IntermediateField 📖 | CompData | 646 mathmath: normalClosure_le_iff, IntermediateField.AdjoinSimple.trace_gen_eq_sum_roots, IntermediateField.finInsepDegree_top, Field.Emb.Cardinal.equivLim_coherence, InfiniteGalois.normal_iff_isGalois, mem_perfectClosure_iff_natSepDegree_eq_one, IntermediateField.aeval_gen_minpoly, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, IntermediateField.LinearDisjoint.iff_inf_eq_bot, IntermediateField.normal_inf, IsGalois.tower_top_intermediateField, IntermediateField.LinearDisjoint.linearIndependent_right', IntermediateField.adjoin.finrank, IntermediateField.algebraMap_mem, IntermediateField.coe_algebraMap_over_bot, IntermediateField.instIsAlgClosureAlgebraicClosureSubtypeMemOfIsAlgebraic, IntermediateField.lift_le, perfectClosure.map_le_of_algHom, mem_subalgebraEquivIntermediateField, minpoly.algEquiv_apply, IntermediateField.relrank_comap_comap_eq_relrank_inf, IntermediateField.isScalarTower_mid', IntermediateField.map_le_iff_le_comap, IntermediateField.adjoinRootEquivAdjoin_symm_apply_gen, IntermediateField.isCyclotomicExtension_singleton_iff_eq_adjoin, IntermediateField.coe_prod, IntermediateField.coe_bot, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateField, FiniteGaloisIntermediateField.subset_adjoin, Field.Emb.Cardinal.directed_filtration, IntermediateField.lift_insepDegree_bot', Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, InfiniteGalois.isOpen_and_normal_iff_finite_and_isGalois, Field.Emb.Cardinal.filtration_succ, IntermediateField.isCyclotomicExtension_le_of_dvd, algebraicClosure.algebraicClosure_eq_bot, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_right, InfiniteGalois.normalAutEquivQuotient_apply, IsGaloisGroup.fixingSubgroup_top, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, IntermediateField.isAlgebraic_tower_bot, IsGaloisGroup.fixedPoints_top, IntermediateField.mem_adjoin_iff, IntermediateField.mem_carrier, IntermediateField.botEquiv_symm, IsGalois.card_fixingSubgroup_eq_finrank, Subfield.relfinrank_eq_finrank_of_le, AlgHom.fieldRange_eq_map, IntermediateField.relfinrank_bot_right, Field.exists_primitive_element, isGalois_iff_isGalois_top, IntermediateField.relrank_eq_one_iff, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, InfiniteGalois.mem_bot_iff_fixed, FiniteGaloisIntermediateField.mem_fixingSubgroup_iff, IntermediateField.normal_iff_forall_map_eq, IntermediateField.extendScalars_injective, IntermediateField.ext_iff, IntermediateField.natCast_mem, IntermediateField.adjoin_simple_isCompactElement, IntermediateField.coe_neg, IntermediateField.adjoin.mono, IntermediateField.restrictScalars_normal, IntermediateField.isScalarTower, Algebra.FormallySmooth.adjoin_of_algebraicIndependent, IntermediateField.algebraAdjoinAdjoin.instIsAlgebraicSubtypeMemSubalgebraAdjoinAdjoin, isPurelyInseparable_iff_fd_isPurelyInseparable, IntermediateField.LinearDisjoint.of_isField', IntermediateField.adjoin_zero, IntermediateField.coe_iInf, PowerBasis.equivAdjoinSimple_symm_aeval, IntermediateField.adjoin_univ, Subfield.coe_toIntermediateField, IntermediateField.lift_adjoin_simple, algebraicClosure.normalClosure_eq_self, IntermediateField.AdjoinDouble.normal_algebraicClosure, IntermediateField.coe_add, IntermediateField.mem_adjoin_simple_self, IntermediateField.isAlgebraic_adjoin_iff_top, IntermediateField.inf_toSubalgebra, algebraicClosure.isAlgebraic, IntermediateField.adjoin_finite_isCompactElement, IsGalois.normalClosure, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow', IntermediateField.finiteDimensional_right, IntermediateField.isAlgebraic_iff, IntermediateField.charZero, NumberField.instIsTotallyRealSubtypeMemIntermediateFieldRatOfIsAlgebraic, IntermediateField.mem_adjoin_of_mem, IntermediateField.subset_adjoin_of_subset_left, IntermediateField.instSMulMemClass, IntermediateField.adjoin_le_iff, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, IsNormalClosure.adjoin_rootSet, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, Field.Emb.Cardinal.two_le_deg, IntermediateField.smulCommClass_left, IntermediateField.isAlgebraic_adjoin_iff, IntermediateField.minpoly_gen, Field.Emb.Cardinal.isLeast_leastExt, IntermediateField.aeval_coe, IntermediateField.instIsScalarTowerSubtypeMem, IntermediateField.inf_relrank_right, normalClosure_eq_iSup_adjoin', IntermediateField.iInf_toSubfield, IntermediateField.fixingSubgroup_top, IntermediateField.coe_toSubalgebra, Field.Emb.Cardinal.succEquiv_coherence, IntermediateField.bot_toSubalgebra, IntermediateField.isScalarTower_bot, IntermediateField.sup_toSubalgebra_of_isAlgebraic_left, IntermediateField.relfinrank_top_right, IntermediateField.restrictScalars_sup, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, solvableByRad.isSolvable, IntermediateField.linearDisjoint_comm, Ring.instIsScalarTowerSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, IntermediateField.restrictScalars_top, IntermediateField.equivOfEq_symm, IntermediateField.coe_type_toSubfield, IntermediateField.restrictRestrictAlgEquivMapHom_apply, IsGalois.intermediateFieldEquivSubgroup_apply, IntermediateField.mem_top, IntermediateField.fieldRange_comp_val, Subfield.extendScalars_le_extendScalars_iff, Field.primitive_element_iff_algHom_eq_of_eval', IntermediateField.adjoin.powerBasis_gen, IntermediateField.equivOfEq_rfl, IntermediateField.normal_iff_normalClosure_le, mem_perfectClosure_iff_pow_mem, Subfield.extendScalars_inf, IntermediateField.relrank_top_right, Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure_1, IntermediateField.LinearDisjoint.bot_left, IntermediateField.isTotallyReal_bot, IntermediateField.continuousSMul, IntermediateField.relfinrank_dvd_finrank_bot, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, IntermediateField.adjoin_simple_adjoin_simple, normalClosure.restrictScalars_eq, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_right, IntermediateField.mem_adjoin_pair_right, IntermediateField.AdjoinSimple.norm_gen_eq_one, IntermediateField.range_val, IntermediateField.instFiniteSubtypeMemBot, IntermediateField.isCyclotomicExtension_lcm_sup, map_mem_perfectClosure_iff, IntermediateField.linearDisjoint_iff', IsGaloisGroup.fixedPoints_fixingSubgroup, IntermediateField.splits_iff_mem, IntermediateField.extendScalars.orderIso_apply, algebraicClosure.isIntegralClosure, Algebra.normalizedTrace_intermediateField, IsGaloisGroup.le_fixedPoints_iff_le_fixingSubgroup, isNormalClosure_normalClosure, IntermediateField.mem_fixedField_iff, IntermediateField.finrank_eq_one_iff, IntermediateField.lift_top, IntermediateField.sInf_toSubalgebra, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, IntermediateField.eq_bot_of_isAlgClosed_of_isAlgebraic, map_mem_separableClosure_iff, IntermediateField.insepDegree_bot', IntermediateField.fixedField_antitone, AlgebraicIndependent.lift_reprField, IntermediateField.isAlgebraic_adjoin, IntermediateField.fg_sup, IntermediateField.inf_relfinrank_right, mem_subalgebraEquivIntermediateField_symm, instIsLiouvilleSubtypeMemIntermediateField, IntermediateField.coe_mul, IntermediateField.sSup_def, IntermediateField.restrictScalars_eq_top_iff, IsTranscendenceBasis.isAlgebraic_field, Ring.instIsFractionRingNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, PowerBasis.equivAdjoinSimple_aeval, IntermediateField.isPurelyInseparable_tower_bot, le_separableClosure_iff, IntermediateField.charP', toIntermediateField'_toSubalgebra, IntermediateField.botContinuousSMul, separableClosure_le, Field.exists_primitive_element_of_finite_bot, IntermediateField.restrictScalars_le_iff, eq_separableClosure_iff, separableClosure.map_le_of_algHom, IntermediateField.mem_toSubfield, mem_algebraicClosure_iff, IntermediateField.normal_iff_forall_fieldRange_le, IsGalois.normalAutEquivQuotient_apply, Field.exists_primitive_element_of_finite_top, IntermediateField.instIsScalarTowerSubtypeMemAdjoinSingletonSetCoeRingHomAlgebraMap, IntermediateField.adjoin_simple_eq_top_iff_of_isAlgebraic, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, IntermediateField.instSubfieldClass, trace_eq_finrank_mul_minpoly_nextCoeff, IntermediateField.rank_adjoin_eq_one_iff, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure_1, IntermediateField.isAlgebraic_tower_top, IntermediateField.adjoin_one, IntermediateField.rank_top, IntermediateField.finrank_eq_fixingSubgroup_index, trace_eq_trace_adjoin, IntermediateField.coe_isIntegral_iff, IntermediateField.adjoin_root_eq_top, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_right, IsGaloisGroup.fixingSubgroup_fixedPoints, normalClosure_def, IntermediateField.lift_inf, IntermediateField.instIsCompactlyGenerated, mem_perfectClosure_iff, IntermediateField.exists_algHom_of_splits, IntermediateField.extendScalars_self, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, PowerBasis.equivAdjoinSimple_gen, IntermediateField.coe_inf, Field.Emb.Cardinal.equivSucc_coherence, IntermediateField.finrank_top, IntermediateField.restrictScalars_adjoin_eq_sup, FiniteGaloisIntermediateField.isGalois, separableClosure.eq_top_iff, IntermediateField.mem_adjoin_iff_div, le_algebraicClosure, IntermediateField.Lifts.lt_iff, IntermediateField.mem_inf, IntermediateField.top_toSubalgebra, instSeminormClassAlgebraNormSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IntermediateField.cardinalMk_adjoin_le, IntermediateField.coe_sum, IntermediateField.relrank_top_left, IsGaloisGroup.fixedPoints_bot, IntermediateField.restrictScalars_injective, Splits.algebraicClosure, PowerBasis.equivAdjoinSimple_symm_gen, IntermediateField.coe_val, exists_root_adjoin_eq_top_of_isCyclic, IsGaloisGroup.ofDual_intermediateFieldEquivSubgroup_apply, IntermediateField.finrank_eq_finrank_subalgebra, IntermediateField.finrank_eq_one_iff_eq_top, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable', IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDual, Subfield.extendScalars_top, Transcendental.algebraicClosure, IntermediateField.coe_toSubfield, NumberField.is_primitive_element_of_infinitePlace_lt, IntermediateField.finrank_adjoin_eq_one_iff, Ring.instIsSeparableFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, algebraicClosure.map_le_of_algHom, IntermediateField.normal_iff_forall_map_le', IntermediateField.normal_iff_forall_fieldRange_eq, exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow_of_essFiniteType, instIsAbelianGaloisSubtypeMemIntermediateField_1, IntermediateField.restrictScalars_inf, IntermediateField.instFaithfulSMulSubtypeMem, IntermediateField.finrank_bot, IntermediateField.fixingSubgroup_antitone, InfiniteGalois.restrict_fixedField, IntermediateField.subset_adjoin_of_subset_right, algebraicClosure.le_restrictScalars, IntermediateField.sepDegree_bot, normalClosure.instIsScalarTowerSubtypeMemIntermediateFieldNormalClosure, trace_eq_sum_roots, IntermediateField.algebraMap_apply, IntermediateField.adjoin_simple_le_iff, IntermediateField.finInsepDegree_bot', Algebra.norm_eq_norm_adjoin, IntermediateField.subset_adjoin, IntermediateField.isAlgebraic_adjoin_iff_isAlgebraic, IntermediateField.restrictScalars_bot_eq_self, IntermediateField.adjoin.range_algebraMap_subset, IntermediateField.fg_bot, IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable, IntermediateField.sup_def, IntermediateField.mem_lift, IntermediateField.isAlgebraic_adjoin_pair, IntermediateField.finrank_sup_le, le_perfectClosure, Differential.instDifferentialAlgebraSubtypeMemIntermediateField_1, IntermediateField.adjoin_empty, IntermediateField.adjoinRootEquivAdjoin_apply_root, IntermediateField.normalClosureOperator_apply, Field.Emb.Cardinal.eq_bot_of_not_nonempty, IntermediateField.finSepDegree_adjoin_simple_eq_natSepDegree, IntermediateField.rank_bot, separableClosure_inf_perfectClosure, IntermediateField.isPurelyInseparable_adjoin_iff_pow_mem, le_restrictScalars_separableClosure, IntermediateField.coe_zero, separableClosure.adjoin_eq_of_isAlgebraic, IntermediateField.adjoin.algebraMap_mem, IntermediateField.coe_restrictScalars, IntermediateField.instIsScalarTowerSubtypeMem_1, IntermediateField.map_injective, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_right, IntermediateField.bot_eq_top_iff_finrank_eq_one, IntermediateField.finiteDimensional_adjoin, IntermediateField.isTranscendenceBasis_adjoin_iff, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_left, IntermediateField.lift_injective, IntermediateField.adjoin_eq_bot_iff, IntermediateField.isSeparable_adjoin_simple_iff_isSeparable, IntermediateField.AdjoinSimple.trace_gen_eq_zero, IntermediateField.lift_sepDegree_bot', IntermediateField.mem_adjoin_range_iff, IntermediateField.relfinrank_inf_mul_relfinrank, IntermediateField.finSepDegree_adjoin_simple_le_finrank, Field.exists_primitive_element_iff_finite_intermediateField, IntermediateField.card_algHom_adjoin_integral, Field.Emb.Cardinal.filtration_apply, IntermediateField.gc_map_comap, IntermediateField.relrank_dvd_rank_bot, IntermediateField.AdjoinPair.algebraMap_gen₁, Subfield.le_extendScalars_iff, IntermediateField.map_comap_eq, IsGalois.intermediateFieldEquivSubgroup_symm_apply, IntermediateField.map_iSup, NumberField.finite_of_discr_bdd, IntermediateField.map_iInf, AlgHom.coe_fieldRange, AlgebraicIndependent.liftAlgHom_comp_reprField, IntermediateField.finrank_top', IntermediateField.inclusion_self, IntermediateField.lift_bot, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, IsGalois.fixedField_top, IntermediateField.normalClosure_of_normal, IntermediateField.charP, Algebra.IsAlgebraic.isNormalClosure_iff, IntermediateField.intCast_mem, IntermediateField.sup_toSubalgebra_of_left, InfiniteGalois.isOpen_iff_finite, Field.Emb.Cardinal.deg_lt_aleph0, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, IntermediateField.adjoin_simple_eq_bot_iff, IntermediateField.relfinrank_bot_left, IntermediateField.toSubalgebra_injective, IntermediateField.iSup_eq_adjoin, Subfield.extendScalars_le_iff, IntermediateField.extendScalars.orderIso_symm_apply_coe, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, IntermediateField.adjoin_intCast, IntermediateField.iSup_toSubfield, IntermediateField.sepDegree_bot', Ring.instIsScalarTowerFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, Differential.instDifferentialAlgebraSubtypeMemIntermediateField, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_right_of_isAlgebraic_left, IntermediateField.LinearDisjoint.bot_right, Field.primitive_element_iff_minpoly_degree_eq, AlgHom.fieldRange_eq_top, IntermediateField.normal_iff_forall_map_le, separableClosure.isAlgebraic, IntermediateField.normalClosureOperator_isClosed, Subfield.extendScalars.orderIso_apply, IntermediateField.expChar, isPurelyInseparable_iff_perfectClosure_eq_top, IntermediateField.rank_eq_one_iff, IsGaloisGroup.intermediateField, IntermediateField.adjoin_rank_le_of_isAlgebraic_right, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_left, IntermediateField.fg_iSup, IntermediateField.eq_bot_of_isPurelyInseparable_of_isSeparable, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply, IntermediateField.mem_adjoin_pair_left, Ring.instFiniteDimensionalFractionRingSubtypeAlgebraicClosureMemIntermediateFieldNormalClosure, IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin, IntermediateField.adjoin_root_eq_top_of_isSplittingField, spectralNorm.eq_of_normalClosure', algebraicClosure.eq_top_iff, IntermediateField.adjoin_iUnion, algebraicClosure.adjoin_le, AlgHom.mem_fieldRange, IntermediateField.finrank_fixedField_eq_card, separableClosure.isSepClosure, IntermediateField.finrank_comap, Field.primitive_element_iff_minpoly_natDegree_eq, IntermediateField.normalClosure_def'', IntermediateField.AdjoinSimple.norm_gen_eq_prod_roots, Subfield.relrank_eq_rank_of_le, Field.Emb.Cardinal.strictMono_filtration, FixedBy.intermediateField_mem_iff, IntermediateField.isScalarTower_over_bot, IntermediateField.isSeparable_tower_bot, IntermediateField.minpoly_eq, IntermediateField.LinearDisjoint.lift_rank_right_mul_lift_adjoin_rank_eq_of_isAlgebraic_left, IntermediateField.mem_toSubalgebra, IntermediateField.isSplittingField_iff, IntermediateField.bot_toSubfield, IntermediateField.topEquiv_symm_apply_coe, FiniteGaloisIntermediateField.adjoin_val, IntermediateField.adjoin_finset_isCompactElement, NumberField.of_intermediateField, IntermediateField.adjoin_eq_range_algebraMap_adjoin, IntermediateField.rank_top', IntermediateField.isAlgebraic_adjoin_simple, IntermediateField.AdjoinSimple.normal_algebraicClosure, IntermediateField.normal_iff_forall_map_eq', IntermediateField.intermediateFieldMap_apply_coe, IntermediateField.topEquiv_apply, IntermediateField.exists_algHom_adjoin_of_splits', Algebra.normalizedTrace_def, IntermediateField.adjoin_natCast, IntermediateField.coe_inv, IntermediateField.AdjoinSimple.isIntegral_gen, map_mem_algebraicClosure_iff, IntermediateField.mem_restrictScalars, IntermediateField.exists_lt_finrank_of_infinite_dimensional, Algebra.IsAlgebraic.isNormalClosure_normalClosure, IntermediateField.isPurelyInseparable_bot, mem_algebraicClosure_iff', IntermediateField.top_toSubfield, AlgebraicIndependent.aevalEquivField_apply_coe, IntermediateField.LinearDisjoint.exists_field_of_isDomain, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_right, Subfield.extendScalars_sup, IntermediateField.isSeparable_adjoin_pair_of_isSeparable, IntermediateField.finiteDimensional_left, le_perfectClosure_iff, perfectClosure.isAlgebraic, IntermediateField.isSeparable_sup, FiniteGaloisIntermediateField.finiteDimensional, AlgHom.fieldRange_le_normalClosure, IntermediateField.smul_def, InfiniteGalois.finGaloisGroupFunctor_map_proj_eq_proj, IntermediateField.coe_smul, IsGaloisGroup.fixingSubgroup_bot, Ring.instFaithfulSMulSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, IntermediateField.set_range_subset, InfiniteGalois.restrictNormalHom_continuous, IsGaloisGroup.subgroup, normalClosure_eq_iSup_adjoin, IntermediateField.LinearDisjoint.rank_right_mul_adjoin_rank_eq_of_isAlgebraic_left, IntermediateField.fixedField.isScalarTower, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, IsGalois.of_separable_splitting_field_aux, IntermediateField.coe_equivMap_apply, IntermediateField.fg_top, IntermediateField.adjoin_insert_adjoin, IntermediateField.mem_adjoin_simple_iff, IntermediateField.finInsepDegree_bot, IsGaloisGroup.intermediateFieldEquivSubgroup_apply, krullTopology_mem_nhds_one_iff, IntermediateField.one_mem, AlgEquiv.fieldRange_eq_top, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_exists_isPrimitiveRoot, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin, Field.Emb.Cardinal.iSup_adjoin_eq_top, IntermediateField.lift_cardinalMk_adjoin_le, krullTopology_mem_nhds_one_iff_of_normal, IntermediateField.finrank_bot', IntermediateField.sInf_toSubfield, IntermediateField.isCyclotomicExtension_adjoin_of_exists_isPrimitiveRoot, IntermediateField.Lifts.exists_lift_of_splits, separableClosure.isSeparable, IntermediateField.adjoin_toSubalgebra_of_isAlgebraic_left, Algebra.norm_eq_prod_roots, IntermediateField.adjoin.finiteDimensional, IntermediateField.botEquiv_def, le_algebraicClosure_iff, IntermediateField.adjoin_adjoin_comm, IntermediateField.adjoin_eq_top_iff, AlgebraicIndependent.algebraicClosure, IntermediateField.toSubalgebra_lt_toSubalgebra, IntermediateField.finSepDegree_bot', IntermediateField.rank_sup_le, IntermediateField.coe_pow, IntermediateField.fixedField_le, IntermediateField.eq_bot_of_isSepClosed_of_isSeparable, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateField, AlgEquiv.restrictNormalHom_apply, instIsAbelianGaloisSubtypeMemIntermediateField, IntermediateField.adjoin_simple_comm, algebraicClosure.isAlgClosure, IntermediateField.relrank_bot_right, IntermediateField.le_iff_le, InfiniteGalois.fixedField_bot, IntermediateField.zero_mem, IntermediateField.adjoin_subset_adjoin_iff, IsSepClosed.separableClosure_eq_bot_iff, perfectClosure.perfectField, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, IntermediateField.mem_mk, InfiniteGalois.proj_of_le, IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_inf, IntermediateField.expChar', exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow, IntermediateField.coe_type_toSubalgebra, IntermediateField.adjoin_union, IntermediateField.inf_toSubfield, IntermediateField.lift_adjoin, FiniteGaloisIntermediateField.val_injective, IntermediateField.smulCommClass_right, IntermediateField.adjoin_eq_top_of_algebra, IsGaloisGroup.fixedPoints_le_of_le, IntermediateField.extendScalars_top, perfectClosure.eq_bot_of_isSeparable, IntermediateField.algebraicIndependent_adjoin_iff, mem_separableClosure_iff, IntermediateField.rank_eq_rank_subalgebra, IntermediateField.fixedField_bot, AlgebraicIndependent.aevalEquivField_algebraMap_apply_coe, IntermediateField.toSubalgebra_strictMono, IntermediateField.lift_sup, normalClosure.normal, IntermediateField.adjoin_adjoin_left, separableClosure_le_iff, solvableByRad.isIntegral, IntermediateField.restrictNormalHom_ker, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, IntermediateField.adjoin_rank_le_of_isAlgebraic_left, isClosed_restrictScalars_separableClosure, IntermediateField.sup_toSubalgebra_of_right, IntermediateField.algebraAdjoinAdjoin.instFaithfulSMulSubtypeMemSubalgebraAdjoinAdjoin, IntermediateField.insepDegree_bot, IsAlgClosed.algebraicClosure_eq_bot_iff, IntermediateField.equivOfEq_apply, IntermediateField.rank_bot', IntermediateField.le_sup_toSubalgebra, IntermediateField.gc, IntermediateField.isAlgebraic_adjoin_iff_bot, FiniteGaloisIntermediateField.le_iff, IntermediateField.fieldRange_val, IntermediateField.liftAlgEquiv_apply, IntermediateField.insepDegree_top, separableClosure_le_separableClosure_iff, IsGalois.tfae, IntermediateField.map_inf, IntermediateField.transcendental_adjoin_iff, Field.Emb.Cardinal.iSup_filtration, IntermediateField.algebraAdjoinAdjoin.instIsScalarTowerSubtypeMemSubalgebraAdjoinAdjoin_1, IntermediateField.isSimpleOrder_of_finrank_prime, IntermediateField.rank_comap, Subfield.extendScalars.orderIso_symm_apply_coe, separableClosure.separableClosure_eq_bot, IntermediateField.adjoin_intermediateField_toSubalgebra_of_isAlgebraic_right, le_separableClosure, IntermediateField.fg_top_iff, IntermediateField.sup_toSubfield, IntermediateField.relfinrank_comap_comap_eq_relfinrank_inf, IntermediateField.sup_toSubalgebra_of_isAlgebraic_right, IntermediateField.toSubalgebra_le_toSubalgebra, IntermediateField.inf_relfinrank_left, IntermediateField.relfinrank_top_left, IntermediateField.map_sup, IntermediateField.finiteDimensional_map, IntermediateField.finSepDegree_top, IntermediateField.lift_rank_comap, IntermediateField.inf_relrank_left, IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraic_right, IsAdjoinRoot.primitive_element_root, IntermediateField.instIsScalarTowerSubtypeMemSubalgebraAdjoinSingletonSetAdjoinCoeRingHomAlgebraMap, IntermediateField.normalClosure_le_iff_of_normal, AlgHom.fieldRange_of_normal, IntermediateField.Lifts.eq_iff, Subfield.extendScalars_self, Field.Emb.Cardinal.adjoin_basis_eq_top, IntermediateField.relrank_inf_mul_relrank, IntermediateField.iInf_toSubalgebra, IsGaloisGroup.card_fixingSubgroup_eq_finrank, IntermediateField.normalClosure_map_eq, IntermediateField.LinearDisjoint.lift_adjoin_rank_eq_lift_rank_right_of_isAlgebraic_left, IntermediateField.relrank_bot_left, IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, Ring.instIsIntegralClosureNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure, Subfield.mem_extendScalars, IntermediateField.isPurelyInseparable_tower_top, IntermediateField.le_normalClosure, IntermediateField.equivOfEq_trans, IntermediateField.Lifts.carrier_union, IntermediateField.toSubfield_injective, IntermediateField.normalClosure_def', IntermediateField.adjoin_self, IntermediateField.mem_bot, Ring.instIsScalarTowerNormalClosureSubtypeAlgebraicClosureFractionRingMemIntermediateFieldNormalClosure_1, perfectClosure.perfectRing, FixedPoints.mem_intermediateField_iff, IntermediateField.LinearDisjoint.isDomain, IntermediateField.fixingSubgroup_bot, IntermediateField.coe_top, IntermediateField.AdjoinSimple.coe_gen, isGalois_bot, IntermediateField.intermediateFieldMap_symm_apply_coe, IntermediateField.coe_sInf, isSplittingField_iff_intermediateField, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, isGalois_iff_isGalois_bot, Algebra.IsAlgebraic.normalClosure_eq_iSup_adjoin_of_splits, IntermediateField.finiteDimensional_adjoin_pair, IntermediateField.normal_sup, IntermediateField.coe_algebraMap_apply, separableClosure.isGalois, IntermediateField.isPurelyInseparable_adjoin_simple_iff_natSepDegree_eq_one, IntermediateField.restrictScalars_adjoin, IntermediateField.finrank_adjoin_simple_eq_one_iff, IntermediateField.isSeparable_tower_top, normalClosure.is_finiteDimensional, Field.primitive_element_iff_algHom_eq_of_eval, IntermediateField.finiteDimensional_sup, IntermediateField.Lifts.le_iff, Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin, separableClosure.eq_bot_iff, trace_adjoinSimpleGen, IntermediateField.fixingSubgroup_sup, IntermediateField.normal_iff_normalClosure_eq, IntermediateField.rank_adjoin_simple_eq_one_iff, separableClosure.adjoin_eq_of_isAlgebraic_of_isSeparable, IntermediateField.AdjoinPair.algebraMap_gen₂, IntermediateField.isIntegral_iff, Subfield.coe_extendScalars, separableClosure.normalClosure_eq_self, IsGaloisGroup.map_mulEquivAlgEquiv_fixingSubgroup, IntermediateField.coe_map, Subfield.extendScalars_injective, IntermediateField.adjoin.powerBasis_dim, IsGalois.of_fixedField_normal_subgroup, IntermediateField.relfinrank_eq_one_iff, IntermediateField.essFiniteType_iff, Field.Emb.cardinal_separableClosure, IntermediateField.AdjoinSimple.algebraMap_gen, IntermediateField.isPurelyInseparable_sup, IsGaloisGroup.intermediateFieldEquivSubgroup_symm_apply_toDual, separableClosure.adjoin_le, IsGalois.mem_bot_iff_fixed, FiniteGaloisIntermediateField.adjoin_simple_le_iff, separableClosure.le_restrictScalars, IntermediateField.map_bot, separableClosure.isPurelyInseparable, IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_mem, isCyclic_tfae, separableClosure.eq_bot_of_isPurelyInseparable, IntermediateField.adjoin_rootSet_isSplittingField, IntermediateField.nonempty_algHom_adjoin_of_splits, IntermediateField.isScalarTower_mid, IntermediateField.finSepDegree_bot, IntermediateField.biSup_adjoin_simple, IsGalois.ofDual_intermediateFieldEquivSubgroup_apply, IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosed, perfectClosure.isPurelyInseparable, IntermediateField.isSeparable_adjoin_iff_isSeparable, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, IntermediateField.sepDegree_top, IsGaloisGroup.fixedPoints_eq_bot, IntermediateField.adjoin_contains_field_as_subfield, IntermediateField.coe_one
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