Documentation Verification Report

Basic

📁 Source: Mathlib/Algebra/GroupWithZero/Basic.lean

Statistics

MetricCount
DefinitionstoDivisionMonoid, IsNilpotent, IsReduced, uniqueOfZeroEqOne
4
Theoremsmul_left_injective, mul_right_injective, eq_zero, mk, of_pow, pow_iff_pos, pow_of_pos, pow_succ, zero, eq_zero, pow_eq_zero, pow_eq_zero_iff, pow_eq_zero_iff', pow_ne_zero, pow_ne_zero_iff, mul, pow, div_div_self, div_mul_eq_mul_div₀, div_self_mul_self, div_self_mul_self', div_sq_cancel, div_zero, eq_of_zero_eq_one, eq_zero_of_mul_eq_self_left, eq_zero_of_mul_eq_self_right, eq_zero_of_mul_self_eq_zero, eq_zero_of_one_div_eq_zero, eq_zero_of_pow_eq_zero, eq_zero_of_zero_eq_one, exists_isNilpotent_of_not_isReduced, exists_right_inv_of_exists_left_inv, instIsCancelMulZero, inv_eq_zero, inv_mul_cancel_left₀, inv_mul_cancel_right₀, inv_mul_mul_self, isNilpotent_iff_eq_zero, isNilpotent_of_subsingleton, isReduced_iff, isReduced_of_noZeroDivisors, isReduced_of_subsingleton, left_eq_mul₀, left_ne_zero_of_mul, left_ne_zero_of_mul_eq_one, mul_eq_left₀, mul_eq_right₀, mul_eq_zero_of_ne_zero_imp_eq_zero, mul_inv_mul_cancel, mul_left_eq_self₀, mul_left_surjective₀, mul_ne_zero, mul_right_eq_self₀, mul_right_surjective₀, mul_self_div_self, mul_self_mul_inv, mul_zero_eq_const, ne_zero_and_ne_zero_of_mul, ne_zero_of_one_div_ne_zero, ne_zero_pow, not_isNilpotent_one, one_div_ne_zero, pow_eq_zero, pow_eq_zero_iff, pow_eq_zero_iff', pow_eq_zero_of_le, pow_mul_eq_zero_of_le, pow_ne_zero, pow_ne_zero_iff, right_eq_mul₀, right_ne_zero_of_mul, right_ne_zero_of_mul_eq_one, sq_eq_zero_iff, subsingleton_iff_zero_eq_one, subsingleton_of_zero_eq_one, zero_div, zero_eq_inv, zero_mul_eq_const, zero_ne_one_or_forall_eq_0, zero_pow, zero_pow_eq, zero_pow_eq_one₀, zero_pow_eq_zero, zero_zpow, zero_zpow_eq, zero_zpow_eq_one₀, zpow_add', zpow_add_one₀, zpow_add₀, zpow_one_add₀, zpow_sub_one₀
91
Total95

GroupWithZero

Definitions

NameCategoryTheorems
toDivisionMonoid 📖CompOp
429 mathmath: le_inv_comm₀, Polynomial.natDegree_mul_leadingCoeff_inv, nnnorm_inv, div_le_one_of_le₀, NormedSpace.exp_neg_of_mem_ball, Homeomorph.smulOfNeZero_symm_apply, Rat.cast_inv_of_ne_zero, hasSum_geometric_of_norm_lt_one, OrderMonoidIso.val_inv_unitsWithZero_symm_apply, Valuation.inversion_estimate', pow_sub_of_lt, Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsub, mul_inv_cancel_of_invertible, inv_eq_zero, RCLike.tendsto_inverse_atTop_nhds_zero_nat, MeasurableEquiv.symm_mulRight₀, CauSeq.Completion.ofRat_inv, TendstoLocallyUniformlyOn.inv₀, support_comp_inv_smul₀, Mathlib.Meta.NormNum.isRat_inv_pos, conj_pow₀, CauSeq.inv_aux, Filter.inv_nhdsWithin_ne_zero, OrderIso.mulRight₀_symm_apply, Commute.inv_right_iff₀, Submonoid.isUnit_iff_and, DifferentiableAt.fun_inv, OrderIso.mulRight₀_symm, Set.inv_mem_centralizer₀, map_mul_left_nhds_one₀, Subgroup.mem_pointwise_smul_iff_inv_smul_mem₀, FiniteField.pow_card_sub_one_eq_one, Function.Antiperiodic.const_mul, inv_smul_smul₀, inv_lt_one₀, one_le_inv₀, mul_inv_le_one, DilationEquiv.smulTorsor_symm_apply, Ring.inverse_eq_inv', Affine.Simplex.centroid_eq_smul_sum_vsub_vadd, Valuation.val_le_one_or_val_inv_lt_one, isConj_iff₀, TrivSqZeroExt.inv_inl, Set.mem_inv_smul_set_iff₀, Differentiable.fun_inv, Set.preimage_smul_inv₀, inv_intCast_smul_eq, TrivSqZeroExt.inv_one, differentiableWithinAt_inv, Mathlib.Meta.NormNum.isNat_inv_zero, Polynomial.degree_mul_leadingCoeff_inv, Mathlib.Tactic.FieldSimp.one_zpow', le_mul_inv_left, AnalyticOn.fun_inv, TendstoLocallyUniformlyOn.fun_inv₀_of_disjoint, lineMap_inv_two, Subring.center.coe_inv, inv_natCast_smul_eq, ENNReal.orderIsoRpow_symm_apply, TendstoLocallyUniformly.fun_inv₀, SemiconjBy.inv_right₀, Filter.inv_nhdsNE_zero, inv_mul_le_of_le_mul₀, inv_intCast_smul_comm, tsum_geometric_of_norm_lt_one, Set.star_inv', dist_inv_inv₀, tendsto_norm_inv_nhdsNE_zero_atTop, inv_le_one_iff₀, Subring.mem_pointwise_smul_iff_inv_smul_mem₀, one_lt_inv_iff₀, lt_inv_smul_iff_of_pos, div_eq_one_iff_eq, Matrix.conjTranspose_inv_intCast_smul, Mathlib.Meta.NormNum.isNat_inv_one, inv_mul_lt_one₀, DualNumber.inv_eps, Equiv.mulLeft₀_symm_apply, Nonneg.inv_mk, mul_eq_one_iff_inv_eq₀, Valuation.val_lt_one_iff, mul_inv_lt_iff₀, Valuation.val_le_one_or_val_inv_le_one, smul_inv_smul₀, GenContFract.convs'_succ, Polynomial.irreducible_mul_leadingCoeff_inv, div_self_mul_self', inv_mul_eq_iff_eq_mul₀, Commute.inv_sub_inv, eq_mul_inv_iff_mul_eq₀, one_div_neg, inv_mul_le_one, MeasurableEquiv.symm_mulLeft₀, Valuation.one_lt_val_iff, Subfield.coe_inv, lt_mul_inv_iff₀, Filter.inv_cobounded₀, inv_mul_le_one₀, le_inv_mul_right, Valuation.val_eq_one_iff, nndist_inv_inv₀, pow_inv_comm₀, Commute.inv_left_iff₀, inv_add_inv', NormedSpace.exp_conj, Rat.cast_inv_int, inv_mul_lt_iff₀, Polynomial.natDegree_mul_leadingCoeff_self_inv, eventually_cobounded_mapsTo, Matrix.conjTranspose_inv_natCast_smul, Filter.tendsto_inv₀_cobounded, Submodule.mem_smul_iff_inv_mul_mem, zero_zpow_eq, div_self_eq_one₀, Submonoid.isUnit_iff_of_ne_zero, Ring.inverse_eq_inv, norm_commutator_sub_one_le, Function.Antiperiodic.const_inv_smul₀, AnalyticWithinAt.inv, fderivWithin_inv', geom_sum_inv, UniformContinuousOn.fun_inv₀, Submonoid.le_pointwise_smul_iff₀, DifferentiableOn.inv, map_inv₀, Submonoid.pointwise_smul_le_iff₀, Set.inv_zero, OrderIso.smulRight_symm_apply, DilationEquiv.mulRight_symm_apply, inv_mul_mul_self, sup_eq_half_smul_add_add_abs_sub', mul_inv_le_iff₀, Finset.smul_finset_subset_iff₀, nhds_translation_mul_inv₀, one_div_nonneg, DilationEquiv.mulLeft_symm_apply, mul_mul_div, Subgroup.mem_inv_pointwise_smul_iff₀, CauSeq.coe_inv, Matrix.conjTranspose_inv_ofNat_smul, inv_pos, inv_nonneg_of_nonneg, Commute.inv_mul_eq_inv_mul_iff, AddSubgroup.pointwise_smul_le_iff₀, star_inv_intCast_smul, Nonneg.val_inv_unitsHomeomorphPos_symm_apply_coe, zero_zpow_eq_one₀, TrivSqZeroExt.mul_inv_cancel, Finset.inv_zero, TrivSqZeroExt.inv_mul_cancel, zero_eq_inv, WithZero.val_inv_expOrderIso_apply, Finset.centroidWeights_apply, inv_natCast_smul_comm, AnalyticWithinAt.fun_inv, inv_neg'', Function.Antiperiodic.const_inv_mul, UniformContinuousOn.inv₀, TrivSqZeroExt.invOf_eq_inv, mul_inv_le_one_of_le₀, IsSelfAdjoint.inv₀, Mathlib.Meta.NormNum.isNNRat_inv_pos, DifferentiableAt.inv, inv_mul_eq_one₀, DifferentiableWithinAt.inv, Polynomial.degree_mul_leadingCoeff_self_inv, eq_inv_mul_iff_mul_eq₀, inv_lt_iff_one_lt_mul₀, map_inv_natCast_smul, Submonoid.mem_inv_pointwise_smul_iff₀, Mathlib.Meta.NormNum.isInt_inv_neg_one, one_le_inv_iff₀, Finset.inv_smul_finset_distrib₀, absorbs_iff_eventually_cobounded_mapsTo, div_self_le_one, le_mul_inv_right, AddSubmonoid.mem_inv_pointwise_smul_iff₀, NormedSpace.exp_conj', Set.inv_smul_set_distrib₀, zpow_eq_one_iff_right₀, nhds_inv₀, Subsemiring.mem_inv_pointwise_smul_iff₀, Affine.Simplex.point_vsub_faceOppositeCentroid_eq_smul_sum_vsub, Filter.tendsto_inv₀_nhdsWithin_ne_zero, mul_one_div_cancel, norm_inv, TrivSqZeroExt.inv_inv, Polynomial.dvd_mul_leadingCoeff_inv, inv_eq_self₀, OnePoint.equivProjectivization_symm_apply_mk, mul_eq_one_iff_eq_inv₀, Right.inv_nonneg, Homeomorph.mulLeft₀_symm_apply, inv_pos_of_pos, Submonoid.mem_pointwise_smul_iff_inv_smul_mem₀, inv_smul_lt_iff_of_pos, AnalyticOn.inv, Subring.le_pointwise_smul_iff₀, mul_inv_left_le, GenContFract.of_s_head, AffineBasis.coord_apply_centroid, Affine.Simplex.faceOppositeCentroid_eq_sum_vsub_vadd, Units.mul_inv', AddSubmonoid.mem_pointwise_smul_iff_inv_smul_mem₀, star_inv_natCast_smul, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, inv_smul_le_iff_of_pos, MonoidWithZeroHom.snd_inl_apply_of_ne_zero, TendstoLocallyUniformly.fun_inv₀_of_disjoint, NormedDivisionRing.to_continuousInv₀, Function.Periodic.const_smul₀, Subfield.inv_mem, mul_self_mul_inv, DifferentiableOn.fun_inv, Metric.unitSphere.coe_inv, lt_inv_mul_iff₀, mul_inv_right_le, Set.inv_Ioi₀, inv_smul_eq_iff₀, TendstoLocallyUniformlyOn.inv₀_of_disjoint, unitary.coe_inv, UniformContinuous.inv₀, TrivSqZeroExt.isUnit_inv_iff, Function.support_inv, le_inv_mul_iff₀, inv_lt_comm₀, Affine.Simplex.centroid_vsub_faceOppositeCentroid_eq_smul_vsub, Valuation.map_inv, lt_inv_comm₀, TrivSqZeroExt.inv_neg, Finset.inv_op_smul_finset_distrib₀, Rat.cast_inv, hasFPowerSeriesOnBall_inv_one_sub, inv_nonneg, Submonoid.mem_nonunits_iff_or, Function.Antiperiodic.const_smul₀, tendsto_inv_iff₀, SemiconjBy.inv_symm_left₀, inv_mul_left_le, Subring.pointwise_smul_le_iff₀, OrderIso.mulLeft₀_symm_apply, Subgroup.pointwise_smul_le_iff₀, Asymptotics.IsBigO.inv_rev, inv_mul_le_iff₀, Function.Periodic.const_inv_mul, DirectLimit.inv₀_def, Equiv.smulRight_symm_apply, Function.Antiperiodic.mul_const, Asymptotics.IsLittleO.inv_rev, GenContFract.of_s_tail, inv_le_comm₀, Algebra.IsIntegral.inv_mem, Polynomial.monic_mul_leadingCoeff_inv, inv_sub_inv', Function.Periodic.mul_const_inv, Mathlib.Tactic.FieldSimp.NF.one_eq_eval, one_le_inv_mul₀, inv_pow_sub₀, zpow_sub_one₀, analyticOn_inv, NNReal.orderIsoRpow_symm_eq, smul_inv₀, IsAbsoluteValue.abv_inv, Polynomial.degree_add_degree_leadingCoeff_inv, mul_inv_eq_one₀, CauSeq.inv_apply, self_eq_inv₀, TendstoLocallyUniformlyOn.fun_inv₀, NormedSpace.exp_neg, Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero, one_div_pos, Right.inv_pos, inv_le_iff_one_le_mul₀, inv_pow_sub_of_lt, inv_lt_zero, inv_mul_right_le, le_mul_inv_iff₀, inv_le_iff_one_le_mul₀', NNReal.tendsto_inverse_atTop_nhds_zero_nat, NNRat.cast_inv, TendstoLocallyUniformly.inv₀_of_disjoint, Submonoid.mem_nonunits_iff_of_ne_zero, MeasurableEquiv.symm_smul₀, nnnorm_commutator_sub_one_le, IsIntegral.inv_mem, TendstoLocallyUniformly.inv₀, AnalyticAt.fun_inv, inv_mul_cancel_of_invertible, zpow_neg_mul_zpow_self, pow_sub₀, GenContFract.get?_of_eq_some_of_get?_intFractPair_stream_fr_ne_zero, Finset.centroid_pair, inv_lt_iff_one_lt_mul₀', inv_strictAnti₀, MonoidWithZeroHom.fst_inr_apply_of_ne_zero, map_mul_right_nhds_one₀, HasContinuousInv₀.measurableInv, Equiv.mulRight₀_symm_apply, Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_point, Mathlib.Meta.NormNum.isRat_inv_neg, mul_inv_eq_iff_eq_mul₀, Homeomorph.mulRight₀_symm_apply, div_self_of_invertible, uniformContinuousOn_inv₀, Rat.cast_inv_nat, Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsub, Set.preimage_smul₀, inv_mul_le_one_of_le₀, inf_eq_half_smul_add_sub_abs_sub', Finset.inv_smul_mem_iff₀, invOf_eq_inv, Mathlib.Tactic.FieldSimp.zpow'_neg, invOf_div, div_mul_cancel_right₀, Finset.centroid_pair_fin, one_div_mul_cancel, Polynomial.degree_leadingCoeff_inv, Asymptotics.IsBigOWith.inv_rev, Finset.centroidWeights_eq_const, AddSubgroup.mem_inv_pointwise_smul_iff₀, analyticAt_inv, absorbent_iff_inv_smul, Function.Antiperiodic.mul_const_inv, OrderIso.mulLeft₀_symm, IsIntegral.inv, Finset.mem_inv_smul_finset_iff₀, one_le_div₀, OrderIso.smulRightDual_symm_apply, inv_nonpos, hasStrictFDerivAt_inv', Finset.subset_smul_finset_iff₀, analyticAt_inv_one_sub, Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid, Commute.mul_inv_eq_mul_inv_iff, one_div_nonpos, tendsto_inverse_atTop_nhds_zero_nat, ContinuousInv₀.measurableInv, eq_on_inv₀, eq_inv_smul_iff₀, inv_le_one₀, GenContFract.IntFractPair.exists_succ_nth_stream_of_fr_zero, Valuation.one_le_val_iff, TrivSqZeroExt.inv_zero, Commute.inv_right₀, CauSeq.const_inv, birkhoffAverage_apply_sub_birkhoffAverage, inv_lt_one_iff₀, analyticOnNhd_inv, Mathlib.Tactic.FieldSimp.zpow'_zero_of_ne_zero, ProbabilityTheory.gaussianPDFReal_mul, Subsemiring.pointwise_smul_le_iff₀, NormedDivisionRing.to_hasContinuousInv₀, Set.smul_set_subset_iff₀, Filter.tendsto_inv₀_nhdsNE_zero, DifferentiableWithinAt.fun_inv, Nonneg.val_inv_unitsEquivPos_symm_apply_coe, IsIntegral.inv_mem_adjoin, mul_inv_le_of_le_mul₀, Set.inv_Ioo_0_left, differentiableAt_inv, AnalyticAt.inv, NNRat.cast_inv_of_ne_zero, algebraMap.coe_inv, Function.support_inv', Function.Periodic.mul_const, hasFDerivAt_inv', OpenPartialHomeomorph.unitBallBall_symm_apply, AddSubgroup.le_pointwise_smul_iff₀, AddSubmonoid.le_pointwise_smul_iff₀, mul_inv_mul_cancel, SignType.coe_zpow, TrivSqZeroExt.mul_inv_rev, Commute.inv_left₀, smul_inv'', enorm_inv, IsTopologicalDivisionRing.toContinuousInv₀, div_lt_one₀, Subgroup.le_pointwise_smul_iff₀, Commute.inv_add_inv, Subsemiring.mem_pointwise_smul_iff_inv_smul_mem₀, Differentiable.inv, mulSupport_comp_inv_smul₀, Set.mem_smul_set_iff_inv_smul_mem₀, AnalyticOnNhd.fun_inv, Function.Periodic.const_mul, Valuation.val_le_one_iff, Units.inv_mul', SemiconjBy.inv_symm_left_iff₀, rat_inv_continuous_lemma, Subfield.inv_mem', SubfieldClass.toInvMemClass, div_self, tendsto_inv_atTop_nhds_zero_nat, Affine.Simplex.faceOppositeCentroid_eq_affineCombination, Function.Periodic.const_inv_smul₀, Subring.mem_inv_pointwise_smul_iff₀, WithZero.val_inv_logOrderIso_symm_apply, le_inv_smul_iff_of_pos, one_lt_div₀, GenContFract.of_s_succ, smul_inv₀', inv_lt_inv₀, differentiableOn_inv, div_le_one₀, GenContFract.IntFractPair.succ_nth_stream_eq_some_iff, TrivSqZeroExt.inv_inr, UniformContinuous.fun_inv₀, map_inv_intCast_smul, inv_anti₀, Filter.tendsto_inv₀_cobounded', Valuation.inversion_estimate, Affine.Simplex.centroid_vsub_eq, Unitary.coe_inv, star_inv₀, Set.inv_op_smul_set_distrib₀, le_inv_mul_left, one_lt_inv_mul₀, GenContFract.IntFractPair.stream_succ_of_some, Set.subset_smul_set_iff₀, SemiconjBy.inv_right_iff₀, AddSubmonoid.pointwise_smul_le_iff₀, AnalyticOnNhd.inv, AddValuation.map_inv, one_lt_inv₀, AddSubgroup.mem_pointwise_smul_iff_inv_smul_mem₀, Subsemiring.le_pointwise_smul_iff₀, GenContFract.IntFractPair.stream_succ, inv_le_inv₀, fderiv_inv'

Theorems

NameKindAssumesProvesValidatesDepends On
mul_left_injective 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
toMonoidWithZero
—mul_assoc
mul_inv_cancel₀
mul_one
mul_right_injective 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
toMonoidWithZero
—inv_mul_cancel₀
one_mul

IsNilpotent

Theorems

NameKindAssumesProvesValidatesDepends On
eq_zero 📖—IsNilpotent——IsReduced.eq_zero
mk 📖mathematical—IsNilpotent——
of_pow 📖—IsNilpotent
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
——pow_mul
pow_iff_pos 📖mathematical—IsNilpotent
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
—of_pow
pow_of_pos
pow_of_pos 📖—IsNilpotent
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
——pow_succ
pow_succ 📖—IsNilpotent
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
——pow_mul
pow_add
MulZeroClass.mul_zero
zero 📖mathematical—IsNilpotent
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
—pow_one

IsReduced

Theorems

NameKindAssumesProvesValidatesDepends On
eq_zero 📖—IsNilpotent———
pow_eq_zero 📖————eq_zero_of_pow_eq_zero
pow_eq_zero_iff 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
—pow_eq_zero_iff
pow_eq_zero_iff' 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
—pow_eq_zero_iff'
pow_ne_zero 📖————pow_ne_zero
pow_ne_zero_iff 📖————pow_ne_zero_iff

NeZero

Theorems

NameKindAssumesProvesValidatesDepends On
mul 📖————mul_ne_zero
pow 📖mathematical—MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
—pow_ne_zero

(root)

Definitions

NameCategoryTheorems
IsNilpotent 📖MathDef
85 mathmath: MvPowerSeries.hasSubst_def, Polynomial.isUnit_C_add_X_mul_iff, Module.End.isNilpotent_restrict_genEigenspace_nat, TrivSqZeroExt.isNilpotent_iff_isNilpotent_fst, Matrix.isNilpotent_transpose_iff, Polynomial.isNilpotent_X_mul_iff, MvPowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, LieModule.isNilpotent_toEnd_genWeightSpace_zero, LinearMap.charpoly_nilpotent_tfae, Matrix.isNilpotent_iff_forall_row, LieModule.isNilpotent_toEnd_of_isNilpotent, Polynomial.coeff_isUnit_isNilpotent_of_isUnit, Matrix.isNilpotent_toLin'_iff, Polynomial.isUnit_iff', TrivSqZeroExt.isNilpotent_inr, MvPolynomial.isUnit_iff, Module.End.isNilpotent_iff_of_finite, not_isNilpotent_one, DualNumber.isNilpotent_iff_eps_dvd, PrimeSpectrum.mem_image_comap_basicOpen, isNilpotent_of_pos_nilpotencyClass, pos_nilpotencyClass_iff, LinearMap.isNilpotent_toMatrix_iff, MvPowerSeries.HasSubst.const_coeff, IsUnit.not_isNilpotent, isNilpotent_iff_eq_zero, LieModule.isNilpotent_toEnd_of_isNilpotent₂, TrivSqZeroExt.isNilpotent_inl_iff, IsSemiprimaryRing.isNilpotent, Polynomial.isUnit_iff_coeff_isUnit_isNilpotent, PowerSeries.WithPiTopology.isTopologicallyNilpotent_iff_constantCoeff_isNilpotent, IsUnit.isNilpotent_unit_mul_of_commute_iff, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, MvPolynomial.isNilpotent_iff, exists_isNilpotent_of_not_isReduced, LieModule.isNilpotent_toEnd_of_mem_rootSpace, Module.End.isNilpotent_restrict_maxGenEigenspace_sub_algebraMap, LinearMap.isNilpotent_iff_charpoly, LinearMap.isNilpotent_mulRight_iff, Commute.isNilpotent_mul_left_iff, IsNilpotent.mk, Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_pow, Polynomial.isNilpotent_monomial_iff, Polynomial.isNilpotent_iff, IsNoetherianRing.isNilpotent_nilradical, Ring.KrullDimLE.isNilpotent_iff_mem_maximalIdeal, RootPairing.GeckConstruction.isNilpotent_f, IsArtinianRing.isNilpotent_jacobson_bot, LieModule.isNilpotent_iff_forall, LieModule.isNilpotent_toEnd_sub_algebraMap, RootPairing.GeckConstruction.isNilpotent_e, IsUnit.isNilpotent_mul_unit_of_commute_iff, isNilpotent_tensor_residueField_iff, Ideal.FG.isNilpotent_iff_le_nilradical, isArtinianRing_iff_isNilpotent_maximalIdeal, IsNilpotent.map_iff, Polynomial.isNilpotent_C_iff, Ring.KrullDimLE.isNilpotent_iff_mem_nonunits, Module.End.isNilpotent_restrict_sub_algebraMap, LieAlgebra.isNilpotent_ad_of_mem_rootSpace, IsNilpotent.pow_iff_pos, nilpotent_iff_mem_prime, Polynomial.isNilpotent_mul_X_iff, isNilpotent_neg_iff, Matrix.isNilpotent_iff, Polynomial.isNilpotent_reflect_iff, LieModule.isNilpotent_iff_forall', Commute.isNilpotent_mul_right_iff, Module.End.isNilpotent_restrict_genEigenspace_top, isSemiprimaryRing_iff, PrimeSpectrum.mem_image_comap_zeroLocus_sdiff, LieAlgebra.isNilpotent_iff_forall, TrivSqZeroExt.isUnit_or_isNilpotent, IsArtinianRing.isNilpotent_nilradical, Polynomial.isNilpotent_reverse_iff, isNilpotent_iff_zero_mem_powers, Module.End.exists_isNilpotent_isSemisimple, LinearMap.isNilpotent_mulLeft_iff, IsNilpotent.zero, isNilpotent_of_subsingleton, DualNumber.isNilpotent_eps, Matrix.isNilpotent_iff_forall_col, PrimeSpectrum.basicOpen_eq_bot_iff, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact, mem_nilradical
IsReduced 📖CompData
28 mathmath: isReduced_of_injective, MvPolynomial.instIsReduced, instIsReducedZModOfFactSquarefreeNat, Algebra.instIsReducedTensorProductOfIsAlgebraicOfIsGeometricallyReduced, Algebra.isGeometricallyReduced_iff, AlgebraicGeometry.IsReduced.component_reduced, isReduced_iff, RingHom.ker_isRadical_iff_reduced_of_surjective, Algebra.IsGeometricallyReduced.isReduced_algebraicClosure_tensorProduct, Algebra.isReduced_of_isGeometricallyReduced, isReduced_of_subsingleton, Ideal.isRadical_bot_iff, zero_isRadical_iff, isReduced_localizationPreserves, isReduced_iff_pow_one_lt, Algebra.FormallyUnramified.isReduced_of_field, instIsReducedLocalization, NoZeroSMulDivisors.isReduced, nilradical_eq_bot_iff, instIsReducedProd, isReduced_zmod, isReduced_ofLocalizationMaximal, instIsReducedOfIsSemisimpleRing, PerfectClosure.instReduced, AlgebraicGeometry.isReduced_stalk_of_isReduced, Ideal.isRadical_iff_quotient_reduced, AlgebraicGeometry.affine_isReduced_iff, isReduced_of_noZeroDivisors
uniqueOfZeroEqOne 📖CompOp—

Theorems

NameKindAssumesProvesValidatesDepends On
div_div_self 📖mathematical—DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
—div_div_eq_mul_div
mul_self_div_self
div_mul_eq_mul_div₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
—div_eq_mul_inv
mul_assoc
mul_comm
div_self_mul_self 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
—div_eq_mul_inv
mul_inv_mul_cancel
div_self_mul_self' 📖mathematical—DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
—div_eq_mul_inv
mul_inv_rev
inv_inv
mul_assoc
inv_mul_mul_self
div_sq_cancel 📖mathematical—DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
CommGroupWithZero.toGroupWithZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
Monoid.toNatPow
MonoidWithZero.toMonoid
—eq_or_ne
zero_pow
MulZeroClass.zero_mul
div_zero
sq
mul_assoc
mul_div_cancel_left₀
GroupWithZero.toMulDivCancelClass
div_zero 📖mathematical—DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—div_eq_mul_inv
inv_zero
MulZeroClass.mul_zero
eq_of_zero_eq_one 📖—MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
——subsingleton_of_zero_eq_one
eq_zero_of_mul_eq_self_left 📖mathematicalMulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulZeroClass.toZero—mul_right_cancel₀
one_mul
eq_zero_of_mul_eq_self_right 📖mathematicalMulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulZeroClass.toZero—mul_left_cancel₀
mul_one
eq_zero_of_mul_self_eq_zero 📖————NoZeroDivisors.eq_zero_or_eq_zero_of_mul_eq_zero
eq_zero_of_one_div_eq_zero 📖—DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
——one_div_ne_zero
eq_zero_of_pow_eq_zero 📖————IsReduced.eq_zero
eq_zero_of_zero_eq_one 📖—MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
——mul_one
MulZeroClass.mul_zero
exists_isNilpotent_of_not_isReduced 📖mathematicalIsReducedIsNilpotent——
exists_right_inv_of_exists_left_inv 📖—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
——subsingleton_or_nontrivial
left_ne_zero_of_mul
Eq.trans_ne
one_ne_zero
NeZero.one
one_mul
mul_assoc
instIsCancelMulZero 📖mathematical—IsCancelMulZero
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
MulZeroClass.toZero
—inv_mul_cancel_left₀
mul_inv_cancel_right₀
inv_eq_zero 📖mathematical—InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—inv_eq_iff_eq_inv
inv_zero
inv_mul_cancel_left₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
DivInvMonoid.toInv
GroupWithZero.toDivInvMonoid
—mul_assoc
inv_mul_cancel₀
one_mul
inv_mul_cancel_right₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
DivInvMonoid.toInv
GroupWithZero.toDivInvMonoid
—mul_assoc
inv_mul_cancel₀
mul_one
inv_mul_mul_self 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
—inv_zero
MulZeroClass.mul_zero
inv_mul_cancel₀
one_mul
isNilpotent_iff_eq_zero 📖mathematical—IsNilpotent
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
—IsNilpotent.eq_zero
IsNilpotent.zero
isNilpotent_of_subsingleton 📖mathematical—IsNilpotent——
isReduced_iff 📖mathematical—IsReduced——
isReduced_of_noZeroDivisors 📖mathematical—IsReduced
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
—pow_zero
mul_one
MulZeroClass.mul_zero
mul_eq_zero
pow_succ
isReduced_of_subsingleton 📖mathematical—IsReduced——
left_eq_mul₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
—mul_eq_left₀
left_ne_zero_of_mul 📖————mul_eq_zero_of_left
left_ne_zero_of_mul_eq_one 📖—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
——left_ne_zero_of_mul
ne_zero_of_eq_one
NeZero.one
mul_eq_left₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
—mul_right_inj'
mul_one
mul_eq_right₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
—mul_left_inj'
one_mul
mul_eq_zero_of_ne_zero_imp_eq_zero 📖mathematicalMulZeroClass.toZeroMulZeroClass.toMul—MulZeroClass.zero_mul
MulZeroClass.mul_zero
mul_inv_mul_cancel 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
—inv_zero
MulZeroClass.mul_zero
mul_inv_cancel₀
one_mul
mul_left_eq_self₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MulZeroClass.toZero
—one_mul
mul_eq_mul_right_iff
mul_left_surjective₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—mul_inv_cancel₀
one_mul
mul_ne_zero 📖————NoZeroDivisors.eq_zero_or_eq_zero_of_mul_eq_zero
mul_right_eq_self₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
MulZeroClass.toZero
—mul_one
mul_eq_mul_left_iff
mul_right_surjective₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—mul_assoc
inv_mul_cancel₀
mul_one
mul_self_div_self 📖mathematical—DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—div_eq_mul_inv
mul_self_mul_inv
mul_self_mul_inv 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
—inv_zero
MulZeroClass.mul_zero
mul_assoc
mul_inv_cancel₀
mul_one
mul_zero_eq_const 📖mathematical—MulZeroClass.toMul
MulZeroClass.toZero
—MulZeroClass.mul_zero
ne_zero_and_ne_zero_of_mul 📖————left_ne_zero_of_mul
right_ne_zero_of_mul
ne_zero_of_one_div_ne_zero 📖————div_zero
ne_zero_pow 📖————zero_pow
not_isNilpotent_one 📖mathematical—IsNilpotent
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
—zero_ne_one
NeZero.one
one_pow
one_div_ne_zero 📖————one_div
inv_ne_zero
pow_eq_zero 📖————eq_zero_of_pow_eq_zero
pow_eq_zero_iff 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
—eq_zero_of_pow_eq_zero
zero_pow
pow_eq_zero_iff' 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
—eq_or_ne
pow_zero
NeZero.one
pow_eq_zero_of_le 📖—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
——pow_succ
MulZeroClass.zero_mul
pow_mul_eq_zero_of_le 📖—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
——pow_add
mul_assoc
MulZeroClass.mul_zero
pow_ne_zero 📖————eq_zero_of_pow_eq_zero
pow_ne_zero_iff 📖————Iff.not
pow_eq_zero_iff
right_eq_mul₀ 📖mathematical—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
—mul_eq_right₀
right_ne_zero_of_mul 📖————mul_eq_zero_of_right
right_ne_zero_of_mul_eq_one 📖—MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
——right_ne_zero_of_mul
ne_zero_of_eq_one
NeZero.one
sq_eq_zero_iff 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
—pow_eq_zero_iff
two_ne_zero
subsingleton_iff_zero_eq_one 📖mathematical—MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
—Unique.instSubsingleton
subsingleton_of_zero_eq_one 📖—MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
——subsingleton_iff_zero_eq_one
zero_div 📖mathematical—DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—div_eq_mul_inv
MulZeroClass.zero_mul
zero_eq_inv 📖mathematical—MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
—inv_eq_zero
zero_mul_eq_const 📖mathematical—MulZeroClass.toMul
MulZeroClass.toZero
—MulZeroClass.zero_mul
zero_ne_one_or_forall_eq_0 📖mathematical—MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
—not_or_of_imp
eq_zero_of_zero_eq_one
zero_pow 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
—pow_succ
MulZeroClass.mul_zero
zero_pow_eq 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
—pow_zero
zero_pow
zero_pow_eq_one₀ 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
MulOne.toOne
MulOneClass.toMulOne
MulZeroOneClass.toMulOneClass
—zero_pow_eq
Ne.ite_eq_left_iff
one_ne_zero
NeZero.one
zero_pow_eq_zero 📖mathematical—Monoid.toNatPow
MonoidWithZero.toMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
—pow_zero
NeZero.one
zero_pow
zero_zpow 📖mathematical—DivInvMonoid.toZPow
GroupWithZero.toDivInvMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—zpow_natCast
zero_pow
zpow_negSucc
inv_zero
zero_zpow_eq 📖mathematical—DivInvMonoid.toZPow
GroupWithZero.toDivInvMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
—zpow_zero
zero_zpow
zero_zpow_eq_one₀ 📖mathematical—DivInvMonoid.toZPow
GroupWithZero.toDivInvMonoid
MulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
—zero_zpow_eq
Ne.ite_eq_left_iff
one_ne_zero
NeZero.one
GroupWithZero.toNontrivial
zpow_add' 📖mathematical—DivInvMonoid.toZPow
GroupWithZero.toDivInvMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—zpow_zero
one_mul
mul_one
zero_zpow
MulZeroClass.zero_mul
zpow_add₀
zpow_add_one₀ 📖mathematical—DivInvMonoid.toZPow
GroupWithZero.toDivInvMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—zpow_natCast
pow_succ
zpow_zero
zpow_neg
zpow_one
inv_mul_cancel₀
pow_succ'
mul_inv_rev
mul_assoc
mul_one
zpow_add₀ 📖mathematical—DivInvMonoid.toZPow
GroupWithZero.toDivInvMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—Int.induction_on
zpow_zero
mul_one
zpow_add_one₀
mul_assoc
zpow_sub_one₀
zpow_one_add₀ 📖mathematical—DivInvMonoid.toZPow
GroupWithZero.toDivInvMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
—zpow_add₀
zpow_one
zpow_sub_one₀ 📖mathematical—DivInvMonoid.toZPow
GroupWithZero.toDivInvMonoid
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
GroupWithZero.toDivisionMonoid
—mul_assoc
mul_inv_cancel₀
mul_one
zpow_add_one₀

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