Documentation Verification Report

Box

📁 Source: Mathlib/Order/Interval/Finset/Box.lean

Statistics

MetricCount
DefinitionsBox, box
2
Theoremsbox_succ_disjUnion, box_succ_eq_sdiff, box_succ_union_prod, box_zero, disjoint_box_succ_prod, eq_zero_iff_eq_zero_of_mem_box, zero_mem_box, card_box, existsUnique_mem_box, mem_box, card_box_succ
11
Total13

BoxIntegral

Definitions

NameCategoryTheorems
Box 📖CompData
181 math, 7 bridgemath: Box.splitCenterBox_le, BoxAdditiveMap.map_split_add, Prepartition.measure_iUnion_toReal, Box.splitLower_def, TaggedPrepartition.tag_mem_Icc, Box.coe_coe, Box.splitUpper_eq_bot, unitPartition.mem_box_iff', Box.upper_mem_Icc, Box.exists_mem_splitCenterBox, Box.face_mono, Box.measurableSet_Icc, Box.coe_bot, BoxAdditiveMap.zero_apply, TaggedPrepartition.filter_boxes_val, Box.le_TFAE, Prepartition.le_of_mem, unitPartition.mem_prepartition_boxes_iff, TaggedPrepartition.isHenstock_single, unitPartition.mem_admissibleIndex_iff, Prepartition.mem_split_iff, Box.disjoint_withBotCoe, Prepartition.top_boxes, Box.Ioo_subset_coe, Box.splitUpper_le, unitPartition.tag_mem, Box.le_iff_Icc, Box.ext_iff, Box.monotone_face, unitPartition.box_injective, integrable_of_continuousOn, Prepartition.card_filter_mem_Icc_le, unitPartition.integralSum_eq_tsum_div, Prepartition.injective_boxes, Prepartition.IsPartition.existsUnique, Box.isCompact_Icc, TaggedPrepartition.mem_toPrepartition, Prepartition.mem_split_iff', Box.splitUpper_def, Prepartition.mem_biUnion, Prepartition.filter_boxes, Prepartition.biUnionIndex_mem, Box.le_iff_bounds, TaggedPrepartition.mem_mk, Prepartition.iUnion_def, BoxAdditiveMap.coe_injective, TaggedPrepartition.isSubordinate_single, Prepartition.sum_fiberwise, Box.measure_Icc_lt_top, Integrable.toBoxAdditive_apply, Box.splitUpper_eq_self, MeasureTheory.AEContinuous.hasBoxIntegral, Prepartition.mem_single, Box.iUnion_Ioo_of_tendsto, Prepartition.mem_restrict', BoxAdditiveMap.upperSubLower_apply, Prepartition.mem_mk, unitPartition.mem_box_iff, integrable_of_bounded_and_ae_continuous, BoxAdditiveMap.volume_apply, Prepartition.sum_biUnion_boxes, integral_nonneg, Box.coe_ae_eq_Icc, Prepartition.bot_boxes, Box.splitLower_le, Integrable.dist_integralSum_sum_integral_le_of_memBaseSet, Box.Ioo_ae_eq_Icc, Prepartition.distortion_biUnionTagged, TaggedPrepartition.mem_iUnion, Prepartition.le_biUnionIndex, Box.mem_splitCenterBox, Prepartition.mem_filter, Prepartition.mem_splitCenter, Box.continuousOn_face_Icc, Box.lower_mem_Icc, Box.mem_mk, Box.mem_coe, TaggedPrepartition.isHenstock_single_iff, TaggedPrepartition.mem_filter, norm_integral_le_of_le_const, Box.isSome_iff, Box.not_disjoint_coe_iff_nonempty_inter, Integrable.sum_integral_congr, Box.biUnion_coe_eq_coe, Box.Icc_def, integralSum_biUnionTagged, Prepartition.iUnion_biUnion, Prepartition.pairwiseDisjoint, Box.isBounded_Icc, BoxAdditiveMap.coe_mk, Prepartition.sum_disj_union_boxes, Prepartition.IsPartition.le_iff, Box.monotone_upper, BoxAdditiveMap.toSMul_apply, integralSum_fiberwise, Box.mapsTo_insertNth_face_Icc, Box.splitLower_eq_bot, Box.coe_inf, Box.mk'_eq_bot, le_hasIntegralVertices_of_isBounded, Box.disjoint_splitLower_splitUpper, Box.le_def, TaggedPrepartition.distortion_biUnionPrepartition, Prepartition.biUnion_boxes, Box.Ioo_subset_Icc, BoxAdditiveMap.sum_partition_boxes, Box.exists_seq_mono_tendsto, MeasureTheory.ContinuousOn.hasBoxIntegral, Box.withBotCoe_subset_iff, Box.mk'_eq_coe, BoxAdditiveMap.map_apply, Prepartition.iUnion_biUnionTagged, hasIntegral_const, Box.diam_Icc_le_of_distortion_le, Prepartition.distortion_biUnion, HasIntegral.of_le_Henstock_of_forall_isLittleO, Prepartition.IsPartition.nonempty_boxes, Box.disjoint_coe, Prepartition.single_boxes, TaggedPrepartition.IsHenstock.card_filter_tag_eq_le, Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq, Prepartition.disjUnion_boxes, TaggedPrepartition.IsSubordinate.diam_le, Box.splitCenterBoxEmb_apply, Box.mem_def, TaggedPrepartition.mem_infPrepartition_comm, Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset, integralSum_sub_partitions, unitPartition.mem_prepartition_iff, Prepartition.iUnion_def', Box.Icc_eq_pi, Prepartition.mem_boxes, MeasureTheory.Measure.toBoxAdditive_apply, TaggedPrepartition.disjUnion_boxes, unitPartition.mem_box_iff_index, Prepartition.mem_ofWithBot, TaggedPrepartition.single_boxes_val, Box.coe_subset_Icc, TaggedPrepartition.unionComplToSubordinate_boxes, integral_const, Prepartition.le_of_mem', Box.volume_apply, Prepartition.disjoint_boxes_of_disjoint_iUnion, Prepartition.mem_inf, TaggedPrepartition.iUnion_def, Box.measurableSet_Ioo, Box.exists_mem, Prepartition.mem_restrict, Box.splitLower_eq_self, Integrable.tendsto_integralSum_sum_integral, BoxAdditiveMap.coe_inj, Prepartition.iUnion_ofWithBot, integrable_of_bounded_and_ae_continuousWithinAt, Box.coe_subset_coe, Prepartition.notMem_bot, Prepartition.mem_biUnionTagged, norm_integral_le_of_norm_le, Prepartition.sum_split_boxes, BoxAdditiveMap.sum_partition_boxes', Prepartition.not_disjoint_imp_le_of_subset_of_mem_splitMany, TaggedPrepartition.mem_single, unitPartition.diam_boxIcc, Prepartition.mem_biUnionIndex, Box.upper_mem, HasIntegral.mcShane_of_forall_isLittleO, Prepartition.ext_iff, BoxAdditiveMap.sum_boxes_congr, Prepartition.biUnionIndex_le, Prepartition.mem_top, BoxAdditiveMap.restrict_apply, Box.mem_univ_Ioc, Box.injective_coe, Prepartition.le_def, Integrable.dist_integralSum_sum_integral_le_of_memBaseSet_of_iUnion_eq, Prepartition.mem_disjUnion, Box.injective_splitCenterBox, Prepartition.mem_iUnion, Box.antitone_lower, TaggedPrepartition.isPartition_single, Prepartition.sum_ofWithBot, TaggedPrepartition.mem_disjUnion
bridge: hasIntegralIndicatorConst, MeasureTheory.SimpleFunc.hasBoxIntegral, MeasureTheory.IntegrableOn.hasBoxIntegral, HasIntegral.of_bRiemann_eq_false_of_forall_isLittleO, HasIntegral.of_aeEq_zero, HasIntegral.congr_ae, MeasureTheory.SimpleFunc.box_integral_eq_integral

Finset

Definitions

NameCategoryTheorems
box 📖CompOp
10 mathmath: box_succ_disjUnion, Int.card_box, Int.existsUnique_mem_box, box_succ_eq_sdiff, Int.mem_box, Prod.card_box_succ, disjoint_box_succ_prod, box_zero, box_succ_union_prod, zero_mem_box

Theorems

NameKindAssumesProvesValidatesDepends On
box_succ_disjUnion 📖mathematicaldisjUnion
box
Icc
PartialOrder.toPreorder
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
disjoint_box_succ_prod
disjoint_box_succ_prod
disjUnion_eq_union
box_succ_union_prod
box_succ_eq_sdiff 📖mathematicalbox
Finset
instSDiff
Icc
PartialOrder.toPreorder
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
box.eq_1
Monotone.disjointed_add_one
Nat.instNoMaxOrder
Nat.cast_add_one
box_succ_union_prod 📖mathematicalFinset
instUnion
box
Icc
PartialOrder.toPreorder
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Monotone.disjointed_add_one_sup
box_zero 📖mathematicalbox
Finset
instSingleton
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
disjointed_zero
Nat.cast_zero
neg_zero
Icc_self
disjoint_box_succ_prod 📖mathematicalDisjoint
Finset
partialOrder
instOrderBot
box
Icc
PartialOrder.toPreorder
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
box_succ_eq_sdiff
disjoint_sdiff_self_left
eq_zero_iff_eq_zero_of_mem_box 📖mathematicalFinset
SetLike.instMembership
instSetLike
box
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
zero_mem_box
mem_singleton
box_zero
zero_mem_box 📖mathematicalFinset
SetLike.instMembership
instSetLike
box
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
box_zero
box_succ_eq_sdiff
Nat.cast_add
Nat.cast_one
neg_add_rev
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
IsOrderedRing.toIsOrderedAddMonoid
zero_add
IsOrderedRing.toZeroLEOneClass

Int

Theorems

NameKindAssumesProvesValidatesDepends On
card_box 📖mathematicalFinset.card
Finset.box
Prod.instRing
instRing
Prod.instPartialOrder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
instLatticeInt
Prod.instLocallyFiniteOrder
PartialOrder.toPreorder
instLocallyFiniteOrder
Prod.instDecidableLE
Prod.card_box_succ
IsStrictOrderedRing.toIsOrderedRing
instIsStrictOrderedRing
card_Icc
sub_neg_eq_add
Nat.cast_one
tsub_eq_of_eq_add
Nat.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
instIsLeftCancelAddOfAddLeftReflectLE
IsOrderedCancelAddMonoid.toAddLeftReflectLE
Nat.instIsOrderedCancelAddMonoid
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
Nat.instAtLeastTwoHAddOfNat
Nat.cast_mul
Nat.cast_add
Mathlib.Tactic.Ring.of_eq
Mathlib.Tactic.Ring.mul_congr
Mathlib.Tactic.Ring.add_congr
Mathlib.Tactic.Ring.atom_pf
Mathlib.Tactic.Ring.cast_pos
Mathlib.Meta.NormNum.isNat_ofNat
Mathlib.Tactic.Ring.add_pf_add_gt
Mathlib.Tactic.Ring.add_pf_add_zero
Mathlib.Tactic.Ring.add_pf_add_overlap
Mathlib.Meta.NormNum.IsNat.to_raw_eq
Mathlib.Meta.NormNum.isNat_add
Mathlib.Meta.NormNum.IsNat.of_raw
Mathlib.Tactic.Ring.add_overlap_pf
Mathlib.Tactic.Ring.add_pf_zero_add
Mathlib.Tactic.Ring.add_mul
Mathlib.Tactic.Ring.mul_add
Mathlib.Meta.NormNum.isNat_mul
Mathlib.Tactic.Ring.mul_pf_right
Mathlib.Tactic.Ring.mul_zero
Mathlib.Tactic.Ring.add_pf_add_lt
Mathlib.Tactic.Ring.mul_pf_left
Mathlib.Tactic.Ring.mul_pp_pf_overlap
Mathlib.Tactic.Ring.zero_mul
Mathlib.Tactic.Ring.mul_one
Mathlib.Tactic.Ring.one_mul
existsUnique_mem_box 📖mathematicalExistsUnique
Finset
SetLike.instMembership
Finset.instSetLike
Finset.box
Prod.instRing
instRing
Prod.instPartialOrder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
instLatticeInt
Prod.instLocallyFiniteOrder
PartialOrder.toPreorder
instLocallyFiniteOrder
Prod.instDecidableLE
mem_box 📖mathematicalFinset
SetLike.instMembership
Finset.instSetLike
Finset.box
Prod.instRing
instRing
Prod.instPartialOrder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
instLatticeInt
Prod.instLocallyFiniteOrder
PartialOrder.toPreorder
instLocallyFiniteOrder
Prod.instDecidableLE
Finset.box_zero
Finset.box_succ_eq_sdiff
instIsOrderedRingProd
IsStrictOrderedRing.toIsOrderedRing
instIsStrictOrderedRing
Nat.cast_add
Nat.cast_one
neg_add_rev
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Prod.instIsOrderedAddMonoid
instIsOrderedAddMonoid
Prod.fst_natCast
Prod.snd_natCast

Prod

Theorems

NameKindAssumesProvesValidatesDepends On
card_box_succ 📖mathematicalFinset.card
Finset.box
instRing
instPartialOrder
instLocallyFiniteOrder
PartialOrder.toPreorder
Finset.Icc
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Finset.box_succ_eq_sdiff
instIsOrderedRingProd
Finset.card_sdiff_of_subset
Finset.card_Icc_prod
Nat.cast_add
Nat.cast_one
neg_add_rev
fst_natCast
snd_natCast

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