Documentation Verification Report

Operations

πŸ“ Source: Mathlib/Data/ENNReal/Operations.lean

Statistics

MetricCount
Definitions0
Theoremsadd_ne_top, Ico_eq_Iio, addLECancellable_iff_ne, addLeftReflectLT, add_biSup, add_biSup', add_eq_top, add_iInf, add_iInfβ‚‚, add_iSup, add_le_add_iff_left, add_le_add_iff_right, add_left_inj, add_lt_add, add_lt_add_iff_left, add_lt_add_iff_right, add_lt_add_left, add_lt_add_of_le_of_lt, add_lt_add_of_lt_of_le, add_lt_add_right, add_lt_top, add_ne_top, add_right_inj, add_sInf, add_sSup, add_sub_add_eq_sub_left, add_sub_add_eq_sub_right, add_sub_cancel_left, add_sub_cancel_right, biSup_add, biSup_add', biSup_add_biSup_le, biSup_add_biSup_le', cancel_coe, cancel_of_lt, cancel_of_lt', cancel_of_ne, coe_sub, eq_sub_of_add_eq, eq_sub_of_add_eq', eq_top_of_pow, exists_add_lt_of_add_lt, exists_lt_add_of_lt_add, iInf_add, iInf_add_iInf, iInf_add_iInf_of_monotone, iInf_gt_eq_self, iInfβ‚‚_add, iSup_add, iSup_add_iSup, iSup_add_iSup_le, iSup_add_iSup_of_monotone, iSup_eq_zero, iSup_lt_eq_self, iSup_natCast, iSup_sub, iSup_zero, image_coe_Icc, image_coe_Ici, image_coe_Ico, image_coe_Iic, image_coe_Iio, image_coe_Ioc, image_coe_Ioi, image_coe_Ioo, image_coe_uIcc, image_coe_uIoc, image_coe_uIoo, le_iInf_add_iInf, le_iInfβ‚‚_add_iInfβ‚‚, le_of_add_le_add_left, le_of_add_le_add_right, le_sub_iff_add_le_left, le_sub_iff_add_le_right, le_sub_of_add_le_left, le_sub_of_add_le_right, le_toReal_sub, lt_add_of_sub_lt_left, lt_add_of_sub_lt_right, lt_add_right, lt_top_of_mul_ne_top_left, lt_top_of_mul_ne_top_right, mem_Iio_self_add, mem_Ioo_self_sub_add, mul_eq_left, mul_eq_right, mul_eq_top, mul_le_mul_iff_left, mul_le_mul_iff_right, mul_le_mul_left, mul_le_mul_right, mul_left_inj, mul_left_strictMono, mul_lt_mul, mul_lt_mul_iff_left, mul_lt_mul_iff_right, mul_lt_mul_left, mul_lt_mul_left', mul_lt_mul_right, mul_lt_mul_right', mul_lt_top, mul_lt_top_iff, mul_ne_top, mul_pos, mul_pos_iff, mul_right_inj, mul_right_strictMono, mul_self_lt_top_iff, mul_sub, mul_top, mul_top', natCast_sub, not_lt_top, not_lt_zero, ofReal_iInf, ofReal_sub, pow_eq_top_iff, pow_le_pow_left, pow_le_pow_left_iff, pow_lt_pow_left, pow_lt_pow_left_iff, pow_lt_top, pow_lt_top_iff, pow_ne_top, pow_ne_top_iff, pow_ne_zero, pow_pos, pow_right_strictMono, sInf_add, sSup_add, sub_add_eq_add_sub, sub_eq_of_eq_add, sub_eq_of_eq_add', sub_eq_of_eq_add_rev, sub_eq_of_eq_add_rev', sub_eq_sInf, sub_eq_top_iff, sub_iInf, sub_iSup, sub_le_sub_iff_left, sub_lt_iff_lt_left, sub_lt_iff_lt_right, sub_lt_of_lt_add, sub_lt_of_sub_lt, sub_lt_self, sub_lt_self_iff, sub_mul, sub_ne_top, sub_ne_top_iff, sub_right_inj, sub_sub_cancel, sub_sub_sub_cancel_left, sub_top, toNNReal_add, toNNReal_iInf, toNNReal_iSup, toNNReal_sInf, toNNReal_sSup, toNNReal_sub, toReal_iInf, toReal_iSup, toReal_le_add, toReal_le_add', toReal_sInf, toReal_sSup, toReal_sub_of_le, top_mul, top_mul', top_mul_top, top_pow, top_sub, top_sub_coe
172
Total172

ENNReal

Theorems

NameKindAssumesProvesValidatesDepends On
Ico_eq_Iio πŸ“–mathematicalβ€”Set.Ico
ENNReal
PartialOrder.toPreorder
instPartialOrder
instZeroENNReal
Set.Iio
β€”Set.Ico_bot
addLECancellable_iff_ne πŸ“–mathematicalβ€”AddLECancellable
ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
β€”WithTop.addLECancellable_iff_ne_top
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftReflectLT
addLeftReflectLT πŸ“–mathematicalβ€”AddLeftReflectLT
ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
β€”WithTop.addLeftReflectLT
NNReal.addLeftReflectLT
add_biSup πŸ“–mathematicalSet.NonemptyENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Set
Set.instMembership
β€”add_biSup'
add_biSup' πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”iSup_subtype'
add_iSup
nonempty_subtype
add_eq_top πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.add_eq_top
add_iInf πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”add_comm
iInf_add
add_iInfβ‚‚ πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”add_iInf
add_iSup πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”eq_or_ne
top_add
ciSup_const
le_antisymm
add_le_of_le_tsub_left_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
instOrderedSub
le_iSup_of_le
le_self_add
iSup_le
le_sub_of_add_le_left
le_iSup
le_imp_le_of_le_of_le
le_refl
add_le_add_right
add_le_add_iff_left πŸ“–mathematicalβ€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_le_add_iff_left
NNReal.addLeftMono
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftReflectLT
add_le_add_iff_right πŸ“–mathematicalβ€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_le_add_iff_right
covariant_swap_add_of_covariant_add
NNReal.addLeftMono
IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT
AddRightCancelSemigroup.toIsRightCancelAdd
contravariant_swap_add_of_contravariant_add
NNReal.addLeftReflectLT
add_left_inj πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”AddLECancellable.inj_left
AddCommMagma.to_isCommutative
cancel_of_ne
add_lt_add πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_lt_add
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftMono
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
add_lt_add_iff_left πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_lt_add_iff_left
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftMono
NNReal.addLeftReflectLT
add_lt_add_iff_right πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_lt_add_iff_right
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
NNReal.addLeftMono
contravariant_swap_add_of_contravariant_add
NNReal.addLeftReflectLT
add_lt_add_left πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_lt_add_left
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftMono
add_lt_add_of_le_of_lt πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Preorder.toLT
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_lt_add_of_le_of_lt
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftMono
covariant_swap_add_of_covariant_add
add_lt_add_of_lt_of_le πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Preorder.toLE
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_lt_add_of_lt_of_le
NNReal.addLeftMono
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
add_lt_add_right πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.add_lt_add_right
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
NNReal.addLeftMono
add_lt_top πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.add_lt_top
add_ne_top πŸ“–β€”β€”β€”β€”add_lt_top
add_right_inj πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”cancel_of_ne
add_sInf πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
iInf
Set
Set.instMembership
β€”sInf_eq_iInf
add_iInfβ‚‚
add_sSup πŸ“–mathematicalSet.Nonempty
ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
iSup
Set
Set.instMembership
β€”sSup_eq_iSup
add_biSup
add_sub_add_eq_sub_left πŸ“–mathematicalENNReal
Top.top
instTopENNReal
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”add_comm
add_sub_add_eq_sub_right
add_sub_add_eq_sub_right πŸ“–mathematicalENNReal
Top.top
instTopENNReal
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”CanLift.prf
canLift
top_add
tsub_self
instCanonicallyOrderedAdd
instOrderedSub
top_sub
sub_top
add_tsub_add_eq_tsub_right
NNReal.instOrderedSub
NNReal.addLeftMono
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftReflectLT
add_sub_cancel_left πŸ“–mathematicalβ€”ENNReal
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”AddLECancellable.add_tsub_cancel_left
instOrderedSub
add_sub_cancel_right πŸ“–mathematicalβ€”ENNReal
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”AddLECancellable.add_tsub_cancel_right
instOrderedSub
biSup_add πŸ“–mathematicalSet.NonemptyENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Set
Set.instMembership
β€”biSup_add'
biSup_add' πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”add_comm
add_biSup'
iSup_congr_Prop
biSup_add_biSup_le πŸ“–mathematicalSet.Nonempty
ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Set
Set.instMembership
β€”biSup_add_biSup_le'
biSup_add_biSup_le' πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”biSup_add'
iSup_congr_Prop
add_biSup'
iSupβ‚‚_le
cancel_coe πŸ“–mathematicalβ€”AddLECancellable
ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
ofNNReal
β€”cancel_of_ne
coe_ne_top
cancel_of_lt πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Top.top
instTopENNReal
AddLECancellable
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Preorder.toLE
β€”cancel_of_ne
LT.lt.ne
cancel_of_lt' πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
AddLECancellable
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Preorder.toLE
β€”cancel_of_ne
LT.lt.ne_top
cancel_of_ne πŸ“–mathematicalβ€”AddLECancellable
ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
β€”addLECancellable_iff_ne
coe_sub πŸ“–mathematicalβ€”ofNNReal
NNReal
NNReal.instSub
ENNReal
instSub
β€”WithTop.coe_sub
eq_sub_of_add_eq πŸ“–mathematicalENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.eq_tsub_of_add_eq
instOrderedSub
cancel_of_ne
eq_sub_of_add_eq' πŸ“–mathematicalENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.eq_tsub_of_add_eq'
instOrderedSub
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
cancel_of_ne
eq_top_of_pow πŸ“–β€”ENNReal
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”β€”WithTop.eq_top_of_pow
NNReal.instNoZeroDivisors
exists_add_lt_of_add_lt πŸ“–β€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”β€”Mathlib.Tactic.Contrapose.contrapose₁
Mathlib.Tactic.Push.not_and_eq
iInf_congr_Prop
iInf_gt_eq_self
le_iInfβ‚‚_add_iInfβ‚‚
exists_lt_add_of_lt_add πŸ“–β€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”β€”Mathlib.Tactic.Contrapose.contrapose₁
Mathlib.Tactic.Push.not_and_eq
iSup_lt_eq_self
biSup_add_biSup_le'
Ne.bot_lt
iInf_add πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”le_antisymm
le_iInf
add_le_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
iInf_le
le_rfl
tsub_le_iff_right
instOrderedSub
iInf_add_iInf πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”le_iInfβ‚‚
iInf_le_of_le
iInf_add
add_iInf
le_antisymm
le_iInf
add_le_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
iInf_le
iInf_add_iInf_of_monotone πŸ“–mathematicalMonotone
ENNReal
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”iInf_add_iInf
add_le_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
exists_le_le
iInf_gt_eq_self πŸ“–mathematicalβ€”iInf
ENNReal
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
β€”le_antisymm
le_of_forall_gt
exists_between
instDenselyOrdered
LE.le.trans_lt
iInfβ‚‚_le_of_le
le_rfl
le_iInfβ‚‚
LT.lt.le
iInfβ‚‚_add πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”add_comm
add_iInfβ‚‚
iSup_add πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”add_comm
add_iSup
iSup_add_iSup πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”isEmpty_or_nonempty
iSup_of_empty
zero_add
le_antisymm
iSup_add_iSup_le
le_iSup_of_le
iSup_le
add_le_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
le_iSup
iSup_add_iSup_le πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”iSup_add
add_iSup
iSupβ‚‚_le
iSup_add_iSup_of_monotone πŸ“–mathematicalMonotone
ENNReal
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”iSup_add_iSup
add_le_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
exists_ge_ge
iSup_eq_zero πŸ“–mathematicalβ€”iSup
ENNReal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
instZeroENNReal
β€”iSup_eq_bot
iSup_lt_eq_self πŸ“–mathematicalβ€”iSup
ENNReal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
β€”le_antisymm
iSupβ‚‚_le
LT.lt.le
le_of_forall_lt
exists_between
instDenselyOrdered
LT.lt.trans_le
le_iSupβ‚‚_of_le
le_rfl
iSup_natCast πŸ“–mathematicalβ€”iSup
ENNReal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
instAddCommMonoidWithOneENNReal
Top.top
instTopENNReal
β€”iSup_eq_top
exists_nat_gt
lt_top_iff_ne_top
iSup_sub πŸ“–mathematicalβ€”ENNReal
instSub
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”le_antisymm
tsub_le_iff_right
instOrderedSub
iSup_le
le_iSup
tsub_le_tsub
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
le_refl
iSup_zero πŸ“–mathematicalβ€”iSup
ENNReal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
instZeroENNReal
β€”β€”
image_coe_Icc πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.Icc
PartialOrder.toPreorder
instPartialOrderNNReal
instPartialOrder
β€”WithTop.image_coe_Icc
image_coe_Ici πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.Ici
PartialOrder.toPreorder
instPartialOrderNNReal
Set.Ico
instPartialOrder
Top.top
instTopENNReal
β€”WithTop.image_coe_Ici
image_coe_Ico πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.Ico
PartialOrder.toPreorder
instPartialOrderNNReal
instPartialOrder
β€”WithTop.image_coe_Ico
image_coe_Iic πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.Iic
PartialOrder.toPreorder
instPartialOrderNNReal
instPartialOrder
β€”WithTop.image_coe_Iic
image_coe_Iio πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.Iio
PartialOrder.toPreorder
instPartialOrderNNReal
instPartialOrder
β€”WithTop.image_coe_Iio
image_coe_Ioc πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.Ioc
PartialOrder.toPreorder
instPartialOrderNNReal
instPartialOrder
β€”WithTop.image_coe_Ioc
image_coe_Ioi πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.Ioi
PartialOrder.toPreorder
instPartialOrderNNReal
Set.Ioo
instPartialOrder
Top.top
instTopENNReal
β€”WithTop.image_coe_Ioi
image_coe_Ioo πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.Ioo
PartialOrder.toPreorder
instPartialOrderNNReal
instPartialOrder
β€”WithTop.image_coe_Ioo
image_coe_uIcc πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.uIcc
ConditionallyCompleteLattice.toLattice
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
NNReal.instConditionallyCompleteLinearOrderBot
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”image_coe_Icc
image_coe_uIoc πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.uIoc
NNReal.instLinearOrder
instLinearOrder
β€”image_coe_Ioc
image_coe_uIoo πŸ“–mathematicalβ€”Set.image
NNReal
ENNReal
ofNNReal
Set.uIoo
NNReal.instLinearOrder
instLinearOrder
β€”image_coe_Ioo
le_iInf_add_iInf πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”iInf_add
add_iInf
le_iInfβ‚‚
le_iInfβ‚‚_add_iInfβ‚‚ πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”iInfβ‚‚_add
add_iInfβ‚‚
le_iInfβ‚‚
le_of_add_le_add_left πŸ“–β€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”β€”WithTop.le_of_add_le_add_left
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftReflectLT
le_of_add_le_add_right πŸ“–β€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”β€”WithTop.le_of_add_le_add_right
IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT
AddRightCancelSemigroup.toIsRightCancelAdd
contravariant_swap_add_of_contravariant_add
NNReal.addLeftReflectLT
le_sub_iff_add_le_left πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”add_le_of_le_tsub_left_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
instOrderedSub
le_sub_of_add_le_left
le_sub_iff_add_le_right πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”add_le_of_le_tsub_right_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
instOrderedSub
le_sub_of_add_le_right
le_sub_of_add_le_left πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.le_tsub_of_add_le_left
instOrderedSub
cancel_of_ne
le_sub_of_add_le_right πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.le_tsub_of_add_le_right
instOrderedSub
cancel_of_ne
le_toReal_sub πŸ“–mathematicalβ€”Real
Real.instLE
Real.instSub
toReal
ENNReal
instSub
β€”CanLift.prf
canLift
zero_sub
top_sub
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
le_max_left
lt_add_of_sub_lt_left πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”eq_or_ne
top_add
lt_top_iff_ne_top
AddLECancellable.lt_add_of_tsub_lt_left
instOrderedSub
cancel_of_ne
lt_add_of_sub_lt_right πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”lt_add_of_sub_lt_left
add_comm
lt_add_right πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”add_zero
add_lt_add_iff_left
pos_iff_ne_zero
instCanonicallyOrderedAdd
lt_top_of_mul_ne_top_left πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Top.top
instTopENNReal
β€”lt_top_iff_ne_top
mul_eq_top
lt_top_of_mul_ne_top_right πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Top.top
instTopENNReal
β€”lt_top_of_mul_ne_top_left
mul_comm
mem_Iio_self_add πŸ“–mathematicalβ€”ENNReal
Set
Set.instMembership
Set.Iio
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”lt_add_right
mem_Ioo_self_sub_add πŸ“–mathematicalβ€”ENNReal
Set
Set.instMembership
Set.Ioo
PartialOrder.toPreorder
instPartialOrder
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”sub_lt_self
lt_add_right
mul_eq_left πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
instAddCommMonoidWithOneENNReal
β€”mul_one
mul_eq_right πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
instAddCommMonoidWithOneENNReal
β€”one_mul
mul_eq_top πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.mul_eq_top_iff
mul_le_mul_iff_left πŸ“–mathematicalβ€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”StrictMono.le_iff_le
mul_left_strictMono
mul_le_mul_iff_right πŸ“–mathematicalβ€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”StrictMono.le_iff_le
mul_right_strictMono
mul_le_mul_left πŸ“–mathematicalβ€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”mul_le_mul_iff_right
mul_le_mul_right πŸ“–mathematicalβ€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”mul_le_mul_iff_left
mul_left_inj πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”mul_comm
mul_left_strictMono πŸ“–mathematicalβ€”StrictMono
ENNReal
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.mul_left_strictMono
IsStrictOrderedRing.toMulPosStrictMono
NNReal.instIsStrictOrderedRing
pos_iff_ne_zero
WithTop.canonicallyOrderedAdd
NNReal.instCanonicallyOrderedAdd
mul_lt_mul πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.mul_lt_mul
NNReal.instCanonicallyOrderedAdd
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
mul_lt_mul_iff_left πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”StrictMono.lt_iff_lt
mul_left_strictMono
mul_lt_mul_iff_right πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”StrictMono.lt_iff_lt
mul_right_strictMono
mul_lt_mul_left πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”mul_right_strictMono
mul_comm
mul_lt_mul_left' πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”mul_lt_mul_right
mul_lt_mul_right πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”mul_right_strictMono
mul_lt_mul_right' πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”mul_lt_mul_left
mul_lt_top πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Top.top
instTopENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.mul_lt_top
mul_lt_top_iff πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
instZeroENNReal
β€”lt_top_of_mul_ne_top_left
LT.lt.ne
lt_top_of_mul_ne_top_right
mul_lt_top
MulZeroClass.zero_mul
MulZeroClass.mul_zero
mul_ne_top πŸ“–β€”β€”β€”β€”WithTop.mul_ne_top
mul_pos πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
instZeroENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”mul_pos_iff
pos_iff_ne_zero
instCanonicallyOrderedAdd
mul_pos_iff πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
instZeroENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”CanonicallyOrderedAdd.mul_pos
instCanonicallyOrderedAdd
instNoZeroDivisors
mul_right_inj πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”StrictMono.injective
mul_right_strictMono
mul_right_strictMono πŸ“–mathematicalβ€”StrictMono
ENNReal
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.mul_right_strictMono
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
pos_iff_ne_zero
WithTop.canonicallyOrderedAdd
NNReal.instCanonicallyOrderedAdd
mul_self_lt_top_iff πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”mul_lt_top_iff
zero_lt_top
mul_sub πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSub
β€”mul_comm
sub_mul
mul_top πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.mul_top
mul_top' πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
instZeroENNReal
LinearOrder.toDecidableEq
instLinearOrder
β€”WithTop.mul_top'
natCast_sub πŸ“–mathematicalβ€”ENNReal
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
instAddCommMonoidWithOneENNReal
instSub
β€”coe_natCast
Nat.cast_tsub
NNReal.instIsOrderedRing
NNReal.instCanonicallyOrderedAdd
NNReal.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftReflectLT
coe_sub
not_lt_top πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Top.top
instTopENNReal
β€”lt_top_iff_ne_top
not_lt_zero πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
instZeroENNReal
β€”instCanonicallyOrderedAdd
ofReal_iInf πŸ“–mathematicalβ€”ofReal
iInf
Real
Real.instInfSet
ENNReal
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
β€”em
iInf_eq_bot
ofReal_of_nonpos
bot_eq_zero'
instCanonicallyOrderedAdd
Real.iInf_nonpos'
le_of_not_ge
eq_of_forall_le_iff
eq_or_ne
le_iInf_iff
le_ofReal_iff_toReal_le
Real.iInf_nonneg
le_ciInf_iff
ofReal_sub πŸ“–mathematicalReal
Real.instLE
Real.instZero
ofReal
Real.instSub
ENNReal
instSub
β€”le_total
ofReal_of_nonpos
sub_nonpos_of_le
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
tsub_eq_zero_of_le
instCanonicallyOrderedAdd
instOrderedSub
ofReal_le_ofReal
eq_sub_of_add_eq
ofReal_ne_top
ofReal_add
sub_nonneg_of_le
sub_add_cancel
pow_eq_top_iff πŸ“–mathematicalβ€”ENNReal
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.pow_eq_top_iff
NNReal.instNoZeroDivisors
pow_le_pow_left πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
β€”pow_le_pow_left'
IsOrderedMonoid.toMulLeftMono
instIsOrderedMonoid
covariant_swap_mul_of_covariant_mul
pow_le_pow_left_iff πŸ“–mathematicalβ€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
β€”StrictMono.le_iff_le
pow_right_strictMono
pow_lt_pow_left πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
β€”pow_lt_pow_left_iff
pow_lt_pow_left_iff πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
β€”StrictMono.lt_iff_lt
pow_right_strictMono
pow_lt_top πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Top.top
instTopENNReal
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.pow_lt_top
NNReal.instNoZeroDivisors
pow_lt_top_iff πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.pow_lt_top_iff
NNReal.instNoZeroDivisors
pow_ne_top πŸ“–β€”β€”β€”β€”WithTop.pow_ne_top
NNReal.instNoZeroDivisors
pow_ne_top_iff πŸ“–β€”β€”β€”β€”WithTop.pow_ne_top_iff
NNReal.instNoZeroDivisors
pow_ne_zero πŸ“–β€”β€”β€”β€”instCanonicallyOrderedAdd
pow_pos
pow_pos πŸ“–mathematicalENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
instZeroENNReal
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
β€”CanonicallyOrderedAdd.pow_pos
instCanonicallyOrderedAdd
instNoZeroDivisors
pow_right_strictMono πŸ“–mathematicalβ€”StrictMono
ENNReal
PartialOrder.toPreorder
instPartialOrder
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
β€”WithTop.pow_right_strictMono
NNReal.instCanonicallyOrderedAdd
LinearOrderedCommMonoidWithZero.toPosMulStrictMono
NNReal.instNoZeroDivisors
sInf_add πŸ“–mathematicalβ€”ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
iInf
Set
Set.instMembership
β€”sInf_eq_iInf
iInf_add
sSup_add πŸ“–mathematicalSet.Nonempty
ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
SupSet.sSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
iSup
Set
Set.instMembership
β€”sSup_eq_iSup
biSup_add
sub_add_eq_add_sub πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSub
β€”add_top
eq_sub_of_add_eq
add_assoc
add_comm
tsub_add_cancel_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
instOrderedSub
sub_eq_of_eq_add πŸ“–mathematicalENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.tsub_eq_of_eq_add
instOrderedSub
cancel_of_ne
sub_eq_of_eq_add' πŸ“–mathematicalENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.tsub_eq_of_eq_add'
instOrderedSub
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
cancel_of_ne
sub_eq_of_eq_add_rev πŸ“–mathematicalENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.tsub_eq_of_eq_add_rev
instOrderedSub
cancel_of_ne
sub_eq_of_eq_add_rev' πŸ“–mathematicalENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.tsub_eq_of_eq_add_rev'
instOrderedSub
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
cancel_of_ne
sub_eq_sInf πŸ“–mathematicalβ€”ENNReal
instSub
InfSet.sInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
setOf
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”le_antisymm
le_sInf
tsub_le_iff_right
instOrderedSub
sInf_le
Set.mem_setOf
le_tsub_add
sub_eq_top_iff πŸ“–mathematicalβ€”ENNReal
instSub
Top.top
instTopENNReal
β€”WithTop.sub_eq_top_iff
sub_iInf πŸ“–mathematicalβ€”ENNReal
instSub
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
β€”eq_of_forall_ge_iff
tsub_le_iff_right
instOrderedSub
add_comm
iInf_add
sub_iSup πŸ“–mathematicalβ€”ENNReal
instSub
iSup
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
iInf
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
β€”em
tsub_eq_zero_iff_le
instCanonicallyOrderedAdd
instOrderedSub
le_iSup_of_le
LT.lt.le
iInf_eq_bot
tsub_eq_zero_of_le
bot_eq_zero
le_antisymm
le_iInf
tsub_le_tsub_left
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
le_iSup
le_sub_of_add_le_left
ne_top_of_le_ne_top
iSup_le
add_le_of_le_tsub_right_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
iInf_le_of_le
tsub_le_self
sub_sub_cancel
iInf_le
sub_le_sub_iff_left πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSubβ€”AddLECancellable.tsub_le_tsub_iff_left
instCanonicallyOrderedAdd
instOrderedSub
cancel_of_ne
ne_top_of_le_ne_top
sub_lt_iff_lt_left πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Preorder.toLT
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”AddLECancellable.tsub_lt_iff_left
CanonicallyOrderedAdd.toExistsAddOfLE
instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
instOrderedSub
cancel_of_ne
sub_lt_iff_lt_right πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Preorder.toLT
instSub
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
β€”AddLECancellable.tsub_lt_iff_right
CanonicallyOrderedAdd.toExistsAddOfLE
instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
instOrderedSub
cancel_of_ne
sub_lt_of_lt_add πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Preorder.toLT
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSubβ€”AddLECancellable.tsub_lt_iff_right
CanonicallyOrderedAdd.toExistsAddOfLE
instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
instOrderedSub
cancel_of_lt'
LE.le.trans_lt
sub_lt_of_sub_lt πŸ“–β€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Preorder.toLT
instSub
β€”β€”sub_lt_of_lt_add
lt_add_of_sub_lt_right
add_comm
sub_lt_self πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
instSub
β€”AddLECancellable.tsub_lt_self
instCanonicallyOrderedAdd
instOrderedSub
cancel_of_ne
pos_iff_ne_zero
sub_lt_self_iff πŸ“–mathematicalβ€”ENNReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
instSub
instZeroENNReal
β€”AddLECancellable.tsub_lt_self_iff
instCanonicallyOrderedAdd
instOrderedSub
cancel_of_ne
sub_mul πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
instSub
β€”le_or_gt
tsub_eq_zero_of_le
instCanonicallyOrderedAdd
instOrderedSub
MulZeroClass.zero_mul
mul_left_mono
covariant_swap_mul_of_covariant_mul
IsOrderedMonoid.toMulLeftMono
instIsOrderedMonoid
eq_or_lt_of_le
zero_le
tsub_zero
AddLECancellable.tsub_mul
LE.total
cancel_of_ne
mul_ne_top
LT.lt.ne_top
sub_ne_top πŸ“–β€”β€”β€”β€”sub_eq_top_iff
sub_ne_top_iff πŸ“–mathematicalβ€”Top.top
ENNReal
instTopENNReal
β€”WithTop.sub_ne_top_iff
sub_right_inj πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSubβ€”instCanonicallyOrderedAdd
instOrderedSub
cancel_of_ne
ne_top_of_le_ne_top
sub_sub_cancel πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSubβ€”AddLECancellable.tsub_tsub_cancel_of_le
CanonicallyOrderedAdd.toExistsAddOfLE
instCanonicallyOrderedAdd
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoid
instOrderedSub
cancel_of_ne
sub_ne_top
sub_sub_sub_cancel_left πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSubβ€”ne_top_of_le_ne_top
CanLift.prf
canLift
sub_top
zero_tsub
instCanonicallyOrderedAdd
instOrderedSub
tsub_tsub_tsub_cancel_left
CanonicallyOrderedAdd.toExistsAddOfLE
NNReal.instCanonicallyOrderedAdd
NNReal.addLeftMono
NNReal.instOrderedSub
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
NNReal.addLeftReflectLT
sub_top πŸ“–mathematicalβ€”ENNReal
instSub
Top.top
instTopENNReal
instZeroENNReal
β€”WithTop.sub_top
toNNReal_add πŸ“–mathematicalβ€”toNNReal
ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
NNReal
instSemiringNNReal
β€”CanLift.prf
canLift
toNNReal_iInf πŸ“–mathematicalβ€”toNNReal
iInf
ENNReal
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
NNReal
NNReal.instConditionallyCompleteLinearOrderBot
β€”isEmpty_or_nonempty
iInf_of_empty
toNNReal_top
NNReal.iInf_empty
CanLift.prf
Pi.canLift
canLift
toNNReal_iSup πŸ“–mathematicalβ€”toNNReal
iSup
ENNReal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
NNReal
NNReal.instConditionallyCompleteLinearOrderBot
β€”CanLift.prf
Pi.canLift
canLift
coe_iSup
toNNReal_coe
NNReal.iSup_of_not_bddAbove
iSup_coe_eq_top
toNNReal_top
toNNReal_sInf πŸ“–mathematicalβ€”toNNReal
InfSet.sInf
ENNReal
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
NNReal
NNReal.instConditionallyCompleteLinearOrderBot
Set.image
β€”Subtype.range_coe_subtype
toNNReal_iInf
toNNReal_sSup πŸ“–mathematicalβ€”toNNReal
SupSet.sSup
ENNReal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
NNReal
NNReal.instConditionallyCompleteLinearOrderBot
Set.image
β€”Subtype.range_coe_subtype
toNNReal_iSup
toNNReal_sub πŸ“–mathematicalβ€”toNNReal
ENNReal
instSub
NNReal
NNReal.instSub
β€”CanLift.prf
canLift
top_sub
zero_tsub
NNReal.instCanonicallyOrderedAdd
NNReal.instOrderedSub
toReal_iInf πŸ“–mathematicalβ€”toReal
iInf
ENNReal
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Real
Real.instInfSet
β€”toNNReal_iInf
NNReal.coe_iInf
toReal_iSup πŸ“–mathematicalβ€”toReal
iSup
ENNReal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Real
Real.instSupSet
β€”toNNReal_iSup
NNReal.coe_iSup
toReal_le_add πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Real
Real.instLE
toReal
Real.instAdd
β€”toReal_le_add'
toReal_le_add' πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
Real
Real.instLE
toReal
Real.instAdd
β€”le_trans
toReal_mono'
toReal_add_le
toReal_sInf πŸ“–mathematicalβ€”toReal
InfSet.sInf
ENNReal
ConditionallyCompletePartialOrderInf.toInfSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderInf
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Real
Real.instInfSet
Set.image
β€”toNNReal_sInf
NNReal.coe_sInf
Set.image_image
Set.image_congr
toReal_sSup πŸ“–mathematicalβ€”toReal
SupSet.sSup
ENNReal
ConditionallyCompletePartialOrderSup.toSupSet
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice
ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder
CompleteLinearOrder.toConditionallyCompleteLinearOrderBot
instCompleteLinearOrder
Real
Real.instSupSet
Set.image
β€”toNNReal_sSup
NNReal.coe_sSup
Set.image_image
Set.image_congr
toReal_sub_of_le πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
toReal
instSub
Real
Real.instSub
β€”toNNReal_sub
ne_top_of_le_ne_top
NNReal.coe_sub
toNNReal_mono
top_mul πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.top_mul
top_mul' πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
instZeroENNReal
LinearOrder.toDecidableEq
instLinearOrder
β€”WithTop.top_mul'
top_mul_top πŸ“–mathematicalβ€”ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.top_mul_top
top_pow πŸ“–mathematicalβ€”ENNReal
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiring
Top.top
instTopENNReal
β€”WithTop.top_pow
NNReal.instNoZeroDivisors
top_sub πŸ“–mathematicalβ€”ENNReal
instSub
Top.top
instTopENNReal
β€”CanLift.prf
canLift
top_sub_coe
top_sub_coe πŸ“–mathematicalβ€”ENNReal
instSub
Top.top
instTopENNReal
ofNNReal
β€”β€”

ENNReal.Finiteness

Theorems

NameKindAssumesProvesValidatesDepends On
add_ne_top πŸ“–β€”β€”β€”β€”ENNReal.add_ne_top

---

← Back to Index