Documentation Verification Report

Cover

📁 Source: Mathlib/Order/Cover.lean

Statistics

MetricCount
DefinitionsinstDecidableRelCovBy, instDecidableRelWCovBy
2
Theoremstrans_covBy, trans_wcovBy, wcovBy, covBy_iff, wcovBy_iff, Icc_eq, Ico_eq, Iio_eq, Ioc_eq, Ioi_eq, Ioo_eq, Ioo_eq_Ico, Ioo_eq_Ioc, eq_of_between, eq_or_eq, exists_set_insert, exists_set_sdiff_singleton, ge_of_gt, image, irrefl, le, le_iff_lt_left, le_iff_lt_right, le_of_lt, lt, lt_iff_le_left, lt_iff_le_right, ne, ne', ofDual, of_image, of_le_of_lt, of_lt_of_le, toDual, trans_antisymmRel, unique_left, unique_right, wcovBy, wcovBy, wcovBy', wcovBy_of_le, exists_disjoint_Iio_Ioi, exists_lt_lt, covBy_of_apply, wcovBy_of_apply, map_covBy, map_wcovBy, covBy_iff, covBy_iff_antisymmRel, covBy_iff_exists_left_eq, covBy_iff_exists_right_eq, exists_forall_antisymmRel_of_covBy, exists_forall_antisymmRel_of_wcovBy, exists_forall_eq_of_covBy, exists_forall_eq_of_wcovBy, wcovBy_iff, wcovBy_iff_antisymmRel, wcovBy_iff_exists_left_eq, wcovBy_iff_exists_right_eq, covBy_iff, fst_eq_or_snd_eq_of_wcovBy, mk_covBy_mk_iff, mk_covBy_mk_iff_left, mk_covBy_mk_iff_right, mk_wcovBy_mk_iff, mk_wcovBy_mk_iff_left, mk_wcovBy_mk_iff_right, swap_covBy_swap, swap_wcovBy_swap, wcovBy_iff, apply_covBy_apply_iff, apply_wcovBy_apply_iff, covBy_iff_exists_insert, covBy_iff_exists_sdiff_singleton, covBy_insert, empty_covBy_singleton, sdiff_singleton_covBy, sdiff_singleton_wcovBy, wcovBy_insert, Icc_eq, Ico_subset, Ioc_subset, Ioo_eq, covBy_of_lt, covBy_of_ne, covBy_of_not_le, covBy_or_eq, covBy_or_le_and_le, eq_or_covBy, eq_or_eq, eval, fst, ge_of_gt, image, inf_eq, le, le_and_le_iff, le_of_lt, ofDual, of_image, of_le_of_le, of_le_of_le', refl, rfl, snd, stdRefl, stdRefl', sup_eq, toDual, trans_antisymm_rel, wcovBy_iff_le, bot_covBy_coe, bot_wcovBy_coe, coe_covBy_coe, coe_wcovBy_coe, coe_covBy_coe, coe_covBy_top, coe_wcovBy_coe, coe_wcovBy_top, apply_covBy_apply_iff, apply_wcovBy_apply_iff, covBy_congr_left, covBy_congr_right, covBy_iff_Ioo_eq, covBy_iff_le_iff_lt_left, covBy_iff_le_iff_lt_right, covBy_iff_lt_and_eq_or_eq, covBy_iff_lt_iff_le_left, covBy_iff_lt_iff_le_right, covBy_iff_wcovBy_and_lt, covBy_iff_wcovBy_and_ne, covBy_iff_wcovBy_and_not_le, covBy_of_eq_or_eq, denselyOrdered_iff_forall_not_covBy, exists_covBy_of_wellFoundedGT, exists_covBy_of_wellFoundedLT, exists_lt_lt_of_not_covBy, instIsNonstrictStrictOrderWCovByCovBy, not_covBy, not_covBy_iff, not_covBy_of_lt_of_lt, not_wcovBy_iff, ofDual_covBy_ofDual_iff, ofDual_wcovBy_ofDual_iff, reflTransGen_wcovBy_eq_reflTransGen_covBy, toDual_covBy_toDual_iff, toDual_wcovBy_toDual_iff, transGen_wcovBy_eq_reflTransGen_covBy, wcovBy_congr_left, wcovBy_congr_right, wcovBy_eq_reflGen_covBy, wcovBy_iff_Ioo_eq, wcovBy_iff_covBy_or_eq, wcovBy_iff_covBy_or_le_and_le, wcovBy_iff_eq_or_covBy, wcovBy_iff_le_and_eq_or_eq, wcovBy_of_eq_or_eq, wcovBy_of_le_of_le
158
Total160

AntisymmRel

Theorems

NameKindAssumesProvesValidatesDepends On
trans_covBy 📖AntisymmRel
Preorder.toLE
CovBy
Preorder.toLT
LE.le.trans_lt
CovBy.lt
trans_wcovBy 📖AntisymmRel
Preorder.toLE
WCovBy
LE.le.trans
WCovBy.le
LE.le.trans_lt
wcovBy 📖mathematicalAntisymmRel
Preorder.toLE
WCovBywcovBy_of_le_of_le

Bool

Definitions

NameCategoryTheorems
instDecidableRelCovBy 📖CompOp
instDecidableRelWCovBy 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
covBy_iff 📖mathematicalCovBy
wcovBy_iff 📖mathematicalWCovBy
PartialOrder.toPreorder
instPartialOrder

CovBy

Theorems

NameKindAssumesProvesValidatesDepends On
Icc_eq 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
Set.Icc
Set
Set.instInsert
Set.instSingletonSet
WCovBy.Icc_eq
wcovBy
Ico_eq 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
Set.Ico
Set
Set.instSingletonSet
Set.Ioo_union_left
lt
Ioo_eq
Set.empty_union
Iio_eq 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Iio
Set.Iic
Set.Iic_union_Ioo_eq_Iio
lt
Ioo_eq
Set.union_empty
Ioc_eq 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
Set.Ioc
Set
Set.instSingletonSet
Set.Ioo_union_right
lt
Ioo_eq
Set.empty_union
Ioi_eq 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ioi
Set.Ici
Set.Ioo_union_Ici_eq_Ioi
lt
Ioo_eq
Set.empty_union
Ioo_eq 📖mathematicalCovBy
Preorder.toLT
Set.Ioo
Set
Set.instEmptyCollection
WCovBy.Ioo_eq
wcovBy
Ioo_eq_Ico 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ioo
Set.Ico
subset_antisymm
Set.instAntisymmSubset
ge_of_gt
Set.Ico_subset_Ioo_left
lt
Ioo_eq_Ioc 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.Ioo
Set.Ioc
subset_antisymm
Set.instAntisymmSubset
le_of_lt
Set.Ioc_subset_Ioo_right
lt
eq_of_between 📖CovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
le_antisymm
le_of_not_gt
eq_or_eq 📖CovBy
Preorder.toLT
PartialOrder.toPreorder
Preorder.toLE
WCovBy.eq_or_eq
wcovBy
exists_set_insert 📖mathematicalCovBy
Set
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
Set.instMembership
Set.instInsert
Set.ssubset_iff_insert
lt
HasSubset.Subset.eq_of_not_ssuperset
Set.instIsNonstrictStrictOrderSubsetSSubset
Set.instAntisymmSubset
Set.ssubset_insert
exists_set_sdiff_singleton 📖mathematicalCovBy
Set
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
Set.instBooleanAlgebra
Set.instMembership
Set.instSDiff
Set.instSingletonSet
Set.ssubset_iff_sdiff_singleton
lt
HasSubset.Subset.eq_of_not_ssubset
Set.instIsNonstrictStrictOrderSubsetSSubset
Set.instAntisymmSubset
sdiff_lt
Set.singleton_subset_iff
Set.singleton_ne_empty
ge_of_gt 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLEWCovBy.ge_of_gt
wcovBy
image 📖mathematicalCovBy
Preorder.toLT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
WCovBy.covBy_of_lt
WCovBy.image
wcovBy
OrderEmbedding.strictMono
lt
irrefl 📖mathematicalCovBy
Preorder.toLT
ne
le 📖mathematicalCovBy
Preorder.toLT
Preorder.toLELT.lt.le
le_iff_lt_left 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLEcovBy_iff_le_iff_lt_left
le_iff_lt_right 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLEcovBy_iff_le_iff_lt_right
le_of_lt 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLEWCovBy.le_of_lt
wcovBy
lt 📖CovBy
lt_iff_le_left 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLEcovBy_iff_lt_iff_le_left
lt_iff_le_right 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLEcovBy_iff_lt_iff_le_right
ne 📖CovBy
Preorder.toLT
LT.lt.ne
lt
ne' 📖CovBy
Preorder.toLT
LT.lt.ne'
lt
ofDual 📖mathematicalCovBy
OrderDual
OrderDual.instLT
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
ofDual_covBy_ofDual_iff
of_image 📖CovBy
Preorder.toLT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
OrderEmbedding.lt_iff_lt
lt
of_le_of_lt 📖CovBy
Preorder.toLT
Preorder.toLE
LE.le.trans_lt
of_lt_of_le 📖CovBy
Preorder.toLT
Preorder.toLE
LT.lt.trans_le
toDual 📖mathematicalCovByOrderDual
OrderDual.instLT
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
toDual_covBy_toDual_iff
trans_antisymmRel 📖CovBy
Preorder.toLT
AntisymmRel
Preorder.toLE
LT.lt.trans_le
lt
unique_left 📖CovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LE.le.antisymm
le_of_lt
lt
unique_right 📖CovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
LE.le.antisymm'
ge_of_gt
lt
wcovBy 📖mathematicalCovBy
Preorder.toLT
WCovByle

Eq

Theorems

NameKindAssumesProvesValidatesDepends On
wcovBy 📖mathematicalWCovByWCovBy.rfl
wcovBy' 📖mathematicalWCovByWCovBy.rfl

LE.le

Theorems

NameKindAssumesProvesValidatesDepends On
wcovBy_of_le 📖mathematicalPreorder.toLEWCovBywcovBy_of_le_of_le

LT.lt

Theorems

NameKindAssumesProvesValidatesDepends On
exists_disjoint_Iio_Ioi 📖Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
exists_lt_lt 📖CovByexists_lt_lt_of_not_covBy

OrderEmbedding

Theorems

NameKindAssumesProvesValidatesDepends On
covBy_of_apply 📖CovBy
Preorder.toLT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
CovBy.of_image
wcovBy_of_apply 📖WCovBy
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
WCovBy.of_image

OrderIso

Theorems

NameKindAssumesProvesValidatesDepends On
map_covBy 📖mathematicalCovBy
Preorder.toLT
DFunLike.coe
EquivLike.toFunLike
apply_covBy_apply_iff
map_wcovBy 📖mathematicalWCovBy
DFunLike.coe
EquivLike.toFunLike
apply_wcovBy_apply_iff

Pi

Theorems

NameKindAssumesProvesValidatesDepends On
covBy_iff 📖mathematicalCovBy
Preorder.toLT
preorder
PartialOrder.toPreorder
instReflLe
instAntisymmLe
covBy_iff_antisymmRel 📖mathematicalCovBy
Preorder.toLT
preorder
AntisymmRel
Preorder.toLE
lt_def
exists_forall_antisymmRel_of_wcovBy
CovBy.wcovBy
covBy_iff_wcovBy_and_lt
WCovBy.eval
by_contra
LE.le.not_gt
wcovBy_iff_antisymmRel
eq_or_ne
LT.lt.le
covBy_iff_exists_left_eq 📖mathematicalCovBy
Preorder.toLT
preorder
PartialOrder.toPreorder
Function.update
covBy_iff
Function.update_self
Function.update_of_ne
covBy_iff_exists_right_eq 📖mathematicalCovBy
Preorder.toLT
preorder
PartialOrder.toPreorder
Function.update
covBy_iff
Function.update_self
Function.update_of_ne
exists_forall_antisymmRel_of_covBy 📖mathematicalCovBy
Preorder.toLT
preorder
AntisymmRel
Preorder.toLE
LT.lt.le
Function.update_self
Function.update_of_ne
exists_forall_antisymmRel_of_wcovBy 📖mathematicalWCovBy
preorder
AntisymmRel
Preorder.toLE
wcovBy_iff_covBy_or_le_and_le
exists_forall_antisymmRel_of_covBy
exists_forall_eq_of_covBy 📖CovBy
Preorder.toLT
preorder
PartialOrder.toPreorder
exists_forall_antisymmRel_of_covBy
AntisymmRel.eq
instReflLe
instAntisymmLe
exists_forall_eq_of_wcovBy 📖WCovBy
preorder
PartialOrder.toPreorder
exists_forall_antisymmRel_of_wcovBy
AntisymmRel.eq
instReflLe
instAntisymmLe
wcovBy_iff 📖mathematicalWCovBy
preorder
PartialOrder.toPreorder
instReflLe
instAntisymmLe
wcovBy_iff_antisymmRel 📖mathematicalWCovBy
preorder
AntisymmRel
Preorder.toLE
exists_forall_antisymmRel_of_wcovBy
WCovBy.eval
eq_or_ne
lt_def
LT.lt.not_ge
lt_of_antisymmRel_of_lt
AntisymmRel.symm
LT.lt.le
lt_of_lt_of_antisymmRel
wcovBy_iff_exists_left_eq 📖mathematicalWCovBy
preorder
PartialOrder.toPreorder
Function.update
wcovBy_iff
Function.update_self
Function.update_of_ne
wcovBy_iff_exists_right_eq 📖mathematicalWCovBy
preorder
PartialOrder.toPreorder
Function.update
wcovBy_iff
Function.update_self
Function.update_of_ne

Prod

Theorems

NameKindAssumesProvesValidatesDepends On
covBy_iff 📖mathematicalCovBy
Preorder.toLT
instPreorder
PartialOrder.toPreorder
mk_covBy_mk_iff
fst_eq_or_snd_eq_of_wcovBy 📖WCovBy
instPreorder
PartialOrder.toPreorder
of_not_not
Ne.lt_of_le
le_rfl
mk_covBy_mk_iff 📖mathematicalCovBy
Preorder.toLT
instPreorder
PartialOrder.toPreorder
fst_eq_or_snd_eq_of_wcovBy
CovBy.wcovBy
mk_covBy_mk_iff_right
mk_covBy_mk_iff_left
mk_covBy_mk_iff_left 📖mathematicalCovBy
Preorder.toLT
instPreorder
PartialOrder.toPreorder
mk_covBy_mk_iff_right 📖mathematicalCovBy
Preorder.toLT
instPreorder
PartialOrder.toPreorder
mk_wcovBy_mk_iff 📖mathematicalWCovBy
instPreorder
PartialOrder.toPreorder
fst_eq_or_snd_eq_of_wcovBy
mk_wcovBy_mk_iff_right
mk_wcovBy_mk_iff_left
mk_wcovBy_mk_iff_left 📖mathematicalWCovBy
instPreorder
PartialOrder.toPreorder
WCovBy.fst
mk_le_mk_iff_left
LE.le.antisymm
LT.lt.le
mk_lt_mk_iff_left
mk_wcovBy_mk_iff_right 📖mathematicalWCovBy
instPreorder
PartialOrder.toPreorder
swap_wcovBy_swap
mk_wcovBy_mk_iff_left
swap_covBy_swap 📖mathematicalCovBy
Preorder.toLT
instPreorder
PartialOrder.toPreorder
apply_covBy_apply_iff
OrderIso.instOrderIsoClass
swap_wcovBy_swap 📖mathematicalWCovBy
instPreorder
PartialOrder.toPreorder
apply_wcovBy_apply_iff
OrderIso.instOrderIsoClass
wcovBy_iff 📖mathematicalWCovBy
instPreorder
PartialOrder.toPreorder
mk_wcovBy_mk_iff

Set

Theorems

NameKindAssumesProvesValidatesDepends On
covBy_iff_exists_insert 📖mathematicalCovBy
Set
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instMembership
instInsert
CovBy.exists_set_insert
covBy_insert
covBy_iff_exists_sdiff_singleton 📖mathematicalCovBy
Set
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instMembership
instSDiff
instSingletonSet
CovBy.exists_set_sdiff_singleton
sdiff_singleton_covBy
covBy_insert 📖mathematicalSet
instMembership
CovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instInsert
WCovBy.covBy_of_lt
wcovBy_insert
ssubset_insert
empty_covBy_singleton 📖mathematicalCovBy
Set
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instEmptyCollection
instSingletonSet
covBy_insert
instLawfulSingleton
notMem_empty
sdiff_singleton_covBy 📖mathematicalSet
instMembership
CovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instSDiff
instSingletonSet
sdiff_lt
singleton_subset_iff
singleton_ne_empty
sdiff_singleton_wcovBy
sdiff_singleton_wcovBy 📖mathematicalWCovBy
Set
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instSDiff
instSingletonSet
ext
insert_diff_self_of_mem
wcovBy_insert
diff_singleton_eq_self
wcovBy_insert 📖mathematicalWCovBy
Set
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
GeneralizedCoheytingAlgebra.toLattice
CoheytingAlgebra.toGeneralizedCoheytingAlgebra
BiheytingAlgebra.toCoheytingAlgebra
BooleanAlgebra.toBiheytingAlgebra
instBooleanAlgebra
instInsert
wcovBy_of_eq_or_eq
subset_insert
subset_antisymm
instAntisymmSubset
insert_subset_iff
diff_singleton_eq_self
diff_singleton_subset_iff

Set.OrdConnected

Theorems

NameKindAssumesProvesValidatesDepends On
apply_covBy_apply_iff 📖mathematicalCovBy
Preorder.toLT
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
CovBy.of_image
CovBy.image
apply_wcovBy_apply_iff 📖mathematicalWCovBy
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
WCovBy.of_image
WCovBy.image

WCovBy

Theorems

NameKindAssumesProvesValidatesDepends On
Icc_eq 📖mathematicalWCovBy
PartialOrder.toPreorder
Set.Icc
Set
Set.instInsert
Set.instSingletonSet
Set.ext
le_and_le_iff
Ico_subset 📖mathematicalWCovBy
PartialOrder.toPreorder
Set
Set.instHasSubset
Set.Ico
Set.instSingletonSet
Set.Icc_diff_right
Icc_eq
Set.diff_singleton_subset_iff
Set.pair_comm
subset_refl
Set.instReflSubset
Ioc_subset 📖mathematicalWCovBy
PartialOrder.toPreorder
Set
Set.instHasSubset
Set.Ioc
Set.instSingletonSet
Set.Icc_diff_left
Icc_eq
Set.diff_singleton_subset_iff
subset_refl
Set.instReflSubset
Ioo_eq 📖mathematicalWCovBySet.Ioo
Set
Set.instEmptyCollection
Set.eq_empty_iff_forall_notMem
covBy_of_lt 📖mathematicalWCovBy
Preorder.toLT
CovBy
covBy_of_ne 📖mathematicalWCovBy
PartialOrder.toPreorder
CovBy
Preorder.toLT
LE.le.lt_of_ne
le
covBy_of_not_le 📖mathematicalWCovBy
Preorder.toLE
CovBy
Preorder.toLT
LE.le.lt_of_not_ge
le
covBy_or_eq 📖mathematicalWCovBy
PartialOrder.toPreorder
CovBy
Preorder.toLT
wcovBy_iff_covBy_or_eq
covBy_or_le_and_le 📖mathematicalWCovByCovBy
Preorder.toLT
Preorder.toLE
wcovBy_iff_covBy_or_le_and_le
eq_or_covBy 📖mathematicalWCovBy
PartialOrder.toPreorder
CovBy
Preorder.toLT
wcovBy_iff_eq_or_covBy
eq_or_eq 📖WCovBy
PartialOrder.toPreorder
Preorder.toLE
LE.le.eq_or_lt
eval 📖WCovBy
Pi.preorder
LT.lt.le
lt_of_le_not_ge
LT.lt.not_ge
fst 📖WCovBy
Prod.instPreorder
PartialOrder.toPreorder
Prod.mk_lt_mk_iff_left
LT.lt.le
LT.lt.not_ge
ge_of_gt 📖mathematicalWCovBy
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
Preorder.toLEnot_lt
image 📖mathematicalWCovByDFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
OrderEmbedding.monotone
le
Set.OrdConnected.out
Set.mem_range_self
LT.lt.le
OrderEmbedding.lt_iff_lt
inf_eq 📖mathematicalWCovBy
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
SemilatticeInf.toMinLE.le.eq_of_not_lt'
le_inf
le
Ne.inf_lt_or_inf_lt
le 📖mathematicalWCovByPreorder.toLE
le_and_le_iff 📖mathematicalWCovBy
PartialOrder.toPreorder
Preorder.toLEeq_or_eq
le_rfl
le
le_of_lt 📖mathematicalWCovBy
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLT
Preorder.toLEnot_lt
ofDual 📖mathematicalWCovBy
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
ofDual_wcovBy_ofDual_iff
of_image 📖WCovBy
DFunLike.coe
OrderEmbedding
Preorder.toLE
instFunLikeOrderEmbedding
OrderEmbedding.le_iff_le
le
OrderEmbedding.lt_iff_lt
of_le_of_le 📖WCovBy
Preorder.toLE
LE.le.trans_lt
of_le_of_le' 📖WCovBy
Preorder.toLE
LE.le.trans_lt'
refl 📖mathematicalWCovByle_rfl
LT.lt.not_gt
rfl 📖mathematicalWCovByrefl
snd 📖WCovBy
Prod.instPreorder
PartialOrder.toPreorder
Prod.mk_lt_mk_iff_right
LT.lt.le
LT.lt.not_ge
stdRefl 📖mathematicalWCovByrefl
stdRefl' 📖mathematicalWCovByrefl
sup_eq 📖mathematicalWCovBy
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
SemilatticeSup.toMaxLE.le.eq_of_not_lt
sup_le
le
Ne.lt_sup_or_lt_sup
toDual 📖mathematicalWCovByOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
toDual_wcovBy_toDual_iff
trans_antisymm_rel 📖WCovBy
AntisymmRel
Preorder.toLE
LE.le.trans
le
LT.lt.trans_le
wcovBy_iff_le 📖mathematicalWCovByPreorder.toLEle
LE.le.wcovBy_of_le

WithBot

Theorems

NameKindAssumesProvesValidatesDepends On
bot_covBy_coe 📖mathematicalCovBy
WithBot
Preorder.toLT
instPreorder
Bot.bot
bot
some
IsMin
Preorder.toLE
bot_wcovBy_coe 📖mathematicalWCovBy
WithBot
instPreorder
Bot.bot
bot
some
IsMin
Preorder.toLE
coe_covBy_coe 📖mathematicalCovBy
WithBot
Preorder.toLT
instPreorder
some
Set.OrdConnected.apply_covBy_apply_iff
range_coe
coe_wcovBy_coe 📖mathematicalWCovBy
WithBot
instPreorder
some
Set.OrdConnected.apply_wcovBy_apply_iff
range_coe

WithTop

Theorems

NameKindAssumesProvesValidatesDepends On
coe_covBy_coe 📖mathematicalCovBy
WithTop
Preorder.toLT
instPreorder
some
Set.OrdConnected.apply_covBy_apply_iff
range_coe
coe_covBy_top 📖mathematicalCovBy
WithTop
Preorder.toLT
instPreorder
some
Top.top
top
IsMax
Preorder.toLE
coe_wcovBy_coe 📖mathematicalWCovBy
WithTop
instPreorder
some
Set.OrdConnected.apply_wcovBy_apply_iff
range_coe
coe_wcovBy_top 📖mathematicalWCovBy
WithTop
instPreorder
some
Top.top
top
IsMax
Preorder.toLE

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
apply_covBy_apply_iff 📖mathematicalCovBy
Preorder.toLT
DFunLike.coe
EquivLike.toFunLike
Set.OrdConnected.apply_covBy_apply_iff
Set.ordConnected_range
OrderIso.instOrderIsoClass
apply_wcovBy_apply_iff 📖mathematicalWCovBy
DFunLike.coe
EquivLike.toFunLike
Set.OrdConnected.apply_wcovBy_apply_iff
Set.ordConnected_range
OrderIso.instOrderIsoClass
covBy_congr_left 📖mathematicalAntisymmRel
Preorder.toLE
CovBy
Preorder.toLT
AntisymmRel.trans_covBy
AntisymmRel.symm
covBy_congr_right 📖mathematicalAntisymmRel
Preorder.toLE
CovBy
Preorder.toLT
CovBy.trans_antisymmRel
AntisymmRel.symm
covBy_iff_Ioo_eq 📖mathematicalCovBy
Preorder.toLT
Set.Ioo
Set
Set.instEmptyCollection
covBy_iff_le_iff_lt_left 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
covBy_iff_le_iff_lt_right 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
covBy_iff_lt_iff_le_right
covBy_iff_lt_and_eq_or_eq 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
CovBy.lt
CovBy.eq_or_eq
covBy_of_eq_or_eq
covBy_iff_lt_iff_le_left 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
CovBy.le_of_lt
LE.le.trans_lt
CovBy.lt
le_rfl
LE.le.not_gt
covBy_iff_lt_iff_le_right 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Preorder.toLE
CovBy.ge_of_gt
LE.le.trans_lt'
CovBy.lt
le_rfl
LE.le.not_gt
covBy_iff_wcovBy_and_lt 📖mathematicalCovBy
Preorder.toLT
WCovBy
CovBy.wcovBy
CovBy.lt
WCovBy.covBy_of_lt
covBy_iff_wcovBy_and_ne 📖mathematicalCovBy
Preorder.toLT
PartialOrder.toPreorder
WCovBy
CovBy.wcovBy
CovBy.ne
WCovBy.covBy_of_ne
covBy_iff_wcovBy_and_not_le 📖mathematicalCovBy
Preorder.toLT
WCovBy
Preorder.toLE
CovBy.wcovBy
LT.lt.not_ge
CovBy.lt
WCovBy.covBy_of_not_le
covBy_of_eq_or_eq 📖mathematicalPreorder.toLTCovByLT.lt.le
LT.lt.ne'
LT.lt.ne
denselyOrdered_iff_forall_not_covBy 📖mathematicalDenselyOrdered
CovBy
not_covBy
exists_lt_lt_of_not_covBy
exists_covBy_of_wellFoundedGT 📖mathematicalIsMin
Preorder.toLE
CovBy
Preorder.toLT
wellFounded_gt
not_isMin_iff
WellFounded.min_mem
WellFounded.not_lt_min
IsWellFounded.wf
exists_covBy_of_wellFoundedLT 📖mathematicalIsMax
Preorder.toLE
CovBy
Preorder.toLT
wellFounded_lt
not_isMax_iff
WellFounded.min_mem
WellFounded.not_lt_min
IsWellFounded.wf
exists_lt_lt_of_not_covBy 📖CovBynot_covBy_iff
instIsNonstrictStrictOrderWCovByCovBy 📖mathematicalIsNonstrictStrictOrder
WCovBy
CovBy
Preorder.toLT
covBy_iff_wcovBy_and_not_le
Iff.not
WCovBy.wcovBy_iff_le
not_covBy 📖mathematicalCovByexists_between
not_covBy_iff 📖mathematicalCovBy
not_covBy_of_lt_of_lt 📖mathematicalPreorder.toLTCovBynot_covBy_iff
LT.lt.trans
not_wcovBy_iff 📖mathematicalPreorder.toLEWCovBy
Preorder.toLT
ofDual_covBy_ofDual_iff 📖mathematicalCovBy
DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
OrderDual.instLT
forall_swap
ofDual_wcovBy_ofDual_iff 📖mathematicalWCovBy
DFunLike.coe
Equiv
OrderDual
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
OrderDual.instPreorder
forall_swap
reflTransGen_wcovBy_eq_reflTransGen_covBy 📖mathematicalRelation.ReflTransGen
WCovBy
PartialOrder.toPreorder
CovBy
Preorder.toLT
wcovBy_eq_reflGen_covBy
Relation.reflTransGen_reflGen
toDual_covBy_toDual_iff 📖mathematicalCovBy
OrderDual
OrderDual.instLT
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
forall_swap
toDual_wcovBy_toDual_iff 📖mathematicalWCovBy
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
forall_swap
transGen_wcovBy_eq_reflTransGen_covBy 📖mathematicalWCovBy
PartialOrder.toPreorder
Relation.ReflTransGen
CovBy
Preorder.toLT
wcovBy_eq_reflGen_covBy
Relation.transGen_reflGen
wcovBy_congr_left 📖mathematicalAntisymmRel
Preorder.toLE
WCovByAntisymmRel.trans_wcovBy
AntisymmRel.symm
wcovBy_congr_right 📖mathematicalAntisymmRel
Preorder.toLE
WCovByWCovBy.trans_antisymm_rel
AntisymmRel.symm
wcovBy_eq_reflGen_covBy 📖mathematicalWCovBy
PartialOrder.toPreorder
Relation.ReflGen
CovBy
Preorder.toLT
wcovBy_iff_Ioo_eq 📖mathematicalWCovBy
Preorder.toLE
Set.Ioo
Set
Set.instEmptyCollection
wcovBy_iff_covBy_or_eq 📖mathematicalWCovBy
PartialOrder.toPreorder
CovBy
Preorder.toLT
le_antisymm_iff
wcovBy_iff_covBy_or_le_and_le
wcovBy_iff_covBy_or_le_and_le 📖mathematicalWCovBy
CovBy
Preorder.toLT
Preorder.toLE
WCovBy.covBy_of_not_le
WCovBy.le
CovBy.wcovBy
LE.le.wcovBy_of_le
wcovBy_iff_eq_or_covBy 📖mathematicalWCovBy
PartialOrder.toPreorder
CovBy
Preorder.toLT
wcovBy_iff_covBy_or_eq
wcovBy_iff_le_and_eq_or_eq 📖mathematicalWCovBy
PartialOrder.toPreorder
Preorder.toLE
WCovBy.le
WCovBy.eq_or_eq
wcovBy_of_eq_or_eq
wcovBy_of_eq_or_eq 📖mathematicalPreorder.toLEWCovByLT.lt.le
LT.lt.ne'
LT.lt.ne
wcovBy_of_le_of_le 📖mathematicalPreorder.toLEWCovByLT.lt.not_ge
LT.lt.trans

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