_iff, Int.odd_pow, Fin.odd_add_one_iff_even, Nat.even_add', Int.Odd.of_mul_right, Nat.odd_add', Odd.pow, Function.Involutive.iterate_eq_self, SimpleGraph.odd_ncard_oddComponents, Fin.odd_of_odd, Int.not_odd_iff, Int.not_odd_iff_even, odd_iff_exists_bit1, Odd.of_isUnit_two, MonoidHom.FixedPointFree.odd_card_of_involutive, Even.odd_add, mersenne_odd, pow_eq_neg_one_iff, odd_sub_one, Nat.eq_two_pow_or_exists_odd_prime_and_dvd, Nat.odd_sub, schnirelmannDensity_setOf_Odd, Nat.Coprime.odd_of_left, SimpleGraph.Coloring.odd_length_iff_not_congr, Nat.isCompl_even_odd, Nat.Prime.odd_iff, odd_abs, Odd.mul, Nat.exists_eq_two_pow_mul_odd, odd_two_mul_add_one, Nat.Coprime.odd_of_right, Nat.even_or_odd, Fin.not_even_iff_odd_of_even, SimpleGraph.ConnectedComponent.odd_oddComponents_ncard_subset_supp, Fin.odd_iff_mod_of_even, CoxeterSystem.IsReflection.odd_length, range_two_mul_add_one, Nat.odd_iff, SimpleGraph.exists_ne_odd_degree_of_exists_odd_degree, SimpleGraph.Walk.IsEulerian.card_odd_degree, Int.even_sub', Nat.Odd.of_mul_left, zpow_eq_neg_one_iff₀, Odd.all, Odd.mod_even_iff, Nat.not_odd_zero, Nat.odd_add, Equiv.Perm.OnCycleFactors.odd_of_centralizer_le_alternatingGroup, Int.Odd.of_mul_left

Theorems

NameKindAssumesProvesValidatesDepends On
antitone_of_odd_of_monotoneOn_nonneg 📖mathematicalNegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
AntitoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ici
NegZeroClass.toZero
Antitone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
monotone_of_odd_of_monotoneOn_nonneg
OrderDual.isOrderedAddMonoid
monotone_of_odd_of_monotoneOn_nonneg 📖mathematicalNegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
MonotoneOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ici
NegZeroClass.toZero
Monotone
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MonotoneOn.Iic_union_Ici
neg_le_neg_iff
IsOrderedAddMonoid.toAddLeftMono
covariant_swap_add_of_covariant_add
neg_nonneg
neg_le_neg
strictAnti_of_odd_strictAntiOn_nonneg 📖mathematicalNegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
StrictAntiOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ici
NegZeroClass.toZero
StrictAnti
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
strictMono_of_odd_strictMonoOn_nonneg
OrderDual.isOrderedAddMonoid
strictMono_of_odd_strictMonoOn_nonneg 📖mathematicalNegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
StrictMonoOn
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ici
NegZeroClass.toZero
StrictMono
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
StrictMonoOn.Iic_union_Ici
neg_lt_neg_iff
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
instIsLeftCancelAddOfAddLeftReflectLE
IsOrderedCancelAddMonoid.toAddLeftReflectLE
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
IsOrderedAddMonoid.toAddLeftMono
IsRightCancelAdd.addRightStrictMono_of_addRightMono
instIsRightCancelAddOfAddRightReflectLE
contravariant_swap_add_of_contravariant_add
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
IsOrderedCancelAddMonoid.toAddLeftReflectLT
covariant_swap_add_of_covariant_add
neg_nonneg
neg_lt_neg

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