map 📖 | CompOp | 559 mathmath: product_cons, Polynomial.splits_iff_exists_multiset, ofAdd_multiset_prod, Polynomial.roots_expand, map_multiset_sum, Polynomial.eval_multiset_prod, Ideal.pow_multiset_sum_mem_span_pow, Set.multiset_prod_subset_multiset_prod, prod_int_mod, map_id, Polynomial.eval₂_multiset_prod, aestronglyMeasurable_fun_prod, Finset.prod_multiset_map_count, map_sort, rel_map_left, pi_cons, convexHull_multiset_sum, Int.ModEq.multisetSum_map_zero, Polynomial.roots_scaleRoots, Polynomial.leadingCoeff_multiset_prod', Height.mulHeight₁_eq, hasFDerivAt_multiset_prod, Asymptotics.IsEquivalent.multisetProd, pmap_eq_map, Equiv.Perm.cycleType_eq', Polynomial.mahlerMeasure_eq_leadingCoeff_mul_prod_roots, IsNonarchimedean.multiset_powerset_image_add, attach_ndinsert, ArithmeticFunction.cardFactors_multiset_prod, prod_X_sub_X_eq_sum_esymm, map_eq_map, Nodup.map, Finsupp.multiset_sum_sum_index, prod_map_neg, Polynomial.prod_multiset_X_sub_C_of_monic_of_roots_card_eq, sum_map_le_sum, fderiv_multiset_prod, WithLp.ofLp_multisetSum, Polynomial.monic_multisetProd_X_sub_C, map_surjective_of_surjective, prod_map_sum, Polynomial.zero_notMem_multiset_map_X_sub_C, range_add_eq_union, prod_join, Polynomial.one_le_prod_max_one_norm_roots, mapAddMonoidHom_apply, stronglyMeasurable_fun_prod, Polynomial.Splits.eval_derivative, fmap_def, card_pi, prod_bind, sum_map_zsmul, antidiagonal_map_snd, Polynomial.eq_prod_roots_of_splits, Polynomial.eq_prod_roots_of_monic_of_splits_id, Equiv.finsuppUnique_symm_apply_support_val, Polynomial.Splits.roots_map_of_injective, powersetCard_one, Polynomial.map_sub_roots_sprod_eq_prod_map_eval, prod_map_pow, prod_X_add_C_coeff, vadd_sum, map_singleton, Polynomial.Splits.eval_root_derivative, Polynomial.roots_map_of_injective_of_card_eq_natDegree, map_mk_eq_map_mk_of_rel, IsUltrametricDist.exists_norm_multiset_prod_le, map_cons, map_eq_zero, tendsto_multiset_prod, bijective_iff_map_univ_eq_univ, Nat.cast_multiset_sum, sum_smul_sum, Polynomial.count_map_roots, IsMulFreimanHom.map_prod_eq_map_prod, CharTwo.multiset_sum_sq, smul_sum, Matrix.trace_multiset_sum, norm_multiset_sum_le, HasFDerivWithinAt.multiset_prod, Finset.map_val_val_powersetCard, range_disjoint_map_add, map_noncommProd_aux, filterMap_eq_map, support_sum_subset, attach_map_val', Polynomial.Splits.eval_derivative_eq_eval_mul_sum, MultilinearMap.dfinsuppFamily_apply_support', Nat.ModEq.multisetSum_map_zero, Nat.antidiagonalTuple_two, Finset.image_toFinset, Int.cast_multiset_sum, map_comp_cons, untrop_sum, map_bind, sum_map_neg, sum_le_sum_map, Real.multiset_prod_map_rpow, hasStrictFDerivAt_multiset_prod, mem_map, toAdd_multiset_sum, filterMap_map, map_filterMap, Nat.ModEq.multisetProd_map, Polynomial.monic_multiset_prod_of_monic, Polynomial.eval_derivative_of_splits, prod_X_sub_C_dvd_iff_le_roots, AddSubmonoidClass.coe_multiset_sum, ofMul_multiset_prod, map_erase, antidiagonal_eq_map_powerset, sum_nat_mod, Polynomial.prod_multiset_root_eq_finset_root, WithLp.toLp_multisetSum, MulHom.map_multiset_ne_zero_prod, NNRat.cast_multisetProd, ChevalleyThm.chevalley_mvPolynomialC, IsMulFreimanIso.map_prod_eq_map_prod, smul_prod', continuous_multiset_sum, prod_lt_prod', map_zero, bind_singleton, antidiagonal_cons, le_prod_of_submultiplicative_on_pred_of_nonneg, multiset_sum_pow_char_pow, count_sum, Ideal.IsPrime.multiset_prod_map_le, Polynomial.prod_multiset_X_sub_C_dvd, NNReal.coe_multiset_prod, IsNonarchimedean.multiset_image_add_of_nonempty, Polynomial.resultant_eq_prod_eval, mem_sup_map_support_iff, map_add_left_Ico, Finset.univ_val_map_subtype_val, AddMonoidAlgebra.sup_support_multiset_prod_le, Pi.multiset_prod_apply, map_add_left_Ioc, attach_map_val, prod_map_lt_prod_map, prod_map_erase, Polynomial.roots_expand_map_frobenius, Finset.gcd_def, multiset_sum_pow_char, Pi.multiset_sum_apply, bell_mul_eq, Polynomial.evalEval_multiset_prod, prod_map_le_prod, rel_map_right, Finset.sum_mk, nnnorm_multiset_sum_le, Ideal.multiset_prod_span_singleton, map_noncommProd, map_fst_le_of_subset_toEnumFinset, map_filterMap_of_inv, prod_hom_rel, sum_hom₂, Nat.ModEq.multisetSum_map, mem_le_prod_of_one_le, Polynomial.count_map_roots_of_injective, nodup_map_iff_of_inj_on, Finset.noncommProd_lemma, powersetCard_cons, aemeasurable_fun_prod, map_const, Asymptotics.IsLittleO.multisetProd, Polynomial.multiset_prod_comp, IsUltrametricDist.exists_norm_multiset_sum_le, MvPolynomial.totalDegree_multiset_prod, Polynomial.eval_derivative_eq_eval_mul_sum_of_splits, Polynomial.Splits.eq_prod_roots, sum_hom_ne_zero, map_set_pairwise, prod_map_add, mem_map_of_mem, map_noncommSum_aux, sum_map_tsub, Polynomial.Splits.eval_derivative_div_eval_of_ne_zero, max_sum_le, Polynomial.prod_max_one_norm_roots_le_mahlerMeasure_of_one_le_leadingCoeff, norm_multiset_prod_le, extract_gcd, prod_nat_mod, Finset.inf_def, Int.cast_multiset_prod, prod_map_nonneg, Polynomial.Splits.aeval_eq_prod_aroots, Set.image_multiset_prod, le_sum_nonempty_of_subadditive_on_pred, Matrix.transpose_multiset_sum, Set.multiset_sum_mem_multiset_sum, Nat.antidiagonal_succ, Matrix.diag_multiset_sum, map_le_map, dedup_map_of_injective, apply_prod_le_sum_map, iSup_mem_map_of_exists_sSup_empty_le, untrop_prod, prod_map_mul, snd_sum, map_count_True_eq_filter_card, sum_hom_rel, disjSum_zero, trop_inf, bind_map_comm, Polynomial.map_roots_le, Polynomial.map_sub_sprod_roots_eq_prod_map_eval, sum_map_erase, MvPolynomial.degrees_rename, Nat.antidiagonal_succ', Polynomial.Splits.roots_map, map_single_le_powerset, Nat.map_swap_antidiagonal, Polynomial.degree_multiset_prod_of_monic, Polynomial.logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots, le_prod_of_submultiplicative_of_nonneg, Polynomial.Splits.eval_eq_prod_roots_of_monic, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues, map_replicate, canLift, Associates.prod_mk, Finset.map_toFinset, map_add_left_Ioo, Finset.sum_pow_of_commute, map_univ_coe, Rat.cast_multiset_prod, Nat.chineseRemainderOfMultiset_lt_prod, map_univ_val_equiv, trop_sum, prod_lt_prod_of_nonempty', AddCon.multiset_sum, HasFDerivAt.multiset_prod, Int.ModEq.multisetSum_map, Polynomial.prod_mahlerMeasure_eq_mahlerMeasure_prod, DirectSum.addEquivProdDirectSum_symm_apply_support', mem_map_of_injective, antidiagonal_map_fst, TwoSidedIdeal.multisetSum_mem, Associates.map_subtype_coe_factors', Polynomial.eq_prod_roots_of_splits_id, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvalues₀, Finset.prod_mk, Polynomial.eval_eq_prod_roots_sub_of_splits_id, Polynomial.natDegree_multiset_prod, prod_map_inv', Height.mulHeight_eq, sections_cons, Finset.lcm_def, iSup_mem_map_of_ne_zero, attach_cons, disjoint_map_map, sum_map_eq_nsmul_single, Polynomial.aeval_eq_prod_aroots_sub_of_monic_of_splits, map_hcongr, tendsto_multiset_sum, countP_map, sum_smul, TensorProduct.exists_multiset, prod_map_product_eq_prod_prod, filter_attach, sum_map_le_apply_prod, Polynomial.roots_expand_pow_map_iterateFrobenius_le, Asymptotics.IsTheta.multisetProd, Polynomial.roots_multiset_prod_X_sub_C, PrimeSpectrum.exists_primeSpectrum_prod_le, continuous_multiset_prod, map_eq_map_of_bij_of_nodup, Polynomial.eval_derivative_div_eval_of_ne_zero_of_splits, prod_map_le_pow_card, map_add_right_Ioo, Set.image_multiset_sum, Polynomial.map_roots_le_of_injective, Polynomial.Splits.eval_eq_prod_roots, prod_map_le_prod_map₀, Associates.rel_associated_iff_map_eq_map, Finset.sum_eq_multiset_sum, prod_map_prod, map_multiset_prod, Asymptotics.IsBigO.multisetProd, map_finset_sup, Polynomial.filter_roots_map_range_eq_map_roots, map_toEnumFinset_fst, fst_sum, fderivWithin_multiset_prod, map_erase_of_mem, NNRat.cast_multisetSum, sum_map_div, Finset.prod_map_val, Finsupp.supportedEquivFinsupp_symm_apply_coe_support_val, Polynomial.natDegree_multiset_prod_X_sub_C_eq_card, Nat.ModEq.multisetProd_map_one, map_mono, count_bind, prod_map_zpow, filter_join, sym2_cons, sum_map_zero, count_map, Finset.univ_val_map_subtype_restrict, Real.exp_multiset_sum, sum_map_neg', Sym.coe_map, Polynomial.Monic.nextCoeff_multiset_prod, Finpartition.ofSetoid_parts_val, CharTwo.multiset_sum_mul_self, Polynomial.ofMultiset_apply, Polynomial.eval_eq_prod_roots_sub_of_monic_of_splits_id, cons_product, Polynomial.multiset_prod_X_sub_C_nextCoeff, map_union, LinearMap.BilinMap.toQuadraticMap_multiset_sum, Nat.cast_multiset_prod, Polynomial.roots_expand_pow_map_iterateFrobenius, Polynomial.aeval_derivative_of_splits, map_univ, map_le_map_iff, map_subset_map, Polynomial.roots_map_of_map_ne_zero_of_card_eq_natDegree, Polynomial.derivative_prod, map_lt_map, sum_map_le_sum_map, map_noncommSum, Finset.sum_multiset_map_count, PrimeMultiset.coePNat_nat, prod_map_le_prod_map, sum_bind, Polynomial.degree_multiset_prod_le, nat_divisors_prod, Polynomial.coeff_zero_multiset_prod, map_pmap, bell_eq, ZMod.Ico_map_valMinAbs_natAbs_eq_Ico_map_id, Set.multiset_prod_singleton, aemeasurable_fun_sum, Polynomial.C_leadingCoeff_mul_prod_multiset_X_sub_C, fold_bind, max_prod_le, sum_lt_sum_of_nonempty, MvPolynomial.aeval_esymm_eq_multiset_esymm, continuousOn_multiset_prod, prod_map_div, Polynomial.Splits.aeval_eq_prod_aroots_of_monic, cons_sigma, count_map_eq_count, Polynomial.Splits.map_roots, Polynomial.Splits.eq_prod_roots_of_monic, map_filter_eq_filterMap, Polynomial.resultant_eq_prod_roots_sub, Polynomial.Monic.roots_map_of_card_eq_natDegree, Polynomial.aeval_eq_prod_aroots_sub_of_splits, sum_hom₂_ne_zero, mapEmbedding_apply, UniqueFactorizationMonoid.normalizedFactors_prod_eq, mapEquiv_apply, Finsupp.single_multiset_sum, erase_attach_map, le_prod_nonempty_of_submultiplicative_on_pred, support_sum_eq, prod_hom, sum_map_sub, Finset.map_val, Polynomial.aeval_root_derivative_of_splits, prod_map_eq_pow_single, powerset_cons, Finset.prod_eq_multiset_prod, RingCon.multisetSum, esymm_neg, filter_map, Ideal.factors_span_eq, pow_smul_esymm, AddEquiv.finsuppUnique_symm_apply_support_val, fold_hom, TwoSidedIdeal.multiSetProd_mem, map_injective, range_add, map_univ_comp_coe, nnnorm_multiset_prod_le, map_congr, Matrix.conjTranspose_multiset_sum, map_multiset_ne_zero_prod, Real.log_multiset_prod, Finset.image_val_of_injOn, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues₀, AddSubmonoid.coe_multiset_sum, powersetCard_map, AddSubgroup.val_multiset_sum, sum_map_singleton, Finset.esymm_map_val, HasStrictFDerivAt.multiset_prod, map_strictMono, Int.ModEq.multisetProd_map_one, MvPolynomial.degrees_rename_of_injective, Finsupp.multiset_map_sum, Finsupp.supportedEquivFinsupp_apply_support_val, NNReal.coe_multiset_sum, exists_multiset_eq_map_quot_mk, nodup_map_iff_inj_on, toMul_multiset_sum, map_map, bind_cons, Polynomial.eval₂_derivative_of_splits, MvPolynomial.esymm_eq_multiset_esymm, sum_lt_sum, prod_le_prod_map, Polynomial.leadingCoeff_multiset_prod, map_multiset_ne_zero_sum, sections_add, Nat.antidiagonal_succ_succ', prod_dvd_prod_of_dvd, one_le_prod_map, card_sections, nodup_map_iff_of_injective, RingEquiv.map_multiset_sum, AddMonoidHom.map_multiset_sum, WithConv.toConv_multisetSum, map_id', IsAddFreimanIso.map_sum_eq_map_sum, Localization.mk_multiset_sum, Finset.nodup_map_iff_injOn, traverse_map, map_filter', KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, prod_map_prod_map, card_join, sum_map_sum, Polynomial.eval₂_multiset_sum, Equiv.Perm.cycleType_def, Polynomial.roots_expand_pow, exists_multiset_prod_cons_le_and_prod_not_le, Finset.sup_def, le_sum_of_subadditive_on_pred, le_sum_of_subadditive, IsNonarchimedean.multiset_image_add, map_swap_product, RingEquiv.map_multiset_prod, le_prod_of_submultiplicative_on_pred, enorm_multisetSum_le, WithConv.ofConv_multisetSum, map_disjSum, MonoidHom.map_multiset_prod, toFinset_map, prod_X_add_C_eq_sum_esymm, Nat.multiset_Ico_map_mod, Polynomial.exists_prod_multiset_X_sub_C_mul, sum_min_le, Polynomial.eval_multisetSum, sum_join, Polynomial.natDegree_multiset_prod', Polynomial.splits_iff_exists_multiset', map_add_right_Ioc, prod_X_add_C_coeff', Polynomial.splits_of_exists_multiset, le_prod_of_submultiplicative, NumberField.prod_archAbsVal_eq, stronglyMeasurable_fun_sum, snd_prod, sum_hom, Set.multiset_sum_singleton, Polynomial.natDegree_multiset_prod_le, Submonoid.coe_multiset_prod, Set.multiset_sum_subset_multiset_sum, Polynomial.map_multiset_prod, Nat.divisors_filter_squarefree, Finset.sum_pow, abs_sum_le_sum_abs, map_coe, measurable_fun_sum, Finset.sum_map_val, Rat.cast_multiset_sum, sum_map_add, Finset.image_val, Polynomial.degree_multiset_prod, map_add_left_Icc, sum_map_mul_right, Polynomial.multiset_prod_X_sub_C_coeff_card_pred, Polynomial.Splits.roots_map_of_ne_zero, AddMonoidAlgebra.le_inf_support_multiset_prod, Fintype.nodup_map_univ_iff_injective, Differential.logDeriv_multisetProd, sum_hom', map_add, prod_hom₂_ne_zero, bind_map, Set.multiset_prod_mem_multiset_prod, smul_prod, Equiv.Perm.sign_of_cycleType', Con.multiset_prod, Height.AdmissibleAbsValues.product_formula, Polynomial.natDegree_multiset_prod_of_monic, le_prod_nonempty_of_submultiplicative, NNReal.multiset_prod_map_rpow, map_const', fold_distrib, sym2_map, Int.ModEq.multisetProd_map, card_bind, gcd_map_mul, Polynomial.zero_notMem_multiset_map_X_add_C, Combinatorics.Line.ColorFocused.distinct_colors, map_eq_singleton, enorm_multisetProd_le, Polynomial.coeff_multiset_prod_of_natDegree_le, Complex.exp_multiset_sum, prod_hom_ne_zero, prod_map_toList, Polynomial.Chebyshev.roots_U_real_nodup, PrimeSpectrum.exists_primeSpectrum_prod_le_and_ne_bot_of_domain, sum_map_sum_map, prod_hom₂, map_add_right_Ico, le_sum_nonempty_of_subadditive, map_nsmul, Finsupp.toMultiset_map, count_map_eq_count', erase_attach_map_val, SubmonoidClass.coe_multiset_prod, Polynomial.Chebyshev.roots_T_real_nodup, sum_map_toList, Finsupp.mapRange_multiset_sum, Nodup.map_on, prod_map_one, filter_attach', Associates.prod_coe, continuousOn_multiset_sum, measurable_fun_prod, IsPrimitiveRoot.nthRoots_eq, Polynomial.roots_map, Polynomial.roots_expand_map_frobenius_le, Finset.noncommSum_lemma, UniqueFactorizationMonoid.normalizedFactors_multiset_prod, map_join, dedup_map_dedup_eq, map_add_right_Icc, Sym.map_mk, IsAddFreimanHom.map_sum_eq_map_sum, sum_map_nsmul, prod_map_inv, pmap_eq_map_attach, Subgroup.val_multiset_prod, card_map, AddHom.map_multiset_ne_zero_sum, zero_disjSum, iInf_mem_map_of_exists_le_sInf_empty, Polynomial.eval_multiset_prod_X_sub_C_derivative, filterMap_join, coe_mapAddMonoidHom, prod_min_le, Fin.univ_val_map, Finpartition.avoid_parts_val, aestronglyMeasurable_fun_sum, Polynomial.natDegree_multiset_sum_le, rel_map, map_eq_cons, prod_hom', fst_prod, prod_X_sub_C_coeff, card_sigma, sum_int_mod, sum_map_mul_left
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