Documentation Verification Report

Support

📁 Source: Mathlib/Algebra/Notation/Support.lean

Statistics

MetricCount
DefinitionsmulSupport, support
2
Theoremscompl_mulSupport, compl_support, disjoint_mulSupport_iff, disjoint_support_iff, ext_iff_mulSupport, ext_iff_support, mem_mulSupport, mem_support, mulSupport_along_fiber_subset, mulSupport_binop_subset, mulSupport_comp_eq, mulSupport_comp_eq_of_range_subset, mulSupport_comp_eq_preimage, mulSupport_comp_subset, mulSupport_const, mulSupport_curry, mulSupport_disjoint_iff, mulSupport_eq_empty_iff, mulSupport_eq_iff, mulSupport_eq_preimage, mulSupport_eq_univ, mulSupport_extend_one, mulSupport_extend_one_subset, mulSupport_fun_curry, mulSupport_fun_one, mulSupport_nonempty_iff, mulSupport_one, mulSupport_prodMk, mulSupport_prodMk', mulSupport_subset_comp, mulSupport_subset_iff, mulSupport_subset_iff', mulSupport_update_eq_ite, mulSupport_update_of_ne_one, mulSupport_update_one, notMem_mulSupport, notMem_support, range_eq_image_or_of_mulSupport_subset, range_eq_image_or_of_support_subset, range_subset_insert_image_mulSupport, range_subset_insert_image_support, support_along_fiber_subset, support_binop_subset, support_comp_eq, support_comp_eq_of_range_subset, support_comp_eq_preimage, support_comp_subset, support_const, support_curry, support_disjoint_iff, support_eq_empty_iff, support_eq_iff, support_eq_preimage, support_eq_univ, support_extend_zero, support_extend_zero_subset, support_fun_curry, support_fun_zero, support_nonempty_iff, support_prodMk, support_prodMk', support_subset_comp, support_subset_iff, support_subset_iff', support_update_eq_ite, support_update_of_ne_zero, support_update_zero, support_zero, mulSupport_mulSingle, mulSupport_mulSingle_disjoint, mulSupport_mulSingle_of_ne, mulSupport_mulSingle_one, mulSupport_mulSingle_subset, subsingleton_mulSupport_mulSingle, subsingleton_support_single, support_single, support_single_disjoint, support_single_of_ne, support_single_subset, support_single_zero, image_inter_mulSupport_eq, image_inter_support_eq, mulSupport_eq, support_eq
84
Total86

Function

Definitions

NameCategoryTheorems
mulSupport 📖CompOp
105 mathmath: mulSupport_prodMk, mulSupport_zero, mulSupport_inv, Pi.mulSupport_mulSingle_subset, mulSupport_comp_subset, tprod_subtype_mulSupport, Subsingleton.mulSupport_eq, mulSupport_along_fiber_finite_of_finite, measurableSet_mulSupport, NumberField.FinitePlace.mulSupport_finite, mulSupport_one_sub', mulSupport_comp_inv_smul, subset_mulTSupport, mulSupport_mul_inv, mulSupport_one_sub, mulSupport_comp_eq, mulSupport_one_add', Multipliable.finite_mulSupport_of_discreteTopology, mulSupport_fun_curry, finite_mulSupport_of_finprod_ne_one, mulSupport_subset_comp, hasCompactMulSupport_def, mulSupport_div, Pi.mulSupport_mulSingle_one, Pi.subsingleton_mulSupport_mulSingle, mulSupport_intCast, FactorizedRational.mulSupport, mulSupport_subset_iff', mulSupport_iSup, mem_mulSupport, Pi.mulSupport_mulSingle, mulSupport_pow, mulSupport_update_one, mulSupport_subset_iff, mulSupport_binop_subset, Set.mulIndicator_ae_eq_one, Set.mulIndicator_mulSupport, range_subset_insert_image_mulSupport, mulSupport_add_one', finprod_mem_eq_prod, mulSupport_nonempty_iff, MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_mulSupport, mulSupport_update_of_ne_one, Multipliable.countable_mulSupport, finprod_def', finprod_mem_mulSupport, ext_iff_mulSupport, mulSupport_comp_eq_preimage, NumberField.FinitePlace.mulSupport_finite_int, Height.AdmissibleAbsValues.mulSupport_finite, disjoint_mulSupport_iff, mulSupport_extend_one_subset, mulSupport_comp_eq_of_range_subset, mulSupport_eq_iff, finprod_cond_ne, mulSupport_min, finprod_mem_eq_prod_filter, Ideal.finite_mulSupport_coe, mulSupport_const, mulSupport_disjoint_iff, Ideal.finite_mulSupport, compl_mulSupport, Set.mulIndicator_eq_one', mulSupport_fun_inv, Finset.mulSupport_prod, Set.mulSupport_mulIndicator_subset, MeasureTheory.StronglyMeasurable.measurableSet_mulSupport, mulSupport_iInf, mulSupport_update_eq_ite, Set.mulSupport_mulIndicator, Set.mulIndicator_eq_one, mulSupport_max, Filter.EventuallyEq.mulSupport, Set.image_inter_mulSupport_eq, mulSupport_curry, mulSupport_extend_one, tprod_def, mulSupport_along_fiber_subset, mulSupport_eq_empty_iff, notMem_mulSupport, mulSupport_natCast, finprod_def, Finset.mulSupport_of_fiberwise_prod_subset_image, Set.mulIndicator_eq_self, mulSupport_fun_one, mulSupport_one_add, finprod_mem_inter_mulSupport, Set.mulIndicator_apply_ne_one, mulSupport_one, hasProd_subtype_mulSupport, mulSupport_eq_preimage, mulSupport_eq_univ, mulSupport_prodMk', Pi.mulSupport_mulSingle_disjoint, mulSupport_comp_inv_smul₀, Ideal.finite_mulSupport_inv, Continuous.isOpen_mulSupport, mulSupport_inf, Set.mulIndicator_inter_mulSupport, Pi.mulSupport_mulSingle_of_ne, mulSupport_mul, locallyFinite_mulSupport_iff, mulSupport_add_one, mulSupport_sup, finprod_eq_prod
support 📖CompOp
247 mathmath: Pi.subsingleton_support_single, DirectSum.finite_support, ExistsContDiffBumpBase.u_support, SmoothBumpFunction.support_eq_symm_image, support_mul_subset_right, MeasureTheory.SimpleFunc.measure_support_lt_top_of_integrable, MvPowerSeries.support_expand, support_comp_inv_smul₀, Finsupp.ofSupportFinite_support, SmoothBumpCovering.mem_support_ind, SmoothBumpCovering.IsSubordinate.support_subset, Summable.finite_support_of_discreteTopology, AddSubmonoid.mem_closure_finset, ContDiffBump.support_normed_eq, support_max, MeasureTheory.setLIntegral_pos_iff, support_sub, SmoothPartitionOfUnity.locallyFinite, MeasureTheory.SimpleFunc.measure_support_lt_top_of_memLp, Set.support_indicator, support_smul_subset_left, Summable.countable_support_nnreal, IsOpen.exists_msmooth_support_eq, IsOpen.exists_smooth_support_eq, SmoothPartitionOfUnity.locallyFinite', support_binop_subset, mulSupport_one_sub', Equiv.finsuppUnique_symm_apply_support_val, MeasureTheory.measure_support_eapprox_lt_top, HVertexOperator.coeff_isPWOsupport, support_mul_of_ne_zero_right, BumpCovering.support_toPOUFun_subset, measurableSet_support, ext_iff_support, Set.indicator_support, finsum_def', support_pow, PartitionOfUnity.locallyFinite, Continuous.exists_contDiff_approx_and_eqOn, mulSupport_one_sub, mulSupport_one_add', intervalIntegral.integral_pos_iff_support_of_nonneg_ae', Pi.support_single, Finsupp.fun_support_eq, finsum_mem_eq_sum_filter, support_eq_univ, finsum_mem_support, PowerSeries.support_expand_subset, subset_tsupport, RootPairing.Base.exists_root_eq_sum_nat_or_neg, ProbabilityTheory.support_gaussianPDF, PowerSeries.support_expand, finsum_eq_sum, Finsupp.finite_support, ArithmeticFunction.vonMangoldt.support_residueClass_prime_div, support_mul', MvPowerSeries.lexOrder_def_of_ne_zero, Submodule.mem_span_finset, MeasureTheory.setIntegral_support, range_subset_insert_image_support, PartitionOfUnity.exists_finset_nhds, Pi.support_single_of_ne, IsOpen.exists_contMDiff_support_eq_aux, HahnEmbedding.Partial.isWF_support_evalCoeff, MeasureTheory.SimpleFunc.measure_support_lt_top, Set.indicator_eq_self, support_update_of_ne_zero, SmoothBumpFunction.support_mem_nhds, support_comp_subset, FactorizedRational.mulSupport, Subsingleton.support_eq, PartitionOfUnity.coe_finsupport, Finset.support_of_fiberwise_sum_subset_image, MeasureTheory.AEStronglyMeasurable.nullMeasurableSet_support, AddSubmonoid.mem_closure_iff_exists_finset_subset, support_const_smul_subset, support_intCast, SmoothBumpFunction.support_eq_inter_preimage, finsum_mem_eq_sum, PartitionOfUnity.exists_finset_nhds_support_subset, Set.indicator_inter_support, support_min, Continuous.exists_contMDiff_approx, HahnSeries.SummableFamily.smul_support_subset_prod, ContDiffBumpBase.support, Submodule.mem_span_iff_exists_finset_subset, SmoothBumpCovering.locallyFinite', finite_support_of_finsum_ne_zero, HahnSeries.SummableFamily.smul_support_finite, support_smul, support_smul_subset_right, ExistsContDiffBumpBase.w_support, support_fun_curry, MeasureTheory.integral_pos_iff_support_of_nonneg_ae, support_mul_of_ne_zero_left, Finsupp.equivFunOnFinite_symm_apply_support, mulSupport_add_one', ExistsContDiffBumpBase.u_exists, support_fun_neg, ContDiffBump.support_eq, MeasureTheory.SimpleFunc.support_indicator, HahnSeries.SummableFamily.coeff_support, finsum_cond_ne, BumpCovering.locallyFinite, support_eq_iff, support_prodMk, support_extend_zero_subset, SmoothPartitionOfUnity.mem_finsupport, IsOpen.exists_contMDiff_support_eq, support_iInf, support_mul_subset_left, support_add, SmoothBumpFunction.nhds_basis_support, support_eq_empty_iff, HahnSeries.isPWO_support', LaurentSeries.Cauchy.coeff_support_bddBelow, PMF.support_ofFintype, Continuous.isOpen_support, Pi.support_single_subset, locallyFinsuppWithin.supportWithinDomain', Set.indicator_eq_zero', locallyFinsuppWithin.supportLocallyFiniteWithinDomain', PartitionOfUnity.locallyFinite', Set.indicator_eq_zero, exists_msmooth_support_eq_eq_one_iff, support_nsmul, SmoothPartitionOfUnity.coe_finsupport, support_deriv_subset, support_comp_eq_preimage, support_add_neg, PMF.support_normalize, Set.indicator_ae_eq_zero, Finsupp.ofSupportFinite_fin_two_eq, finsum_def, support_prodMk', notMem_support, support_along_fiber_finite_of_finite, MeasureTheory.integral_pos_iff_support_of_nonneg, SmoothBumpFunction.c_mem_support, support_neg, MvPolynomial.weightedHomogeneousComponent_finsupp, support_fun_zero, PMF.support_ofFinset, MeasureTheory.SimpleFunc.measurableSet_support, Set.support_indicator_subset, Pi.support_single_disjoint, Set.image_inter_support_eq, locallyFinite_support_iff, support_const_smul_of_ne_zero, IsOpen.exists_msmooth_support_eq_aux, support_sup, intervalIntegral.integral_pos_iff_support_of_nonneg_ae, Filter.EventuallyEq.support, support_iSup, support_subset_iff, hasCompactSupport_def, support_inv, Finsupp.finite_vaddAntidiagonal, support_inf, MeromorphicNFOn.zero_set_eq_divisor_support, MeasureTheory.SimpleFunc.measure_support_lt_top_of_lintegral_ne_top, support_curry, support_iteratedFDeriv_subset, support_div', support_disjoint_iff, Continuous.exists_contMDiff_approx_and_eqOn, support_comp_inv_smul, RootPairing.Base.exists_root_eq_sum_int, SmoothBumpCovering.locallyFinite, SmoothBumpFunction.isOpen_support, exists_contMDiff_support_eq_eq_one_iff, Finset.support_prod_subset, AddEquiv.finsuppUnique_symm_apply_support_val, HahnSeries.SummableFamily.sum_vAddAntidiagonal_eq, Submonoid.mem_closure_finset, IsOpen.exists_contDiff_support_eq, support_const, Continuous.exists_contDiff_approx, support_extend_zero, mem_support, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, support_zero, support_comp_eq, support_along_fiber_subset, support_one, MeasureTheory.setIntegral_pos_iff_support_of_nonneg_ae, ExistsContDiffBumpBase.y_support, ContDiffMapSupportedIn.support_subset, PowerSeries.coeff_subst_finite, support_update_eq_ite, MeasureTheory.lintegral_pos_iff_support, support_translate, Summable.countable_support_ennreal, support_subset_comp, HahnSeries.forallLTEqZero_supp_BddBelow, MeasureTheory.Measure.measure_support_eq_zero_iff, DirectSum.support_subset, support_mul, MeasureTheory.support_convolution_subset_swap, compl_support, MvPowerSeries.coeff_subst_finite, MeasureTheory.FinStronglyMeasurable.fin_support_approx, MvPowerSeries.support_expand_subset, ContDiffBump.tendsto_support_normed_smallSets, SmoothBumpFunction.support_subset_source, MeasureTheory.SimpleFunc.support_eq, support_nonempty_iff, support_fderiv_subset, Pi.support_single_zero, BumpCovering.locallyFinite', MeasureTheory.StronglyMeasurable.measurableSet_support, PartitionOfUnity.exists_finset_nhds', mulSupport_one_add, support_conjneg, support_eq_preimage, support_inv', tsum_subtype_support, SmoothBumpFunction.support_updateRIn, PowerSeries.coeff_subst_finite', finite_support_of_finsum_eq_one, Urysohns.CU.disjoint_C_support_lim, MeasureTheory.support_convolution_subset, Finset.support_sum, tsum_def, support_update_zero, finsum_mem_inter_support, support_pow', Submonoid.mem_closure_iff_exists_finset_subset, support_comp_eq_of_range_subset, Finset.support_prod, SmoothBumpFunction.nonempty_support, Finsupp.instCanLift, HahnSeries.SummableFamily.finite_co_support, MeasureTheory.SimpleFunc.finMeasSupp_iff_support, hasSum_subtype_support, disjoint_support_iff, support_div, support_subset_iff', support_natCast, BumpCovering.support_toPartitionOfUnity_subset, HahnSeries.BddBelow_zero, mulSupport_add_one, PartitionOfUnity.mem_finsupport, Finsupp.sym2_support_eq_preimage_support_mul, MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closed, Set.indicator_apply_ne_zero, Summable.countable_support

Theorems

NameKindAssumesProvesValidatesDepends On
compl_mulSupport 📖mathematicalCompl.compl
Set
Set.instCompl
mulSupport
setOf
Set.ext
notMem_mulSupport
compl_support 📖mathematicalCompl.compl
Set
Set.instCompl
support
setOf
Set.ext
notMem_support
disjoint_mulSupport_iff 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
mulSupport
Set.EqOn
Pi.instOne
disjoint_comm
mulSupport_disjoint_iff
disjoint_support_iff 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
support
Set.EqOn
Pi.instZero
disjoint_comm
support_disjoint_iff
ext_iff_mulSupport 📖mathematicalmulSupportnotMem_mulSupport
Set.ext_iff
ext_iff_support 📖mathematicalsupportnotMem_support
Set.ext_iff
mem_mulSupport 📖mathematicalSet
Set.instMembership
mulSupport
mem_support 📖mathematicalSet
Set.instMembership
support
mulSupport_along_fiber_subset 📖mathematicalSet
Set.instHasSubset
mulSupport
Set.image
mulSupport_binop_subset 📖mathematicalSet
Set.instHasSubset
mulSupport
Set.instUnion
not_or_of_imp
mulSupport_comp_eq 📖mathematicalmulSupportSet.ext
mulSupport_comp_eq_of_range_subset 📖mathematicalmulSupportSet.ext
Set.mem_range_self
mulSupport_comp_eq_preimage 📖mathematicalmulSupport
Set.preimage
mulSupport_comp_subset 📖mathematicalSet
Set.instHasSubset
mulSupport
mulSupport_const 📖mathematicalmulSupport
Set.univ
Set.ext
mulSupport_curry 📖mathematicalmulSupport
Pi.instOne
Set.image
mulSupport_disjoint_iff 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
mulSupport
Set.EqOn
Pi.instOne
mulSupport_eq_empty_iff 📖mathematicalmulSupport
Set
Set.instEmptyCollection
Pi.instOne
Set.subset_empty_iff
mulSupport_subset_iff'
mulSupport_eq_iff 📖mathematicalmulSupport
mulSupport_eq_preimage 📖mathematicalmulSupport
Set.preimage
Compl.compl
Set
Set.instCompl
Set.instSingletonSet
mulSupport_eq_univ 📖mathematicalmulSupport
Set.univ
Set.eq_univ_of_forall
mulSupport_extend_one 📖mathematicalmulSupport
extend
Pi.instOne
Set.image
HasSubset.Subset.antisymm
Set.instAntisymmSubset
mulSupport_extend_one_subset
mem_mulSupport
Injective.extend_apply
mulSupport_extend_one_subset 📖mathematicalSet
Set.instHasSubset
mulSupport
extend
Pi.instOne
Set.image
mulSupport_subset_iff'
extend.eq_1
notMem_mulSupport
extend_apply'
mulSupport_fun_curry 📖mathematicalmulSupport
Pi.instOne
Set.image
mulSupport_curry
mulSupport_fun_one 📖mathematicalmulSupport
Set
Set.instEmptyCollection
mulSupport_one
mulSupport_nonempty_iff 📖mathematicalSet.Nonempty
mulSupport
Set.nonempty_iff_ne_empty
mulSupport_eq_empty_iff
mulSupport_one 📖mathematicalmulSupport
Pi.instOne
Set
Set.instEmptyCollection
mulSupport_eq_empty_iff
mulSupport_prodMk 📖mathematicalmulSupport
Prod.instOne
Set
Set.instUnion
Set.ext
mulSupport_prodMk' 📖mathematicalmulSupport
Prod.instOne
Set
Set.instUnion
mulSupport_subset_comp 📖mathematicalSet
Set.instHasSubset
mulSupport
mulSupport_subset_iff 📖mathematicalSet
Set.instHasSubset
mulSupport
Set.instMembership
mulSupport_subset_iff' 📖mathematicalSet
Set.instHasSubset
mulSupport
not_imp_comm
mulSupport_update_eq_ite 📖mathematicalmulSupport
update
Set
Set.instSDiff
Set.instSingletonSet
Set.instInsert
eq_or_ne
mulSupport_update_one
mulSupport_update_of_ne_one
mulSupport_update_of_ne_one 📖mathematicalmulSupport
update
Set
Set.instInsert
Set.ext
eq_or_ne
update_self
update_of_ne
mulSupport_update_one 📖mathematicalmulSupport
update
Set
Set.instSDiff
Set.instSingletonSet
Set.ext
eq_or_ne
update_self
update_of_ne
notMem_mulSupport 📖mathematicalSet
Set.instMembership
mulSupport
notMem_support 📖mathematicalSet
Set.instMembership
support
range_eq_image_or_of_mulSupport_subset 📖mathematicalSet
Set.instHasSubset
mulSupport
Set.range
Set.image
Set.instInsert
HasSubset.Subset.trans
Set.instIsTransSubset
range_subset_insert_image_mulSupport
Set.insert_subset_insert
Set.image_mono
range_eq_image_or_of_support_subset 📖mathematicalSet
Set.instHasSubset
support
Set.range
Set.image
Set.instInsert
HasSubset.Subset.trans
Set.instIsTransSubset
range_subset_insert_image_support
Set.insert_subset_insert
Set.image_mono
range_subset_insert_image_mulSupport 📖mathematicalSet
Set.instHasSubset
Set.range
Set.instInsert
Set.image
mulSupport
Set.mem_image_of_mem
range_subset_insert_image_support 📖mathematicalSet
Set.instHasSubset
Set.range
Set.instInsert
Set.image
support
Set.range_subset_iff
Set.mem_insert_iff
Set.mem_image_of_mem
support_along_fiber_subset 📖mathematicalSet
Set.instHasSubset
support
Set.image
mem_support
support_binop_subset 📖mathematicalSet
Set.instHasSubset
support
Set.instUnion
not_or_of_imp
support_comp_eq 📖mathematicalsupportSet.ext
support_comp_eq_of_range_subset 📖mathematicalsupportSet.ext
Set.mem_range_self
support_comp_eq_preimage 📖mathematicalsupport
Set.preimage
support_comp_subset 📖mathematicalSet
Set.instHasSubset
support
support_const 📖mathematicalsupport
Set.univ
Set.ext
mem_support
Set.mem_univ
support_curry 📖mathematicalsupport
Pi.instZero
Set.image
support_disjoint_iff 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
support
Set.EqOn
Pi.instZero
Set.subset_compl_iff_disjoint_right
support_subset_iff'
Set.notMem_compl_iff
support_eq_empty_iff 📖mathematicalsupport
Set
Set.instEmptyCollection
Pi.instZero
Set.subset_empty_iff
support_subset_iff'
Set.mem_empty_iff_false
support_eq_iff 📖mathematicalsupportSet.ext_iff
mem_support
not_imp_comm
support_eq_preimage 📖mathematicalsupport
Set.preimage
Compl.compl
Set
Set.instCompl
Set.instSingletonSet
support_eq_univ 📖mathematicalsupport
Set.univ
Set.eq_univ_of_forall
support_extend_zero 📖mathematicalsupport
extend
Pi.instZero
Set.image
HasSubset.Subset.antisymm
Set.instAntisymmSubset
support_extend_zero_subset
mem_support
Injective.extend_apply
support_extend_zero_subset 📖mathematicalSet
Set.instHasSubset
support
extend
Pi.instZero
Set.image
support_subset_iff'
extend.eq_1
notMem_support
extend_apply'
support_fun_curry 📖mathematicalsupport
Pi.instZero
Set.image
support_curry
support_fun_zero 📖mathematicalsupport
Set
Set.instEmptyCollection
support_zero
support_nonempty_iff 📖mathematicalSet.Nonempty
support
Set.nonempty_iff_ne_empty
support_eq_empty_iff
support_prodMk 📖mathematicalsupport
Prod.instZero
Set
Set.instUnion
Set.ext
Prod.mk_eq_zero
not_and_or
Set.mem_union
support_prodMk' 📖mathematicalsupport
Prod.instZero
Set
Set.instUnion
support_prodMk
support_subset_comp 📖mathematicalSet
Set.instHasSubset
support
support_subset_iff 📖mathematicalSet
Set.instHasSubset
support
Set.instMembership
support_subset_iff' 📖mathematicalSet
Set.instHasSubset
support
not_imp_comm
support_update_eq_ite 📖mathematicalsupport
update
Set
Set.instSDiff
Set.instSingletonSet
Set.instInsert
eq_or_ne
support_update_zero
support_update_of_ne_zero
support_update_of_ne_zero 📖mathematicalsupport
update
Set
Set.instInsert
Set.ext
eq_or_ne
mem_support
update_self
Set.mem_insert_iff
update_of_ne
support_update_zero 📖mathematicalsupport
update
Set
Set.instSDiff
Set.instSingletonSet
Set.ext
eq_or_ne
mem_support
update_self
Set.mem_diff
Set.mem_singleton_iff
update_of_ne
support_zero 📖mathematicalsupport
Pi.instZero
Set
Set.instEmptyCollection
support_eq_empty_iff

Pi

Theorems

NameKindAssumesProvesValidatesDepends On
mulSupport_mulSingle 📖mathematicalFunction.mulSupport
mulSingle
Set
Set.instEmptyCollection
Set.instSingletonSet
mulSingle_one
Function.mulSupport_one
mulSupport_mulSingle_of_ne
mulSupport_mulSingle_disjoint 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
Function.mulSupport
mulSingle
mulSupport_mulSingle_of_ne
Set.disjoint_singleton
mulSupport_mulSingle_of_ne 📖mathematicalFunction.mulSupport
mulSingle
Set
Set.instSingletonSet
HasSubset.Subset.antisymm
Set.instAntisymmSubset
mulSupport_mulSingle_subset
Function.mem_mulSupport
mulSingle_eq_same
mulSupport_mulSingle_one 📖mathematicalFunction.mulSupport
mulSingle
Set
Set.instEmptyCollection
mulSingle_one
Function.mulSupport_one
mulSupport_mulSingle_subset 📖mathematicalSet
Set.instHasSubset
Function.mulSupport
mulSingle
Set.instSingletonSet
by_contra
mulSingle_eq_of_ne
subsingleton_mulSupport_mulSingle 📖mathematicalSet.Subsingleton
Function.mulSupport
mulSingle
mulSupport_mulSingle
subsingleton_support_single 📖mathematicalSet.Subsingleton
Function.support
single
support_single
Set.subsingleton_empty
Set.subsingleton_singleton
support_single 📖mathematicalFunction.support
single
Set
Set.instEmptyCollection
Set.instSingletonSet
single_zero
Function.support_zero
support_single_of_ne
support_single_disjoint 📖mathematicalDisjoint
Set
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
HeytingAlgebra.toOrderBot
BiheytingAlgebra.toHeytingAlgebra
Function.support
single
support_single_of_ne
Set.disjoint_singleton
support_single_of_ne 📖mathematicalFunction.support
single
Set
Set.instSingletonSet
HasSubset.Subset.antisymm
Set.instAntisymmSubset
support_single_subset
Function.mem_support
single_eq_same
support_single_subset 📖mathematicalSet
Set.instHasSubset
Function.support
single
Set.instSingletonSet
by_contra
single_eq_of_ne
support_single_zero 📖mathematicalFunction.support
single
Set
Set.instEmptyCollection
single_zero
Function.support_zero

Set

Theorems

NameKindAssumesProvesValidatesDepends On
image_inter_mulSupport_eq 📖mathematicalSet
instInter
image
Function.mulSupport
Function.mulSupport_comp_eq_preimage
image_inter_preimage
image_inter_support_eq 📖mathematicalSet
instInter
image
Function.support
Function.support_comp_eq_preimage
image_inter_preimage

Subsingleton

Theorems

NameKindAssumesProvesValidatesDepends On
mulSupport_eq 📖mathematicalFunction.mulSupport
Set
Set.instEmptyCollection
Function.mulSupport_eq_empty_iff
support_eq 📖mathematicalFunction.support
Set
Set.instEmptyCollection
Function.support_eq_empty_iff

---

← Back to Index