funLike 📖 | CompOp | 499 mathmath: normalize_one, Quaternion.normSq_eq_zero, Quaternion.star_mul_self, Polynomial.degree_normalize, Quaternion.coe_normSq_add, Cardinal.toNat_ofENat, Cardinal.toNat_surjective, comp_apply, Cardinal.toNat_ofNat, GrpWithZero.forget_map, Polynomial.roots_normalize, Complex.UnitDisc.normSq_lt_one, RCLike.normSq_to_real, Ideal.finite_setOf_absNorm_le₀, Complex.normSq_pos, normalize_dvd_iff, NumberField.mixedEmbedding.norm_eq_sup'_normAtPlace, WithZero.map'_mono, Ideal.absNorm_span_insert, summable_riemannZetaSummand, Complex.normSq_natCast, WithZero.map'_zero, Ideal.relNorm_smul, UpperHalfPlane.normSq_pos, Complex.norm_mul_self_eq_normSq, NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm_nnreal, Cardinal.toNat_eq_iff, WithZero.map'_coe, Cardinal.toNat_congr, MulChar.toMonoidWithZeroHom_apply, WithZero.lift'_symm_apply_apply, NumberField.mixedEmbedding.normAtAllPlaces_apply, signHom_apply, NumberField.mixedEmbedding.norm_eq_zero_iff', Ring.ordFrac_eq_div, gcd_mul_left, NumberField.mixedEmbedding.fundamentalCone.integerSetEquivNorm_apply_fst, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, Quaternion.normSq_natCast, gcd_greatest, mrange_nontrivial, NumberField.mixedEmbedding.norm_unit_smul, Complex.nndist_self_conj, NumberField.mixedEmbedding.norm_eq_norm, NumberField.FinitePlace.norm_def', Ideal.finite_setOf_absNorm_eq, UpperHalfPlane.im_smul_eq_div_normSq, smulMonoidWithZeroHom_apply, RCLike.normSq_neg, one_apply_zero, Cardinal.toNat_mul, UpperHalfPlane.moebius_im, Ideal.relNorm_mono, FractionalIdeal.absNorm_eq', ModularGroup.one_lt_normSq_T_zpow_smul, Complex.normSq_ratCast, RCLike.continuous_normSq, Ideal.relNorm_relNorm, map_eq_zero_iff, one_apply_eq_zero_iff, WithZero.map'_strictMono, Ideal.absNorm_pos_iff_mem_nonZeroDivisors, normalize_eq_normalize, Complex.normSq_mk, ValuationSubring.mapOfLE_valuation_apply, NormalizedGCDMonoid.normalize_lcm, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_dvd_norm_le, GaussianInt.normSq_le_normSq_of_re_le_of_im_le, Ring.ordFrac_eq_ord, Ideal.absNorm_eq_pow_inertiaDeg', Cardinal.toNat_apply_of_aleph0_le, fst_mono, Int.normalize_of_nonneg, Ideal.relNorm_top, NumberField.mixedEmbedding.fundamentalCone.card_isPrincipal_norm_eq_mul_torsion, Quaternion.normSq_smul, Ideal.relNorm_eq_pow_of_isPrime_isGalois, Ideal.absNorm_eq_pow_inertiaDeg_of_liesOver, ValuativeRel.ValueGroupWithZero.embed_strictMono, Ideal.absNorm_mem, NumberField.mixedEmbedding.normAtPlace_apply_of_isReal, Multiset.lcm_singleton, GrpWithZero.hom_comp, Complex.normSq_mul, GrpWithZero.coe_id, ValuativeExtension.mapValueGroupWithZero_mk, coe_mk, Quaternion.normSq_le_zero, Quaternion.inv_def, map_one, Finset.lcm_singleton, Polynomial.Monic.normalize_eq_self, gcd_eq_normalize, MonoidWithZero.coe_inverse, one_apply_val_unit, Quaternion.normSq_nonneg, WithZeroMulInt.toNNReal_pos, GrpWithZero.coe_comp, Ideal.relNorm_singleton, Matrix.cRank_toNat_eq_rank, Ideal.map_relNorm, NumberField.mixedEmbedding.fundamentalCone.norm_pos_of_mem, normHom_apply, UniqueFactorizationMonoid.normalize_normalized_factor, Associates.out_mk, Ideal.relNorm_le_comap, Cardinal.cast_toNat_eq_iff_lt_aleph0, normalize_eq_normalize_iff, Complex.sq_norm, ValuativeExtension.mapValueGroupWithZero_strictMono, MulEquiv.withZero_apply_symm_apply, Matrix.cRank_toNat_eq_finrank, inl_strictMono, Cardinal.toNat_monotoneOn, Complex.normSq_I, Polynomial.leadingCoeff_normalize, Real.nnabs_of_nonneg, WithZeroMulInt.toNNReal_lt_one_iff, RCLike.div_im, Valuation.coe_coe, Cardinal.mk_toNat_eq_card, powMonoidWithZeroHom_apply, Complex.tendsto_normSq_cocompact_atTop, NumberField.mixedEmbedding.convexBodySumFun_apply, WithZero.lift'_coe, NumberField.det_basisOfFractionalIdeal_eq_absNorm, RCLike.normSq_inv, FractionalIdeal.absNorm_bot, Complex.normSq_add, MulEquiv.toMonoidWithZeroHom_apply, lcm_mul_left, Complex.re_sq_le_normSq, Complex.div_im, WithZero.map'_surjective, monoidWithZeroHomClass, NumberField.mixedEmbedding.fundamentalCone.mem_normLeOne, toZeroHom_coe, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, MulEquiv.withZero_apply_apply, Complex.normSq_eq_norm_sq, Finset.gcd_mul_left, RCLike.normSq_nonneg, Finset.normalize_lcm, Real.coe_nnabs, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, OrderMonoidIso.withZero_apply_symm_apply, SignType.castHom_apply, MulEquiv.toMonoidWithZeroHom_injective, mulMonoidWithZeroHom_apply, WithZeroMulInt.toNNReal_neg_apply, RingHom.toMonoidWithZeroHom_eq_coe, Complex.normSq_sub, one_apply_def, Complex.inv_re, ValuativeExtension.mapValueGroupWithZero_valuation, Ideal.exists_relNorm_eq_pow_of_isPrime, WithZero.map'_injective, Valuation.RankOne.strictMono, Multiset.gcd_singleton, Valued.coe_valuation_eq_rankOne_hom_comp_valuation, lipschitzWith_circleMap, range_nontrivial, Associates.normalize_out, Quaternion.normSq_inv, one_apply_of_ne_zero, UniqueFactorizationMonoid.radical_of_prime, NumberField.mixedEmbedding.covolume_idealLattice, NumberField.mixedEmbedding.normAtPlace_add_le, Polynomial.content_C_mul, one_apply_apply_eq, HahnSeries.map_one, map_zero, RCLike.inv_im, Int.normalize_coe_nat, normalize_eq_zero, UpperHalfPlane.normSq_denom_pos, lcm_mul_right, Quaternion.normSq_eq_norm_mul_self, Polynomial.normalize_content, WithZeroMulInt.toNNReal_le_one_iff, Complex.inv_def, legendreSym.hom_apply, NormalizedGCDMonoid.normalize_gcd, normalize_gcd, ENat.coe_toNatHom, Complex.normSq_ofNat, tsum_riemannZetaSummand, Ideal.relNorm_algebraMap', normalize_apply, Cardinal.toNat_rightInverse, Cardinal.toNat_strictMonoOn, Complex.normSq_ofReal_add_I_mul_sqrt_one_sub, Ideal.relNorm_int, Cardinal.toNat_le_toNat, Ideal.absNorm_dvd_absNorm_of_le, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, one_apply_eq_one_iff, NumberField.Ideal.tendsto_norm_le_div_atTop₀, inl_mul_inr_eq_mk_of_unit, OrderMonoidIso.withZero_apply_apply, Cardinal.toNat_lt_iff_lt_of_lt_aleph0, ValuationSubring.monotone_mapOfLE, Int.absNorm_under_mem, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, ValuativeRel.RankLeOneStruct.strictMono, Complex.normSq_zero, Cardinal.toNat_lift, ENat.toNatHom_apply, Ideal.spanNorm_eq, FractionalIdeal.absNorm_eq, RCLike.normSq_mul, summable_dirichletSummand, Cardinal.toNat_eq_one, NumberField.mixedEmbedding.norm_nonneg, Ideal.relNorm_algebraMap, Submodule.spanSingleton_apply, normalize_coe_units, Complex.normSq_conj, Complex.continuous_normSq, Quaternion.normSq_add, ModularGroup.tendsto_normSq_coprime_pair, NumberField.mixedEmbedding.norm_smul, Complex.normSq_intCast, Cardinal.toNat_toENat, Ideal.relNorm_eq_bot_iff, coe_coe, Valued.norm_def, IsPrimitiveRoot.not_coprime_norm_of_mk_eq_one, NumberField.FinitePlace.norm_def_int, inr_mono, Ideal.card_norm_le_eq_card_norm_le_add_one, NumberField.mixedEmbedding.continuous_norm, Associates.mk_normalize, Quaternion.normSq_exp, IntermediateField.relfinrank_eq_toNat_relrank, Complex.div_re, FractionalIdeal.absNorm_span_singleton, OrderMonoidWithZeroHom.coe_mk, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, toMonoidHom_coe, gcd_same, Subfield.relfinrank_eq_toNat_relrank, gcd_zero_right, snd_inr, snd_inl_apply_of_ne_zero, Cardinal.mk_toNat_of_infinite, lcm_one_left, inl_injective, NumberField.absNorm_differentIdeal, Ideal.absNorm_top, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, Ideal.absNorm_apply, Ideal.absNorm_pos_of_nonZeroDivisors, Orientation.normSq_kahler, IsLocalization.toLocalizationMap_toMonoidHom, Complex.normSq_inv, Cardinal.cast_toNat_of_aleph0_le, NumberField.mixedEmbedding.fundamentalCone.normAtPlace_pos_of_mem, Int.normalize_of_nonpos, Complex.normSq_div, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, Complex.normSq_ofReal, Quaternion.sq_eq_neg_normSq, RCLike.normSq_eq_def', Real.nndist_eq, Algebra.norm_complex_apply, Complex.norm_def, Finset.gcd_singleton, apply_one_apply_eq, normalize_lcm, Cardinal.toNat_inj_of_lt_aleph0, lcm_same, Int.absNorm_under_dvd_absNorm, Quaternion.sq_eq_normSq, Cardinal.toNat_injOn, Polynomial.normalize_eq_self_iff_monic, Submodule.mker_spanSingleton, NumberField.mixedEmbedding.normAtPlace_neg, coe_powMonoidWithZeroHom, NumberField.mixedEmbedding.continuous_normAtPlace, Irreducible.normalizedFactors_pow, Int.natAbsHom_apply, GaussianInt.intCast_real_norm, Quaternion.self_mul_star, Valuation.toMonoidWithZeroHom_coe_eq_coe, Cardinal.toNat_le_iff_le_of_lt_aleph0, snd_mono, UniqueFactorizationMonoid.normalizedFactors_irreducible, Int.abs_eq_normalize, MulEquiv.toMonoidWithZeroHom_bijective, Complex.normSq_nonneg, Valuation.RankOne.strictMono', Quaternion.normSq_def', tsum_dirichletSummand, NumberField.exists_ideal_in_class_of_norm_le, NumberField.mixedEmbedding.normAtPlace_apply, Complex.nndist_conj_self, RCLike.normSq_pos, lcm_units_coe_left, ModularGroup.im_smul_eq_div_normSq, NumberField.Ideal.tendsto_norm_le_div_atTop, fst_apply_coe, fst_inl, fst_surjective, Cardinal.toNat_eq_one_iff_unique, Real.nnabs_coe, NumberField.mixedEmbedding.normAtPlace_apply_of_isComplex, FractionalIdeal.absNorm_nonneg, gcd_zero_left, NumberField.mixedEmbedding.forall_normAtPlace_eq_zero_iff, Ideal.natAbs_det_equiv, Complex.normSq_add_mul_I, Quaternion.normSq_zpow, Ideal.absNorm_eq_one_iff, WithZeroMulInt.toNNReal_eq_one_iff, coe_comp, UniqueFactorizationMonoid.normalizedFactors_prod_eq, Quaternion.inner_self, WithZero.lift'_surjective, UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors, count_span_normalizedFactors_eq, Real.toNNReal_abs, Quaternion.normSq_def, NumberField.mixedEmbedding.logMap_apply, Cardinal.toNat_lt_toNat, ValuativeRel.ValueGroupWithZero.embed_mk, inr_apply_unit, NumberField.mixedEmbedding.fundamentalCone.intNorm_coe, NumberField.mixedEmbedding.norm_eq_zero_iff, gcd_mul_right, val_mrange_zero, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, LinearOrderedCommGroupWithZero.fst_apply, GrpWithZero.hom_id, NumberField.mixedEmbedding.normAtPlace_nonneg, Quaternion.normSq_neg, RCLike.mul_self_norm, dvd_normalize_iff, WithZeroMulInt.toNNReal_strictMono, associated_normalize_iff, Multiset.normalize_lcm, Complex.mul_conj, Cardinal.cast_toNat_of_lt_aleph0, Cardinal.toNat_eq_zero, Complex.inv_im, RCLike.normSq_div, RCLike.im_sq_le_normSq, fst_inr_apply_of_ne_zero, NumberField.mixedEmbedding.normAtPlace_negAt, Field.finSepDegree_eq, nnnormHom_apply, Circle.normSq_coe, Ideal.finite_setOf_absNorm_le, NumberField.mixedEmbedding.normAtPlace_smul, CommGroupWithZero.normalize_eq_one, ext_iff, FractionalIdeal.abs_det_basis_change, divMonoidWithZeroHom_apply, Finset.gcd_mul_right, Field.finInsepDegree_def', UniqueFactorizationMonoid.mem_normalizedFactors_iff', Mathlib.Meta.Positivity.nnabs_pos_of_pos, NumberField.toNNReal_valued_eq_adicAbv, RCLike.re_sq_le_normSq, inr_strictMono, Complex.normSq_eq_conj_mul_self, FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm, WithZero.map'_surjective_iff, WithZeroMulInt.toNNReal_pos_apply, Ideal.absNorm_eq_pow_inertiaDeg, RCLike.normSq_zero, NumberField.mixedEmbedding.norm_real, RCLike.normSq_eq_zero, Ideal.absNorm_eq_zero_iff, IsCyclotomicExtension.Rat.absNorm_span_zeta_sub_one, Cardinal.aleph0_toNat, Real.nnabs_pos, ext_nat_iff, Cardinal.toNat_natCast, inl_mono, UniqueFactorizationMonoid.normalizedFactors_of_irreducible_pow, Quaternion.normSq_intCast, Polynomial.content_C, Ideal.absNorm_bot, Ideal.relNorm_apply, UniqueFactorizationMonoid.prod_normalizedFactors_eq, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, Complex.normSq_apply, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, RCLike.normSq_to_complex, map_mul, RCLike.normSq_add, UniqueFactorizationMonoid.radical_pow_of_prime, RCLike.div_re, Cardinal.toNat_apply_of_lt_aleph0, Complex.im_sq_le_normSq, Int.ideal_span_absNorm_eq_self, Ideal.relNorm_bot, Ideal.norm_mem_relNorm, Valuation.coe_mk, Cardinal.toNat_lift_add_lift, normalize_eq_one, id_apply, Cardinal.toNat_pos, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, WithZero.lift'_zero, RCLike.sqrt_normSq_eq_norm, snd_apply_coe, MonoidWithZero.inverse_apply, Cardinal.toNat_add, Ideal.absNorm_relNorm, RCLike.normSq_apply, Int.absNorm_under_eq_sInf, Ideal.absNorm_span_singleton, FractionalIdeal.coeIdeal_absNorm, Valuation.RankOne.hom_eq_zero_iff, lcm_units_coe_right, Quaternion.im_sq, Ideal.absNorm_algebraMap, Multiset.normalize_gcd, AbsoluteValue.coe_toMonoidWithZeroHom, LinearOrderedCommGroupWithZero.inl_apply, Int.cast_mem_ideal_iff, LinearOrderedCommGroupWithZero.inr_apply, Ideal.relNorm_map_algEquiv, normalize_associated, OrderMonoidWithZeroHom.coe_monoidWithZeroHom, FractionalIdeal.absNorm_eq_zero_iff, NumberField.RingOfIntegers.HeightOneSpectrum.one_lt_absNorm, RCLike.normSq_one, Ideal.span_singleton_absNorm_le, Polynomial.monic_normalize, Real.nndist_eq', Ideal.natAbs_det_basis_change, Multiset.gcd_map_mul, Quaternion.normSq_div, inr_injective, Ideal.ringChar_quot, Complex.normSq_neg, WithZero.map'_id, commute_inl_inr, NumberField.mixedEmbedding.norm_negAt, normalize_zero, NumberField.mixedEmbedding.norm_unit, ValuativeRel.ValueGroupWithZero.embed_valuation, Int.liesOver_span_absNorm, Quaternion.normSq_star, UpperHalfPlane.c_mul_im_sq_le_normSq_denom, Cardinal.zero_toNat, ValuationSubring.mapOfLE_comp_valuation, ext_int_iff, normalize_idem, Complex.range_normSq, Quaternion.normSq_ratCast, UpperHalfPlane.smulAux'_im, Finset.normalize_gcd, lcm_eq_normalize, Quaternion.continuous_normSq, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, Complex.normSq_ofReal_sub_I_mul_sqrt_one_sub, Cardinal.aleph_toNat, Ideal.relNorm_eq_pow_of_isMaximal, Cardinal.natCast_toNat_le, NumberField.mixedEmbedding.nnnorm_eq_sup_normAtPlace, Complex.normSq_eq_zero, RCLike.normSq_sub, Nat.absNorm_under_prime, GaussianInt.normSq_div_sub_div_lt_one, Int.nonneg_iff_normalize_eq_self, normalize_eq_normalize_iff_associated, GaussianInt.intCast_complex_norm, PowerSeries.X_eq_normalizeX, Quaternion.normSq_coe, inl_apply_unit, Ideal.relNorm_comap_algEquiv, Cardinal.toNat_eq_ofNat, Real.cast_natAbs_eq_nnabs_cast, Cardinal.one_toNat, normalize_associated_iff, Polynomial.X_eq_normalize, snd_surjective, Cardinal.continuum_toNat, Polynomial.content_monomial, Polynomial.map_normalize, normalize_eq, NumberField.mixedEmbedding.norm_apply, RCLike.normSq_conj, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, RCLike.inv_re, Complex.normSq_one, NumberField.mixedEmbedding.normAtPlace_real, MulEquiv.toMonoidWithZeroHom_surjective, lcm_one_right, NumberField.mixedEmbedding.fundamentalCone.intNorm_idealSetEquiv_apply, WithZero.map'_injective_iff, Ideal.absNorm_dvd_norm_of_mem, associated_normalize, WithZero.map'_map', FractionalIdeal.absNorm_one
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