Documentation Verification Report

Commute

πŸ“ Source: Mathlib/Data/Nat/Cast/Commute.lean

Statistics

MetricCount
DefinitionsCommute, Commute
2
TheoremsnatCast_mul_left, natCast_mul_natCast_mul, natCast_mul_right, natCast_mul_self, ofNat_left, ofNat_right, self_natCast_mul, self_natCast_mul_natCast_mul, cast_comm, cast_commute, commute_cast, natCast_mul_left, natCast_mul_natCast_mul, natCast_mul_right
14
Total16

Commute

Theorems

NameKindAssumesProvesValidatesDepends On
natCast_mul_left πŸ“–mathematicalCommute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”SemiconjBy.natCast_mul_left
natCast_mul_natCast_mul πŸ“–mathematicalCommute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”β€”
natCast_mul_right πŸ“–mathematicalCommute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”SemiconjBy.natCast_mul_right
natCast_mul_self πŸ“–mathematicalβ€”Commute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”natCast_mul_left
refl
ofNat_left πŸ“–mathematicalβ€”Commute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”Nat.cast_commute
ofNat_right πŸ“–mathematicalβ€”Commute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”Nat.commute_cast
self_natCast_mul πŸ“–mathematicalβ€”Commute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”natCast_mul_right
refl
self_natCast_mul_natCast_mul πŸ“–mathematicalβ€”Commute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”natCast_mul_natCast_mul
refl

Function

Definitions

NameCategoryTheorems
Commute πŸ“–MathDef
21 mathmath: CircleDeg1Lift.commute_nat_add, Commute.id_left, CircleDeg1Lift.commute_iff_commute, CliffordAlgebra.reverse_involute_commute, Commute.refl, Commute.iterate_self, Commute.iterate_iterate_self, CircleDeg1Lift.commute_add_int, CircleDeg1Lift.commute_sub_int, CircleDeg1Lift.commute_add_nat, Commute.function_commute_mul_left, CircleDeg1Lift.commute_int_add, Commute.self_iterate, iterate_commute, Semiconj.commute, WittVector.verschiebung_frobenius_comm, Commute.function_commute_mul_right, AddCommute.function_commute_add_left, AddCommute.function_commute_add_right, CircleDeg1Lift.commute_sub_nat, Commute.id_right

Nat

Theorems

NameKindAssumesProvesValidatesDepends On
cast_comm πŸ“–mathematicalβ€”Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”Commute.eq
cast_commute
cast_commute πŸ“–mathematicalβ€”Commute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”cast_zero
Commute.zero_left
cast_succ
Commute.add_left
Commute.one_left
commute_cast πŸ“–mathematicalβ€”Commute
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”Commute.symm
cast_commute

SemiconjBy

Theorems

NameKindAssumesProvesValidatesDepends On
natCast_mul_left πŸ“–mathematicalSemiconjBy
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”mul_left
Nat.cast_commute
natCast_mul_natCast_mul πŸ“–mathematicalSemiconjBy
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”β€”
natCast_mul_right πŸ“–mathematicalSemiconjBy
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
β€”mul_right
Nat.commute_cast

(root)

Definitions

NameCategoryTheorems
Commute πŸ“–MathDef
162 mathmath: Units.commute_iff_inv_mul_cancel, Nat.commute_cast, Units.commute_inv_coe, Matrix.Commute.zpow_self, LaurentPolynomial.commute_T, Prod.commute_iff, Commute.inv_right_iffβ‚€, LinearMap.IsIdempotentElem.commute_iff, cfc_commute_cfc, Commute.units_inv_right_iff, MvPowerSeries.commute_X_pow, commute_star_star, CircleDeg1Lift.commute_iff_commute, Commute.ofNat_left, NNRat.cast_commute, Matrix.mem_range_scalar_iff_commute_transvectionStruct, Commute.inv_left_iff, Commute.neg_right_iff, Matrix.PosSemidef.commute_iff, MulAction.not_commute_of_disjoint_movedBy_preimage, commute_invOf, CliffordAlgebra.commute_map_mul_map_of_isOrtho_of_mem_evenOdd_zero_right, Commute.intCast_right, Equiv.Perm.Disjoint.commute, card_comm_eq_card_conjClasses_mul_card, Equiv.Perm.IsCycle.commute_iff', Pi.commute_iff, commute_lmul_rmul, IsStarNormal.star_comm_self, Commute.zero_left, DihedralGroup.card_commute_odd, Module.Basis.mem_center_iff, LinearMap.commute_mulLeft_right, Equiv.Perm.cycleFactorsFinset_eq_finset, Algebra.commute_of_mem_adjoin_self, Equiv.Perm.commute_iff_of_mem_cycleFactorsFinset, AddMonoidAlgebra.of'_commute, Int.commute_cast, MvPowerSeries.commute_X, isStarNormal_iff, MulOpposite.commute_unop, Commute.inv_left_iffβ‚€, PowerSeries.commute_X_pow, commute_lmul_sq_rmul, Equiv.Perm.self_mem_cycle_factors_commute, commute_iff_eq, DihedralGroup.oddCommuteEquiv_symm_apply, OrderMonoidHom.commute_inl_inr, MonoidHom.noncommPiCoprod_apply, IsSelfAdjoint.commute_iff, Commute.smul_left_iff, DihedralGroup.oddCommuteEquiv_apply, Commute.inv_inv_iff, Commute.neg_left_iff, Equiv.Perm.support_noncommProd, commute_lmul_rmul_sq, Commute.zero_right, IsMulCentral.comm, Commute.self_zpow, isMulCentral_iff, Matrix.mem_range_scalar_iff_commute_single, LinearMap.IsIdempotentElem.commute_iff_of_isUnit, Commute.instRefl, NonUnitalNonAssocCommSemiring.mem_center_iff, Units.commute_iff_inv_mul_cancel_assoc, Commute.units_inv_left_iff, Commute.zpow_zpow_selfβ‚€, Commute.symm_iff, Matrix.PosDef.commute_iff, IsLprojection.commute, Matrix.Commute.zpow_zpow_self, NonUnitalAlgebra.commute_of_mem_adjoin_self, Commute.smul_right_iff, Units.commute_coe_inv, commute_lmul_lmul_sq, Commute.pow_pow_self, Commute.zpow_selfβ‚€, Commute.zpow_zpow_self, Matrix.IsHermitian.commute_iff, Rat.commute_cast, Equiv.Perm.OnCycleFactors.mem_ker_toPermHom_iff, Commute.self_intCast_mul_intCast_mul, AddMonoidHom.mulRight_eq_mulLeft_iff_forall_commute, Matrix.mem_range_scalar_iff_commute_single', instInfiniteProdSubtypeCommute, QuaternionAlgebra.coe_commute, commute_iff_mul_nonneg, CliffordAlgebra.commute_map_mul_map_of_isOrtho_of_mem_evenOdd_zero_left, Commute.smul_right_iffβ‚€, Polynomial.commute_X, Commute.pow_self, Algebra.commute_algebraMap_left, commutatorElement_eq_one_iff_commute, Matrix.Commute.self_zpow, Module.End.commute_id_right, Commute.on_refl, NonUnitalStarAlgebra.commute_of_mem_adjoin_self, Commute.inv_right_iff, MonoidHom.commute_inl_inr, OrderMonoidHom.commute_inlβ‚—_inrβ‚—, Commute.refl, IsStrictlyPositive.commute_iff, LieModule.commute_toEnd_of_mem_center_right, Commute.of_orderOf_dvd_two, CFC.commute_abs_self, MulOpposite.commute_op, Algebra.commute_algebraMap_right, Commute.neg_one_left, Commute.neg_one_right, DualNumber.commute_eps_left, ContinuousLinearMap.IsIdempotentElem.commute_iff_of_isUnit, Commute.units_val_iff, ContinuousLinearMap.IsIdempotentElem.commute_iff, Quaternion.coe_commute, DualNumber.commute_eps_right, Commute.ofNat_right, Commute.conj_iff, Int.cast_commute, Equiv.Perm.cycleFactorsFinset_mem_commute, Pi.mulSingle_apply_commute, Units.commute_iff_mul_inv_cancel_assoc, Commute.natCast_mul_self, Matrix.commute_diagonal, IsIdempotentElem.commute_of_anticommute, Commute.self_zpowβ‚€, Subgroup.commute_of_normal_of_disjoint, commute_map_iff, Equiv.Perm.IsCycle.forall_commute_iff, commute_star_comm, NNRat.commute_cast, Equiv.Perm.IsCycle.commute_iff, Commute.smul_left_iffβ‚€, Commute.self_natCast_mul_natCast_mul, Commute.self_intCast_mul, Equiv.Perm.cycleFactorsFinset_mem_commute', Subgroup.commute_subtype_of_commute, Polynomial.commute_X_pow, Rat.cast_commute, Commute.all, MonoidHom.FixedPointFree.commute_all_of_involutive, Commute.one_right, Matrix.scalar_commute_iff, RootPairing.isOrthogonal_comm, LieModule.commute_toEnd_of_mem_center_left, MonoidWithZeroHom.commute_inl_inr, Units.commute_iff_mul_inv_cancel, cfcβ‚™_commute_cfcβ‚™, commute_iff_lie_eq, Commute.intCast_mul_self, commProb_def, Commute.self_pow, AddMonoidHom.mulLeft_eq_mulRight_iff_forall_commute, Nat.cast_commute, PowerSeries.commute_X, commute_rmul_rmul_sq, Module.End.commute_id_left, Commute.self_natCast_mul, Commute.intCast_left, Equiv.Perm.commute_ofSubtype_noncommPiCoprod, Commute.zpow_self, MvPowerSeries.commute_monomial, Commute.one_left

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