Documentation Verification Report

Basic

πŸ“ Source: Mathlib/Order/Monotone/Basic.lean

Statistics

MetricCount
Definitions0
Theoremsdual, dual_left, dual_right, eq_of_ge_of_le, ne_of_lt_of_lt_int, ne_of_lt_of_lt_nat, strictAnti_iff_injective, dual, dual_left, dual_right, strictAntiOn_of_injOn, strictAnti_iff_injOn, exists_strictAnti, exists_strictMono, rel_of_forall_rel_succ_of_le, rel_of_forall_rel_succ_of_lt, foldl_monotone, foldl_strictMono, foldr_monotone, foldr_strictMono, dual, dual_left, dual_right, eq_of_ge_of_le, ne_of_lt_of_lt_int, ne_of_lt_of_lt_nat, strictMono_iff_injective, dual, dual_left, dual_right, strictMonoOn_iff_injOn, strictMonoOn_of_injOn, exists_strictAnti, exists_strictAnti', exists_strictMono, exists_strictMono', exists_strictMono_subsequence, pow_monotoneOn, pow_self_mono, pow_self_strictMonoOn, rel_of_forall_rel_succ_of_le, rel_of_forall_rel_succ_of_le_of_le, rel_of_forall_rel_succ_of_le_of_lt, rel_of_forall_rel_succ_of_lt, stabilises_of_monotone, cmp_map_eq, compares, dual, dual_left, dual_right, injective, isMax_of_apply, isMin_of_apply, ite, ite', le_iff_ge, lt_iff_gt, maximal_of_minimal_image, minimal_of_maximal_image, wellFoundedGT, wellFoundedLT, cmp_map_eq, compares, dual, dual_left, dual_right, eq_iff_eq, injOn, le_iff_ge, lt_iff_gt, add_le_nat, cmp_map_eq, compares, dual, dual_left, dual_right, injective, isMax_of_apply, isMin_of_apply, ite, ite', le_iff_le, lt_iff_lt, maximal_of_maximal_image, minimal_of_minimal_image, wellFoundedGT, wellFoundedLT, cmp_map_eq, compares, dual, dual_left, dual_right, eq_iff_eq, injOn, le_iff_le, lt_iff_lt, antitoneOn_comp_ofDual_iff, antitoneOn_dual_iff, antitoneOn_nat_Ici_of_succ_le, antitoneOn_toDual_comp_iff, antitone_add_nat_iff_antitoneOn_nat_Ici, antitone_add_nat_of_succ_le, antitone_comp_ofDual_iff, antitone_dual_iff, antitone_int_of_succ_le, antitone_nat_of_succ_le, antitone_toDual_comp_iff, converges_of_monotone_of_bounded, monotoneOn_comp_ofDual_iff, monotoneOn_dual_iff, monotoneOn_nat_Ici_of_le_succ, monotoneOn_toDual_comp_iff, monotone_add_nat_iff_monotoneOn_nat_Ici, monotone_add_nat_of_le_succ, monotone_comp_ofDual_iff, monotone_dual_iff, monotone_int_of_le_succ, monotone_nat_of_le_succ, monotone_toDual_comp_iff, not_monotone_not_antitone_iff_exists_le_le, not_monotone_not_antitone_iff_exists_lt_lt, strictAntiOn_comp_ofDual_iff, strictAntiOn_dual_iff, strictAntiOn_toDual_comp_iff, strictAnti_comp_ofDual_iff, strictAnti_dual_iff, strictAnti_int_of_succ_lt, strictAnti_nat_of_succ_lt, strictAnti_toDual_comp_iff, strictMonoOn_comp_ofDual_iff, strictMonoOn_dual_iff, strictMonoOn_toDual_comp_iff, strictMono_comp_ofDual_iff, strictMono_dual_iff, strictMono_int_of_lt_succ, strictMono_nat_of_lt_succ, strictMono_toDual_comp_iff
137
Total137

Antitone

Theorems

NameKindAssumesProvesValidatesDepends On
dual πŸ“–mathematicalAntitoneOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”antitone_dual_iff
dual_left πŸ“–mathematicalAntitoneMonotone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
β€”monotone_comp_ofDual_iff
dual_right πŸ“–mathematicalAntitoneMonotone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
β€”monotone_toDual_comp_iff
eq_of_ge_of_le πŸ“–β€”Antitone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLE
β€”β€”le_antisymm
ne_of_lt_of_lt_int πŸ“–β€”Antitone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Int.instLinearOrder
Preorder.toLT
β€”β€”LT.lt.not_ge
reflect_lt
ne_of_lt_of_lt_nat πŸ“–β€”Antitone
Nat.instPreorder
Preorder.toLT
β€”β€”LT.lt.not_ge
reflect_lt
strictAnti_iff_injective πŸ“–mathematicalAntitone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
StrictAntiβ€”StrictAnti.injective
strictAnti_of_injective

AntitoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
dual πŸ“–mathematicalAntitoneOnOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”antitoneOn_dual_iff
dual_left πŸ“–mathematicalAntitoneOnMonotoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
β€”monotoneOn_comp_ofDual_iff
dual_right πŸ“–mathematicalAntitoneOnMonotoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
β€”monotoneOn_toDual_comp_iff
strictAntiOn_of_injOn πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
Set.InjOn
StrictAntiOnβ€”LE.le.lt_of_ne'
LT.lt.le
LT.lt.ne
strictAnti_iff_injOn πŸ“–mathematicalAntitoneOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
StrictAntiOn
Set.InjOn
β€”StrictAntiOn.injOn
strictAntiOn_of_injOn

Int

Theorems

NameKindAssumesProvesValidatesDepends On
exists_strictAnti πŸ“–mathematicalβ€”StrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
instLinearOrder
β€”exists_strictMono
OrderDual.instNonempty
OrderDual.noMinOrder
OrderDual.noMaxOrder
exists_strictMono πŸ“–mathematicalβ€”StrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
instLinearOrder
β€”Nat.exists_strictMono'
Nat.exists_strictAnti'
strictMono_int_of_lt_succ
rel_of_forall_rel_succ_of_le πŸ“–β€”β€”β€”β€”LE.le.eq_or_lt
refl
rel_of_forall_rel_succ_of_lt
rel_of_forall_rel_succ_of_lt πŸ“–β€”β€”β€”β€”trans

List

Theorems

NameKindAssumesProvesValidatesDepends On
foldl_monotone πŸ“–β€”Monotoneβ€”β€”β€”
foldl_strictMono πŸ“–β€”StrictMonoβ€”β€”β€”
foldr_monotone πŸ“–β€”Monotoneβ€”β€”β€”
foldr_strictMono πŸ“–β€”StrictMonoβ€”β€”β€”

Monotone

Theorems

NameKindAssumesProvesValidatesDepends On
dual πŸ“–mathematicalMonotoneOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”monotone_dual_iff
dual_left πŸ“–mathematicalMonotoneAntitone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
β€”antitone_comp_ofDual_iff
dual_right πŸ“–mathematicalMonotoneAntitone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
β€”antitone_toDual_comp_iff
eq_of_ge_of_le πŸ“–β€”Monotone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLE
β€”β€”le_antisymm
ne_of_lt_of_lt_int πŸ“–β€”Monotone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Int.instLinearOrder
Preorder.toLT
β€”β€”LT.lt.not_ge
reflect_lt
ne_of_lt_of_lt_nat πŸ“–β€”Monotone
Nat.instPreorder
Preorder.toLT
β€”β€”LT.lt.not_ge
reflect_lt
strictMono_iff_injective πŸ“–mathematicalMonotone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
StrictMonoβ€”StrictMono.injective
strictMono_of_injective

MonotoneOn

Theorems

NameKindAssumesProvesValidatesDepends On
dual πŸ“–mathematicalMonotoneOnOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”monotoneOn_dual_iff
dual_left πŸ“–mathematicalMonotoneOnAntitoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
β€”antitoneOn_comp_ofDual_iff
dual_right πŸ“–mathematicalMonotoneOnAntitoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
β€”antitoneOn_toDual_comp_iff
strictMonoOn_iff_injOn πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
StrictMonoOn
Set.InjOn
β€”StrictMonoOn.injOn
strictMonoOn_of_injOn
strictMonoOn_of_injOn πŸ“–mathematicalMonotoneOn
PartialOrder.toPreorder
Set.InjOn
StrictMonoOnβ€”LE.le.lt_of_ne
LT.lt.le
LT.lt.ne

Nat

Theorems

NameKindAssumesProvesValidatesDepends On
exists_strictAnti πŸ“–mathematicalβ€”StrictAnti
instPreorder
β€”exists_strictMono
OrderDual.instNonempty
OrderDual.noMaxOrder
exists_strictAnti' πŸ“–mathematicalβ€”StrictAnti
instPreorder
β€”exists_strictMono'
OrderDual.noMaxOrder
exists_strictMono πŸ“–mathematicalβ€”StrictMono
instPreorder
β€”exists_strictMono'
exists_strictMono' πŸ“–mathematicalβ€”StrictMono
instPreorder
β€”strictMono_nat_of_lt_succ
NoMaxOrder.exists_gt
exists_strictMono_subsequence πŸ“–mathematicalβ€”StrictMono
instPreorder
β€”exists_strictMono'
pow_monotoneOn πŸ“–mathematicalβ€”MonotoneOn
Prod.instPreorder
instPreorder
setOf
β€”LE.le.trans
pow_self_mono πŸ“–mathematicalβ€”Monotone
instPreorder
β€”monotone_nat_of_le_succ
LE.le.trans
pow_self_strictMonoOn πŸ“–mathematicalβ€”StrictMonoOn
instPreorder
setOf
β€”LT.lt.trans_le
LT.lt.le
rel_of_forall_rel_succ_of_le πŸ“–β€”β€”β€”β€”rel_of_forall_rel_succ_of_le_of_le
le_rfl
rel_of_forall_rel_succ_of_le_of_le πŸ“–β€”β€”β€”β€”LE.le.eq_or_lt
refl
rel_of_forall_rel_succ_of_le_of_lt
rel_of_forall_rel_succ_of_le_of_lt πŸ“–β€”β€”β€”β€”trans
LT.lt.le
LE.le.trans_lt
rel_of_forall_rel_succ_of_lt πŸ“–β€”β€”β€”β€”rel_of_forall_rel_succ_of_le_of_lt
le_rfl
stabilises_of_monotone πŸ“–β€”Monotone
instPreorder
β€”β€”Mathlib.Tactic.Contrapose.contrapose₁
Mathlib.Tactic.Push.not_and_eq
Mathlib.Tactic.Push.not_forall_eq
le_rfl
LE.le.trans

StrictAnti

Theorems

NameKindAssumesProvesValidatesDepends On
cmp_map_eq πŸ“–mathematicalStrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
cmp
Preorder.toLT
LinearOrder.toDecidableLT
β€”StrictAntiOn.cmp_map_eq
strictAntiOn
compares πŸ“–mathematicalStrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Ordering.Compares
Preorder.toLT
β€”StrictAntiOn.compares
strictAntiOn
dual πŸ“–mathematicalStrictAntiOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”strictAnti_dual_iff
dual_left πŸ“–mathematicalStrictAntiStrictMono
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
β€”strictMono_comp_ofDual_iff
dual_right πŸ“–mathematicalStrictAntiStrictMono
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
β€”strictMono_toDual_comp_iff
injective πŸ“–β€”StrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
β€”β€”compares
isMax_of_apply πŸ“–mathematicalStrictAnti
IsMin
Preorder.toLE
IsMaxβ€”of_not_not
not_isMax_iff
LT.lt.not_isMin
isMin_of_apply πŸ“–mathematicalStrictAnti
IsMax
Preorder.toLE
IsMinβ€”of_not_not
not_isMin_iff
LT.lt.not_isMax
ite πŸ“–β€”StrictAnti
Preorder.toLE
β€”β€”ite'
LE.le.trans_lt
ite' πŸ“–β€”StrictAnti
Preorder.toLT
β€”β€”StrictMono.ite'
dual_right
le_iff_ge πŸ“–mathematicalStrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLEβ€”StrictAntiOn.le_iff_ge
strictAntiOn
lt_iff_gt πŸ“–mathematicalStrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLTβ€”StrictAntiOn.lt_iff_gt
strictAntiOn
maximal_of_minimal_image πŸ“–β€”StrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLE
β€”β€”le_iff_ge
minimal_of_maximal_image πŸ“–β€”StrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLE
β€”β€”le_iff_ge
wellFoundedGT πŸ“–mathematicalStrictAntiWellFoundedGT
Preorder.toLT
β€”StrictMono.wellFoundedLT
wellFoundedLT πŸ“–mathematicalStrictAntiWellFoundedLT
Preorder.toLT
β€”StrictMono.wellFoundedLT
instWellFoundedLTOrderDualOfWellFoundedGT

StrictAntiOn

Theorems

NameKindAssumesProvesValidatesDepends On
cmp_map_eq πŸ“–mathematicalStrictAntiOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
cmp
Preorder.toLT
LinearOrder.toDecidableLT
β€”StrictMonoOn.cmp_map_eq
dual_right
compares πŸ“–mathematicalStrictAntiOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
Ordering.Compares
Preorder.toLT
β€”toDual_compares_toDual
StrictMonoOn.compares
dual_right
dual πŸ“–mathematicalStrictAntiOnOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”strictAntiOn_dual_iff
dual_left πŸ“–mathematicalStrictAntiOnStrictMonoOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
β€”strictMonoOn_comp_ofDual_iff
dual_right πŸ“–mathematicalStrictAntiOnStrictMonoOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
β€”strictMonoOn_toDual_comp_iff
eq_iff_eq πŸ“–β€”StrictAntiOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
β€”β€”StrictMonoOn.eq_iff_eq
dual_right
injOn πŸ“–mathematicalStrictAntiOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set.InjOnβ€”StrictMonoOn.injOn
dual_left
le_iff_ge πŸ“–mathematicalStrictAntiOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
Preorder.toLEβ€”StrictMonoOn.le_iff_le
dual_right
lt_iff_gt πŸ“–mathematicalStrictAntiOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
Preorder.toLTβ€”StrictMonoOn.lt_iff_lt
dual_right

StrictMono

Theorems

NameKindAssumesProvesValidatesDepends On
add_le_nat πŸ“–β€”StrictMono
Nat.instPreorder
β€”β€”le_refl
LE.le.trans_lt
cmp_map_eq πŸ“–mathematicalStrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
cmp
Preorder.toLT
LinearOrder.toDecidableLT
β€”StrictMonoOn.cmp_map_eq
strictMonoOn
compares πŸ“–mathematicalStrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Ordering.Compares
Preorder.toLT
β€”StrictMonoOn.compares
strictMonoOn
dual πŸ“–mathematicalStrictMonoOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”strictMono_dual_iff
dual_left πŸ“–mathematicalStrictMonoStrictAnti
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
β€”strictAnti_comp_ofDual_iff
dual_right πŸ“–mathematicalStrictMonoStrictAnti
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
β€”strictAnti_toDual_comp_iff
injective πŸ“–β€”StrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
β€”β€”compares
isMax_of_apply πŸ“–β€”StrictMono
IsMax
Preorder.toLE
β€”β€”of_not_not
not_isMax_iff
LT.lt.not_isMax
isMin_of_apply πŸ“–β€”StrictMono
IsMin
Preorder.toLE
β€”β€”of_not_not
not_isMin_iff
LT.lt.not_isMin
ite πŸ“–β€”StrictMono
Preorder.toLE
β€”β€”ite'
LT.lt.trans_le
ite' πŸ“–β€”StrictMono
Preorder.toLT
β€”β€”β€”
le_iff_le πŸ“–mathematicalStrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLEβ€”StrictMonoOn.le_iff_le
strictMonoOn
lt_iff_lt πŸ“–mathematicalStrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLTβ€”StrictMonoOn.lt_iff_lt
strictMonoOn
maximal_of_maximal_image πŸ“–β€”StrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLE
β€”β€”le_iff_le
minimal_of_minimal_image πŸ“–β€”StrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Preorder.toLE
β€”β€”le_iff_le
wellFoundedGT πŸ“–mathematicalStrictMonoWellFoundedGT
Preorder.toLT
β€”wellFoundedLT
instWellFoundedLTOrderDualOfWellFoundedGT
wellFoundedLT πŸ“–mathematicalStrictMonoWellFoundedLT
Preorder.toLT
β€”Subrelation.isWellFounded
instIsWellFoundedInvImage

StrictMonoOn

Theorems

NameKindAssumesProvesValidatesDepends On
cmp_map_eq πŸ“–mathematicalStrictMonoOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
cmp
Preorder.toLT
LinearOrder.toDecidableLT
β€”Ordering.Compares.cmp_eq
compares
cmp_compares
compares πŸ“–mathematicalStrictMonoOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
Ordering.Compares
Preorder.toLT
β€”lt_iff_lt
LE.le.antisymm
le_iff_le
Eq.le
dual πŸ“–mathematicalStrictMonoOnOrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”strictMonoOn_dual_iff
dual_left πŸ“–mathematicalStrictMonoOnStrictAntiOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
β€”strictAntiOn_comp_ofDual_iff
dual_right πŸ“–mathematicalStrictMonoOnStrictAntiOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
β€”strictAntiOn_toDual_comp_iff
eq_iff_eq πŸ“–β€”StrictMonoOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
β€”β€”le_antisymm
le_iff_le
Eq.le
Eq.ge
injOn πŸ“–mathematicalStrictMonoOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set.InjOnβ€”compares
le_iff_le πŸ“–mathematicalStrictMonoOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
Preorder.toLEβ€”le_of_not_gt
LT.lt.not_ge
LE.le.lt_or_eq_dec
LT.lt.le
le_rfl
lt_iff_lt πŸ“–mathematicalStrictMonoOn
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Set
Set.instMembership
Preorder.toLTβ€”lt_iff_le_not_ge
le_iff_le

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
antitoneOn_comp_ofDual_iff πŸ“–mathematicalβ€”AntitoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
MonotoneOn
β€”forallβ‚‚_swap
antitoneOn_dual_iff πŸ“–mathematicalβ€”AntitoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”antitoneOn_toDual_comp_iff
monotoneOn_comp_ofDual_iff
antitoneOn_nat_Ici_of_succ_le πŸ“–mathematicalPreorder.toLEAntitoneOn
Nat.instPreorder
setOf
β€”monotoneOn_nat_Ici_of_le_succ
antitoneOn_toDual_comp_iff πŸ“–mathematicalβ€”AntitoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
MonotoneOn
β€”β€”
antitone_add_nat_iff_antitoneOn_nat_Ici πŸ“–mathematicalβ€”Antitone
Nat.instPreorder
AntitoneOn
setOf
β€”monotone_add_nat_iff_monotoneOn_nat_Ici
antitone_add_nat_of_succ_le πŸ“–mathematicalPreorder.toLEAntitone
Nat.instPreorder
β€”monotone_add_nat_of_le_succ
antitone_comp_ofDual_iff πŸ“–mathematicalβ€”Antitone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
Monotone
β€”forall_swap
antitone_dual_iff πŸ“–mathematicalβ€”Antitone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”antitone_toDual_comp_iff
monotone_comp_ofDual_iff
antitone_int_of_succ_le πŸ“–mathematicalPreorder.toLEAntitone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Int.instLinearOrder
β€”Int.rel_of_forall_rel_succ_of_le
instReflGe
instIsTransGe
antitone_nat_of_succ_le πŸ“–mathematicalPreorder.toLEAntitone
Nat.instPreorder
β€”monotone_nat_of_le_succ
antitone_toDual_comp_iff πŸ“–mathematicalβ€”Antitone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
Monotone
β€”β€”
converges_of_monotone_of_bounded πŸ“–β€”Monotone
Nat.instPreorder
β€”β€”Mathlib.Tactic.Push.not_forall_eq
monotoneOn_comp_ofDual_iff πŸ“–mathematicalβ€”MonotoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
AntitoneOn
β€”forallβ‚‚_swap
monotoneOn_dual_iff πŸ“–mathematicalβ€”MonotoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”monotoneOn_toDual_comp_iff
antitoneOn_comp_ofDual_iff
monotoneOn_nat_Ici_of_le_succ πŸ“–mathematicalPreorder.toLEMonotoneOn
Nat.instPreorder
setOf
β€”Nat.rel_of_forall_rel_succ_of_le_of_le
instReflLe
instIsTransLe
monotoneOn_toDual_comp_iff πŸ“–mathematicalβ€”MonotoneOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
AntitoneOn
β€”β€”
monotone_add_nat_iff_monotoneOn_nat_Ici πŸ“–mathematicalβ€”Monotone
Nat.instPreorder
MonotoneOn
setOf
β€”β€”
monotone_add_nat_of_le_succ πŸ“–mathematicalPreorder.toLEMonotone
Nat.instPreorder
β€”Nat.rel_of_forall_rel_succ_of_le_of_le
instReflLe
instIsTransLe
monotone_comp_ofDual_iff πŸ“–mathematicalβ€”Monotone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
Antitone
β€”forall_swap
monotone_dual_iff πŸ“–mathematicalβ€”Monotone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”monotone_toDual_comp_iff
antitone_comp_ofDual_iff
monotone_int_of_le_succ πŸ“–mathematicalPreorder.toLEMonotone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Int.instLinearOrder
β€”Int.rel_of_forall_rel_succ_of_le
instReflLe
instIsTransLe
monotone_nat_of_le_succ πŸ“–mathematicalPreorder.toLEMonotone
Nat.instPreorder
β€”Nat.rel_of_forall_rel_succ_of_le
instReflLe
instIsTransLe
monotone_toDual_comp_iff πŸ“–mathematicalβ€”Monotone
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
Antitone
β€”β€”
not_monotone_not_antitone_iff_exists_le_le πŸ“–mathematicalβ€”Monotone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Antitone
Preorder.toLE
Preorder.toLT
β€”β€”
not_monotone_not_antitone_iff_exists_lt_lt πŸ“–mathematicalβ€”Monotone
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Antitone
Preorder.toLT
β€”Iff.and
Ne.le_iff_lt
strictAntiOn_comp_ofDual_iff πŸ“–mathematicalβ€”StrictAntiOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
StrictMonoOn
β€”forallβ‚‚_swap
strictAntiOn_dual_iff πŸ“–mathematicalβ€”StrictAntiOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”strictAntiOn_toDual_comp_iff
strictMonoOn_comp_ofDual_iff
strictAntiOn_toDual_comp_iff πŸ“–mathematicalβ€”StrictAntiOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
StrictMonoOn
β€”β€”
strictAnti_comp_ofDual_iff πŸ“–mathematicalβ€”StrictAnti
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
StrictMono
β€”forall_swap
strictAnti_dual_iff πŸ“–mathematicalβ€”StrictAnti
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”strictAnti_toDual_comp_iff
strictMono_comp_ofDual_iff
strictAnti_int_of_succ_lt πŸ“–mathematicalPreorder.toLTStrictAnti
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Int.instLinearOrder
β€”Int.rel_of_forall_rel_succ_of_lt
instIsTransGt
strictAnti_nat_of_succ_lt πŸ“–mathematicalPreorder.toLTStrictAnti
Nat.instPreorder
β€”strictMono_nat_of_lt_succ
strictAnti_toDual_comp_iff πŸ“–mathematicalβ€”StrictAnti
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
StrictMono
β€”β€”
strictMonoOn_comp_ofDual_iff πŸ“–mathematicalβ€”StrictMonoOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
StrictAntiOn
β€”forallβ‚‚_swap
strictMonoOn_dual_iff πŸ“–mathematicalβ€”StrictMonoOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”strictMonoOn_toDual_comp_iff
strictAntiOn_comp_ofDual_iff
strictMonoOn_toDual_comp_iff πŸ“–mathematicalβ€”StrictMonoOn
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
StrictAntiOn
β€”β€”
strictMono_comp_ofDual_iff πŸ“–mathematicalβ€”StrictMono
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.ofDual
StrictAnti
β€”forall_swap
strictMono_dual_iff πŸ“–mathematicalβ€”StrictMono
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
OrderDual.ofDual
β€”strictMono_toDual_comp_iff
strictAnti_comp_ofDual_iff
strictMono_int_of_lt_succ πŸ“–mathematicalPreorder.toLTStrictMono
PartialOrder.toPreorder
LinearOrder.toPartialOrder
Int.instLinearOrder
β€”Int.rel_of_forall_rel_succ_of_lt
instIsTransLt
strictMono_nat_of_lt_succ πŸ“–mathematicalPreorder.toLTStrictMono
Nat.instPreorder
β€”Nat.rel_of_forall_rel_succ_of_lt
instIsTransLt
strictMono_toDual_comp_iff πŸ“–mathematicalβ€”StrictMono
OrderDual
OrderDual.instPreorder
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
OrderDual.toDual
StrictAnti
β€”β€”

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