Documentation Verification Report

Finrank

πŸ“ Source: Mathlib/LinearAlgebra/Dimension/Finrank.lean

Statistics

MetricCount
Definitionsfinrank
1
Theoremsfinrank_eq_of_equiv_equiv, finrank_self, finrank_eq, finrank_map_eq, finrank_range_of_inj, finrank_eq_of_rank_eq, finrank_le_finrank_of_rank_le_rank, finrank_le_of_rank_le, finrank_lt_of_rank_lt, finrank_subsingleton, lt_rank_of_lt_finrank, one_lt_rank_of_one_lt_finrank, rank_eq_ofNat_iff_finrank_eq_ofNat, rank_eq_one_iff_finrank_eq_one, finrank_map_subtype_eq, finrank_top
16
Total17

Algebra

Theorems

NameKindAssumesProvesValidatesDepends On
finrank_eq_of_equiv_equiv πŸ“–mathematicalRingHom.comp
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
algebraMap
RingEquiv.toRingHom
Module.finrank
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
toModule
β€”Cardinal.toNat_lift
lift_rank_eq_of_equiv_equiv

CommSemiring

Theorems

NameKindAssumesProvesValidatesDepends On
finrank_self πŸ“–mathematicalβ€”Module.finrank
toSemiring
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Semiring.toModule
β€”Module.finrank_eq_of_rank_eq
rank_self

LinearEquiv

Theorems

NameKindAssumesProvesValidatesDepends On
finrank_eq πŸ“–mathematicalβ€”Module.finrankβ€”RingHomInvPair.ids
Cardinal.toNat_lift
lift_rank_eq
finrank_map_eq πŸ“–mathematicalβ€”Module.finrank
Submodule
SetLike.instMembership
Submodule.setLike
Submodule.map
RingHom.id
Semiring.toNonAssocSemiring
RingHomSurjective.ids
toLinearMap
RingHomInvPair.ids
Submodule.addCommMonoid
Submodule.module
β€”RingHomInvPair.ids
RingHomSurjective.invPair
finrank_eq

LinearMap

Theorems

NameKindAssumesProvesValidatesDepends On
finrank_range_of_inj πŸ“–mathematicalDFunLike.coe
LinearMap
RingHom.id
Semiring.toNonAssocSemiring
instFunLike
Module.finrank
Submodule
SetLike.instMembership
Submodule.setLike
range
RingHomSurjective.ids
Submodule.addCommMonoid
Submodule.module
β€”RingHomSurjective.ids
RingHomSurjective.invPair
RingHomInvPair.ids
LinearEquiv.finrank_eq

Module

Definitions

NameCategoryTheorems
finrank πŸ“–CompOp
536 mathmath: MeasureTheory.Measure.integral_comp_inv_smul, Submodule.finrank_sup_add_finrank_inf_eq, IsIntegralClosure.rank, finrank_span_finset_eq_card, finrank_span_set_eq_card, finrank_of_isPerfPair, FixedPoints.finrank_eq_card, Real.dimH_of_mem_nhds, NumberField.Units.finrank_eq_rank, Submodule.finrank_add_finrank_le_of_disjoint, NumberField.InfinitePlace.sum_mult_eq, End.exists_ker_pow_eq_ker_pow_succ, Ideal.finrank_eq_finrank, IntermediateField.adjoin.finrank, IsLocalRing.finrank_CotangentSpace_eq_one_iff, finrank_real_complex_fact', RootPairing.finrank_corootSpan_eq', IsGalois.card_aut_eq_finrank, finrank_eq_zero_of_not_exists_basis_finset, Algebra.normalizedTrace_eq_of_finiteDimensional, NumberField.norm_norm_le_norm_mul_house_pow, CategoryTheory.finrank_hom_simple_simple_le_one, finrank_quotient_span_eq_natDegree_norm, CommSemiring.finrank_self, Quaternion.finrank_eq_four, rankAtStalk_eq, finrank_vectorSpan_image_finset_le, Ideal.ramificationIdx_le_finrank, LieAlgebra.finrank_engel, Subalgebra.finrank_sup_eq_finrank_right_mul_finrank_of_free, LieModule.traceForm_eq_sum_finrank_nsmul', GaussianFourier.integral_cexp_neg_mul_sq_norm, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, LinearMap.det_zero, IntermediateField.relfinrank_mul_finrank_top, IsLocalRing.finrank_cotangentSpace_eq_zero, SpecialLinearGroup.mem_center_iff_spec, IsLocalRing.finrank_quotient_map, IsAdjoinRootMonic.finrank, CategoryTheory.finrank_hom_simple_simple_eq_one_iff, fourierIntegral_gaussian_innerProductSpace', RootPairing.finrank_range_polarization_eq_finrank_span_coroot, IsPurelyInseparable.finInsepDegree_eq, finrank_eq_one_iff, MeasureTheory.isAddHaarMeasure_hausdorffMeasure, Subfield.relfinrank_mul_finrank_top, finrank_vectorSpan_le_iff_not_affineIndependent, SpecialLinearGroup.mem_center_iff, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, Ideal.inertiaDeg_algebraMap, IsGalois.card_fixingSubgroup_eq_finrank, Subfield.relfinrank_eq_finrank_of_le, NumberField.natAbs_discr_eq_natAbs_discr_pow_mul_natAbs_discr_pow, NumberField.abs_discr_ge', Field.finSepDegree_mul_finInsepDegree, IsPurelyInseparable.finrank_eq_pow, Submodule.finrank_quotient_add_finrank, finrank_quotient_span_eq_natDegree', LinearMap.charpoly_nilpotent_tfae, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, MeasureTheory.Measure.toSphere_real_apply_univ, LieModule.trace_toEnd_genWeightSpace, MeasureTheory.Measure.addHaar_ball_of_pos, finrank_zero_iff_forall_zero, MeasureTheory.Measure.addHaar_preimage_smul, QuadraticForm.equivalent_signType_weighted_sum_squared, finrank_top_le_finrank_of_isScalarTower_of_free, End.maxGenEigenspace_eq_genEigenspace_finrank, finrank_algHom, FiniteField.orderOf_frobeniusAlgEquivOfAlgebraic, fourier_gaussian_innerProductSpace, NumberField.IsTotallyComplex.finrank, MeasureTheory.measure_lt_one_eq_integral_div_gamma, SpecialLinearGroup.centerCongr_toLin_equiv_trans_centerEquivRootsOfUnity_eq, NumberField.IsTotallyReal.finrank, Algebra.trace_algebraMap, RootPairing.finrank_rootSpan_map_polarization_eq_finrank_corootSpan, Euclidean.closedBall_eq_image, LieModule.rank_le_finrank, QuadraticForm.equivalent_one_neg_one_weighted_sum_squared, AffineIndependent.finrank_vectorSpan_add_one, Projectivization.finrank_submodule, MeasureTheory.Measure.addHaar_ball_mul, Submodule.finrank_add_inf_finrank_orthogonal, Subspace.finrank_dualCoannihilator_eq, EuclideanSpace.instFactEqNatFinrankFin, finrank_top_le_finrank_of_isScalarTower, RootPairing.finrank_corootSpanIn_int, Real.dimH_univ_eq_finrank, ContDiffBump.measure_closedBall_div_le_integral, ZLattice.rank, MulOpposite.finrank, AffineIndependent.card_le_finrank_succ, Coplanar.finrank_le_two, Algebra.Generators.exists_presentation_of_free_cotangent, Affine.Simplex.finrank_direction_altitude, FiniteDimensional.nonempty_continuousLinearEquiv_iff_finrank_eq, PowerBasis.finrank, Algebra.discr_powerBasis_eq_norm, MeasureTheory.Measure.integral_comp_smul_of_nonneg, IsPrimitiveRoot.norm_eq_neg_one_pow, IntermediateField.relfinrank_top_right, Submodule.finrank_lt_finrank_of_lt, Ideal.finrank_quotient_eq_sum, GradedObject.finrankSupport_subset_iff, FiniteField.algebraMap_trace_eq_sum_pow, IntermediateField.finSepDegree_adjoin_simple_eq_finrank_iff, Representation.IsIrreducible.finrank_eq_one_of_isMulCommutative, finrank_vectorSpan_insert_le, ContDiffBump.normed_le_div_measure_closedBall_rOut, LinearMap.trace_one, FiniteField.instIsScalarTowerZModExtension, RootPairing.finrank_rootSpanIn_int, NumberField.mixedEmbedding.exists_ne_zero_mem_ringOfIntegers_of_norm_le, Ideal.sum_ramification_inertia, minpoly.degree_le, Ideal.card_primesOverFinset_le_finrank, IsLocalRing.finrank_CotangentSpace_eq_one, Matrix.cRank_toNat_eq_finrank, IsLocalRing.finrank_cotangentSpace_eq_zero_iff, Subfield.finrank_comap, Subalgebra.finrank_toSubmodule, GaloisField.finrank, LinearMap.finrank_range_of_inj, IntermediateField.relfinrank_dvd_finrank_bot, fourier_gaussian_innerProductSpace', NumberField.Units.finrank_mul_regOfFamily_eq_det, finrank_span_le_card, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, Real.tendsto_integral_gaussian_smul', FixedPoints.finrank_le_card, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, AlgEquiv.card_le, collinear_iff_finrank_le_one, finrank_quotient_span_eq_natDegree, MeasureTheory.Measure.toSphere_apply_univ, MeasureTheory.Measure.integral_comp_smul, finrank_eq_card_basis', exteriorPower.finrank_eq, LinearMap.finrank_genEigenspace_le, IsNilpotent.charpoly_eq_X_pow_finrank, Submodule.finiteQuotient_iff, IntermediateField.finrank_eq_one_iff, exists_mem_interior_convexHull_affineBasis, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, IntermediateField.finrank_lt_of_gt, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, FDRep.average_char_eq_finrank_invariants, CategoryTheory.finrank_endomorphism_eq_one, finrank_linearMap, IsBaseChange.finrank_eq, Subalgebra.finrank_right_dvd_finrank_sup_of_free, NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_pow, IsCyclotomicExtension.finrank, RootPairing.finrank_corootSpanIn, LinearMap.charpoly_eq_X_pow_iff, FiniteField.pow_finrank_eq_natCard, Ideal.finrank_prime_pow_ramificationIdx, Submodule.finrank_strictMono, Submodule.linearEquiv_det_reflection, RingOfIntegers.norm_algebraMap, NumberField.Units.rank_modTorsion, Matrix.rank_eq_finrank_range_toLin, iSupIndep.subtype_ne_bot_le_finrank, Matrix.eRank_toNat_eq_finrank, finrank_le_of_rank_le, End.maxUnifEigenspaceIndex_le_finrank, affineIndependent_iff_not_finrank_vectorSpan_le, FiniteField.finrank_zmod_extension, QuadraticForm.equivalent_one_zero_neg_one_weighted_sum_squared, finrank_of_isLocalizedModule_of_free, IntermediateField.LinearDisjoint.finrank_right_eq_finrank, QuadraticForm.equivalent_weightedSumSquares, trace_eq_finrank_mul_minpoly_nextCoeff, InnerProductSpace.volume_ball, Algebra.IsQuadraticExtension.finrank_eq_two', NumberField.InfinitePlace.even_finrank_of_not_isUnramifiedIn, Submodule.finrank_orthogonal_span_singleton, Algebra.normalizedTrace_eq_of_fininteDimensional, Submodule.one_le_finrank_iff, LinearMap.BilinForm.exists_orthogonal_basis, IntermediateField.finrank_eq_fixingSubgroup_index, MvPolynomial.finrank_R, FiniteField.algebraMap_norm_eq_prod_pow, trace_eq_trace_adjoin, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, NumberField.Embeddings.card, card_eq_pow_finrank, FinitePresentation.exists_free_localizedModule_powers, IsGalois.IntermediateField.AdjoinSimple.card_aut_eq_finrank, finrank_pi, NumberField.InfinitePlace.card_isUnramified, SpecialLinearGroup.centerEquivRootsOfUnity_symm_apply, Subspace.dual_finrank_eq, sum_embeddings_eq_finrank_mul, rankAtStalk_eq_finrank_tensorProduct, finrank_euclideanSpace, IntermediateField.finrank_top, finrank_le_finrank_of_rank_le_rank, LinearEquiv.mem_dilatransvections_iff_finrank, Matrix.rank_eq_finrank_span_row, LinearEquiv.finrank_eq, MeasureTheory.Measure.addHaar_real_closedBall', NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, IntermediateField.LinearDisjoint.finrank_left_eq_finrank, finrank_of_isSplittingField_X_pow_sub_C, Subalgebra.finrank_left_dvd_finrank_sup_of_free, ModN.natCard_eq, Subfield.relfinrank_top_right, Ideal.relNorm_algebraMap', finrank_bot_le_finrank_of_isScalarTower_of_free, CategoryTheory.finrank_hom_simple_simple_eq_zero_iff, RCLike.finrank_le_two, CategoryTheory.finrank_hom_simple_simple_eq_zero_of_not_iso, NumberField.InfinitePlace.card_isUnramified_compl, IntermediateField.finrank_eq_finrank_subalgebra, finrank_subsingleton, IntermediateField.finrank_eq_one_iff_eq_top, AffineIndependent.finrank_vectorSpan_image_finset, finrank_eq_card_basis, IntermediateField.LinearDisjoint.finrank_sup, IntermediateField.finrank_adjoin_eq_one_iff, NumberField.RingOfIntegers.rank, FiniteDimensional.nonempty_linearEquiv_iff_finrank_eq, Field.finSepDegree_le_finrank, IntermediateField.finrank_bot, Real.dimH_of_nonempty_interior, LieModule.trace_comp_toEnd_genWeightSpace_eq, AlgHom.natCard_of_splits, Submodule.finrank_map_le, finrank_span_eq_card, tfae_of_isNoetherianRing_of_isLocalRing_of_isDomain, trace_eq_sum_roots, natCard_eq_pow_finrank, Submodule.finrank_eq_zero, LinearMap.trace_id, MeasureTheory.Measure.toSphere_apply', Submodule.exists_fun_fin_finrank_span_eq, Algebra.norm_eq_norm_adjoin, affineIndependent_iff_le_finrank_vectorSpan, Field.finSepDegree_eq_finrank_of_isSeparable, LinearMap.finrank_range_le, finrank_eq_zero_iff_of_free, Ideal.relNorm_algebraMap, finrank_eq_zero_of_not_exists_basis, Ideal.finrank_quotient_map, NumberField.mixedEmbedding.norm_smul, IntermediateField.finrank_sup_le, Algebra.finrank_eq_of_equiv_equiv, finrank_matrix, MeasureTheory.integral_fun_norm_addHaar, IsSimpleModule.finrank_eq_one_of_isMulCommutative, Submodule.IsLattice.finrank_of_pi, Subalgebra.finrank_sup_eq_finrank_left_mul_finrank_of_free, IntermediateField.finrank_bot_mul_relfinrank, RootPairing.ncard_eq_finrank_of_linearIndepOn_of, finrank_eq_rank, Subalgebra.finrank_sup_le_of_free, QuadraticForm.equivalent_sum_squares, IntermediateField.bot_eq_top_iff_finrank_eq_one, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, finrank_eq_zero_of_basis_imp_not_finite, Submodule.finrank_eq_rank, Subspace.finrank_add_finrank_dualCoannihilator_eq, LinearIndependent.finrank_eq_zero_of_infinite, finrank_bot_le_finrank_of_isScalarTower, fourierIntegral_gaussian_innerProductSpace, LinearMap.isNilpotent_iff_charpoly, HomologicalComplex.eulerChar_eq_sum_finSet_of_finrankSupport_subset, Submodule.det_reflection, NumberField.mixedEmbedding.exists_ne_zero_mem_ideal_of_norm_le, IntermediateField.finSepDegree_adjoin_simple_le_finrank, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, LieModule.traceForm_eq_sum_finrank_nsmul, Invertible.finrank_eq_one, Algebra.IsAlgebraic.finrank_of_isFractionRing, Subalgebra.bot_eq_top_iff_finrank_eq_one, NumberField.fractionalIdeal_rank, IsLocalRing.finrank_cotangentSpace_le_one_iff, finrank_fin_fun, Real.Convex.dimH_eq_finrank_vectorSpan, LinearMap.det_eq_sign_charpoly_coeff, finrank_eq_one_iff', CategoryTheory.finrank_hom_simple_simple, SpecialLinearGroup.centerEquivRootsOfUnity_apply, Field.Algebra.IsSeparable.finSepDegree_eq, IntermediateField.finrank_top', Algebra.IsQuadraticExtension.finrank_eq_two, finrank_tensorProduct, finrank_top, ZLattice.covolume.tendsto_card_div_pow', FDRep.char_one, mk_finrank_eq_card_basis, isSimpleModule_iff_finrank_eq_one, finrank_pi_fintype, finrank_eq_card_chooseBasisIndex, NumberField.InfinitePlace.even_finrank_of_not_isUnramified, LinearMap.finrank_maxGenEigenspace, IntermediateField.relfinrank_bot_left, IsBaseChange.finrank_eq_of_le_nonZeroDivisors, Euclidean.closedBall_eq_preimage, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, AlgHom.card, MeasureTheory.Measure.addHaar_smul_of_nonneg, Subalgebra.LinearDisjoint.finrank_sup_of_free, FDRep.simple_iff_end_is_rank_one, MeasureTheory.Measure.map_addHaar_smul, Field.primitive_element_iff_minpoly_degree_eq, QuaternionAlgebra.finrank_eq_four, MvPolynomial.finrank_eq_zero, finrank_eq_nat_card_basis, finrank_pos_iff, AffineIndependent.finrank_vectorSpan, Ideal.ramificationIdx_mul_inertiaDeg_of_isLocalRing, AlgHom.card_le, LinearMap.finrank_range_dualMap_eq_finrank_range, MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, NumberField.Embeddings.coeff_bdd_of_norm_le, finrank_le_one, AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_one, Ideal.Factors.finrank_pow_ramificationIdx, NumberField.exists_ideal_in_class_of_norm_le, LinearMap.BilinForm.finrank_orthogonal, LinearIndependent.fintype_card_le_finrank, IntermediateField.finrank_fixedField_eq_card, IntermediateField.finrank_comap, FiniteField.pow_finrank_eq_card, Field.primitive_element_iff_minpoly_natDegree_eq, Euclidean.ball_eq_preimage, finrank_mul_finrank, finrank_real_of_complex, LinearMap.det_smul, AffineBasis.card_eq_finrank_add_one, IntermediateField.relfinrank_eq_finrank_of_le, Submodule.exists_finset_span_eq_linearIndepOn, Submodule.finrank_span_eq_finrank_span, Algebra.normalizedTrace_eq_of_finiteDimensional_apply, LieAlgebra.rank_le_finrank_engel, Submodule.finrank_map_subtype_eq, MeasureTheory.Measure.addHaar_ball_mul_of_pos, LinearMap.charpoly_one, Algebra.normalizedTrace_def, ExistsContDiffBumpBase.w_def, FiniteField.minpoly_frobeniusAlgHom, MeasureTheory.Measure.setIntegral_comp_smul, NumberField.exists_ne_zero_mem_ringOfIntegers_of_norm_le_mul_sqrt_discr, finrank_pos_iff_exists_ne_zero, rank_eq_ofNat_iff_finrank_eq_ofNat, finrank_le_of_span_eq_top, finrank_eq_of_rank_eq, Submodule.finrank_mono, IntermediateField.exists_lt_finrank_of_infinite_dimensional, MeasureTheory.Measure.addHaar_nnreal_smul, NumberField.mixedEmbedding.logMap_apply, Submodule.finrank_add_le_finrank_add_finrank, End.generalized_eigenvec_disjoint_range_ker, strongRankCondition_iff_forall_zero_lt_finrank, IsDiscreteValuationRing.TFAE, Submodule.finrank_le_one_iff_isPrincipal, Subfield.relfinrank_dvd_finrank_top_of_le, LinearIndependent.finset_card_le_finrank, Submodule.finrank_span_eq_finrank, Collinear.finrank_le_one, Complex.finrank_real_complex, Ideal.inertiaDeg_bot, QuadraticForm.equivalent_sign_ne_zero_weighted_sum_squared, rank_eq_one_iff_finrank_eq_one, LieAlgebra.rank_le_finrank, LinearMap.IsProj.trace, finrank_directSum, Complex.finrank_real_complex_fact, IntermediateField.relfinrank_dvd_finrank_top_of_le, Field.finSepDegree_dvd_finrank, Besicovitch.card_le_of_separated, finrank_of_not_finite, Ideal.card_stabilizer_eq_card_inertia_mul_finrank, NumberField.abs_discr_ge_of_isTotallyComplex, FiniteField.bijective_frobeniusAlgHom_pow, IsGalois.of_separable_splitting_field_aux, LieModule.traceForm_genWeightSpace_eq, LieAlgebra.IsKilling.finrank_rootSpace_eq_one, IntermediateField.finrank_le_of_le_left, RatFunc.finrank_ratFunc_ratFunc, LieModule.zero_lt_finrank_genWeightSpace, IsCyclotomicExtension.Rat.map_eq_span_zeta_sub_one_pow, finrank_ulift, IsCyclotomicExtension.Rat.finrank, finrank_eq_rank', LinearMap.charpoly_natDegree, IsLocalizedModule.finrank_eq, LinearIsometryEquiv.reflections_generate_dim, IntermediateField.finrank_bot', finrank_linearMap_self, finrank_of_infinite_dimensional, Submodule.finrank_add_finrank_orthogonal, NumberField.mixedEmbedding.finrank, IsUnramifiedAtInfinitePlaces.card_infinitePlace, finrank_eq_one, minpoly.natDegree_le, Algebra.norm_eq_prod_roots, finrank_span_singleton, subalgebra_top_finrank_eq_submodule_top_finrank, Field.finSepDegree_eq_finrank_iff, LinearMap.finrank_maxGenEigenspace_zero_eq, RootPairing.finrank_corootSpan_eq, finrank_eq_zero_of_not_exists_basis_finite, QuadraticAlgebra.finrank_eq_two, finrank_finsupp_self, MeasureTheory.Measure.addHaar_closedBall, Real.tendsto_integral_gaussian_smul, NumberField.Units.unitLattice_rank, Submodule.finrank_le, finrank_self, FiniteField.bijective_frobeniusAlgEquivOfAlgebraic_pow, length_eq_finrank, FiniteField.nonempty_algHom_iff_finrank_dvd, ContDiff.dimH_range_le, Algebra.discr_powerBasis_eq_prod'', Dual.finrank_ker_add_one_of_ne_zero, NumberField.mixedEmbedding.norm_real, affineIndependent_iff_finrank_vectorSpan_eq, RootPairing.finrank_rootSpanIn, LieModule.traceForm_eq_sum_finrank_nsmul_mul, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, Besicovitch.multiplicity_le, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, LinearMap.finrank_eq_of_isPerfPair, NumberField.InfinitePlace.card_add_two_mul_card_eq_rank, InnerProductSpace.volume_closedBall, SpecialLinearGroup.centerEquivRootsOfUnity_apply_apply, Ideal.inertiaDeg_le_finrank, finrank_pos_iff_of_free, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, Ideal.ncard_primesOver_mul_card_inertia_mul_finrank, finrank_eq_one_iff_of_nonzero, End.ker_pow_le_ker_pow_finrank, LieAlgebra.isRegular_iff_finrank_engel_eq_rank, NumberField.mixedEmbedding.euclidean.finrank, CategoryTheory.finrank_endomorphism_simple_eq_one, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, finrank_eq_zero_of_rank_eq_zero, card_algHom_le_finrank, MeasureTheory.Measure.addHaar_closedBall_mul, finrank_eq_card_finset_basis, finrank_fintype_fun_eq_card, NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discr, LinearMap.charpoly_zero, Algebra.norm_algebraMap, finrank_prod, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, IsGaloisGroup.card_eq_finrank, finrank_vectorSpan_range_add_one_le, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, MeasureTheory.Measure.addHaar_ball, cardinalMk_algHom, IsGalois.tfae, LinearEquiv.finrank_map_eq, finrank_bot, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_natDegree, Algebra.normalizedTrace_eq_of_fininteDimensional_apply, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, LinearMap.polyCharpoly_natDegree, LinearMap.finrank_maxGenEigenspace_eq, Submodule.finrank_lt, minpoly.degree_dvd, NumberField.Units.finrank_mul_regulator_eq_det, IsPrimitiveRoot.lcm_totient_le_finrank, coplanar_iff_finrank_le_two, Submodule.finrank_quotient_le, GradedObject.eulerChar_eq_sum_finSet_of_finrankSupport_subset, length_of_free_of_finite, finrank_eq_zero_of_basis_imp_false, FiniteField.orderOf_frobeniusAlgHom, End.genEigenspace_le_genEigenspace_finrank, LinearMap.BilinForm.finrank_add_finrank_orthogonal, Submodule.finrank_quotient, IsGaloisGroup.card_fixingSubgroup_eq_finrank, IsGaloisGroup.finrank_fixedPoints_eq_card_subgroup, AlgHom.card_of_splits, Ideal.absNorm_algebraMap, Subalgebra.finrank_bot, MvPolynomial.finrank_eq_one, NumberField.mixedEmbedding.convexBodySum_volume, LinearMap.nilRank_le_finrank, MeasureTheory.integrable_fun_norm_addHaar, LinearMap.finrank_le_finrank_of_injective, FDRep.scalar_product_char_eq_finrank_equivariant, NumberField.hermiteTheorem.rank_le_rankOfDiscrBdd, finrank_lt_of_rank_lt, MeasureTheory.measure_unitBall_eq_integral_div_gamma, LinearMap.finrank_range_add_finrank_ker, finrank_eq_one_iff_of_nonzero', IntermediateField.finrank_dvd_of_le_right, finrank_baseChange, Submodule.finrank_add_eq_of_isCompl, IntermediateField.finrank_le_of_le_right, Polynomial.Gal.card_of_separable, finrank_eq_zero_iff_isTorsion, IntermediateField.finrank_dvd_of_le_left, Algebra.prod_embeddings_eq_finrank_pow, Matrix.rank_eq_finrank_span_cols, FiniteField.algebraMap_norm_eq_pow_sum, IntermediateField.finrank_adjoin_simple_eq_one_iff, finrank_euclideanSpace_fin, LinearMap.finrank_eigenspace_le, finrank_pos, finrank_quotient_add_finrank_le, End.pos_finrank_genEigenspace_of_hasEigenvalue, finrank_eq_zero_iff, HomologicalComplex.homologyEulerChar_eq_sum_finSet_of_finrankSupport_subset, finrank_le_one_iff, EuclideanGeometry.Sphere.finrank_orthRadius, finrank_vectorSpan_insert_le_set, MeasureTheory.Measure.toSphere_apply_univ', Subspace.finrank_add_finrank_dualAnnihilator_eq, PeriodPair.finrank_lattice, LinearMap.finrank_le_of_isSMulRegular, Subalgebra.finrank_eq_one_iff, FiniteField.finrank_extension, finrank_finsupp, MeasureTheory.Measure.addHaar_closedBall', finrank_vectorSpan_range_le, finrank_zero_of_subsingleton, iSupIndep.subtype_ne_bot_le_finrank_aux, ZLattice.exists_finsetSum_norm_rpow_le_tsum, rankAtStalk_eq_finrank_of_free, GaussianFourier.integral_rexp_neg_mul_sq_norm, LinearIndependent.cardinalMk_le_finrank, MeasureTheory.Measure.addHaar_real_closedBall, finrank_le_one_iff_top_isPrincipal, QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate', FDRep.finrank_hom_simple_simple, MeasureTheory.Measure.addHaar_smul, finrank_zero_iff, MeasureTheory.Measure.addHaar_image_homothety

Theorems

NameKindAssumesProvesValidatesDepends On
finrank_eq_of_rank_eq πŸ“–mathematicalrank
Cardinal
Cardinal.instNatCast
finrankβ€”Cardinal.toNat_natCast
finrank_le_finrank_of_rank_le_rank πŸ“–mathematicalCardinal
Cardinal.instLE
Cardinal.lift
rank
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.aleph0
finrankβ€”Cardinal.toNat_lift
Cardinal.toNat_le_toNat
Cardinal.lift_lt_aleph0
finrank_le_of_rank_le πŸ“–mathematicalCardinal
Cardinal.instLE
rank
Cardinal.instNatCast
finrankβ€”Cardinal.toNat_natCast
Cardinal.toNat_le_iff_le_of_lt_aleph0
LE.le.trans_lt
Cardinal.natCast_lt_aleph0
finrank_lt_of_rank_lt πŸ“–mathematicalCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
rank
Cardinal.instNatCast
finrankβ€”Cardinal.toNat_natCast
Cardinal.toNat_lt_iff_lt_of_lt_aleph0
LT.lt.trans
Cardinal.natCast_lt_aleph0
finrank_subsingleton πŸ“–mathematicalβ€”finrankβ€”finrank.eq_1
rank_subsingleton
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
MonoidWithZeroHom.monoidWithZeroHomClass
lt_rank_of_lt_finrank πŸ“–mathematicalfinrankCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.instNatCast
rank
β€”Cardinal.toNat_lt_iff_lt_of_lt_aleph0
Cardinal.natCast_lt_aleph0
Mathlib.Tactic.Contrapose.contrapose₁
finrank.eq_1
Cardinal.toNat_apply_of_aleph0_le
Cardinal.toNat_natCast
one_lt_rank_of_one_lt_finrank πŸ“–mathematicalfinrankCardinal
Preorder.toLT
PartialOrder.toPreorder
Cardinal.partialOrder
Cardinal.instOne
rank
β€”Nat.cast_one
lt_rank_of_lt_finrank
rank_eq_ofNat_iff_finrank_eq_ofNat πŸ“–mathematicalβ€”rank
Cardinal
instOfNatAtLeastTwo
Cardinal.instNatCast
finrank
β€”Cardinal.toNat_eq_ofNat
rank_eq_one_iff_finrank_eq_one πŸ“–mathematicalβ€”rank
Cardinal
Cardinal.instOne
finrank
β€”Cardinal.toNat_eq_one

Submodule

Theorems

NameKindAssumesProvesValidatesDepends On
finrank_map_subtype_eq πŸ“–mathematicalβ€”Module.finrank
Submodule
SetLike.instMembership
setLike
map
addCommMonoid
module
RingHom.id
Semiring.toNonAssocSemiring
RingHomSurjective.ids
subtype
β€”LinearEquiv.finrank_eq
RingHomSurjective.ids
RingHomInvPair.ids

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
finrank_top πŸ“–mathematicalβ€”Module.finrank
Submodule
SetLike.instMembership
Submodule.setLike
Top.top
Submodule.instTop
Submodule.addCommMonoid
Submodule.module
β€”rank_top

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