Documentation Verification Report

Operations

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

Statistics

MetricCount
DefinitionsinstHasDistribNeg, instInvolutiveNeg, instNeg, instSubNegZeroMonoid, neg, negOrderIso, recENNReal, evalERealAdd, evalERealMul
9
TheoremstoEReal_sub, addLECancellable_coe, add_bot, add_eq_bot_iff, add_le_of_forall_lt, add_le_of_le_sub, add_lt_add, add_lt_add_left_coe, add_lt_add_of_lt_of_le, add_lt_add_of_lt_of_le', add_lt_add_right_coe, add_lt_of_lt_sub, add_lt_top, add_ne_bot_iff, add_ne_top, add_ne_top_iff_ne_top_left, add_ne_top_iff_ne_top_right, add_ne_top_iff_ne_topβ‚‚, add_ne_top_iff_of_ne_bot_of_ne_top, add_pos, add_pos_of_pos_of_nonneg, add_sub_cancel_left, add_sub_cancel_right, add_top_iff_ne_bot, add_top_of_ne_bot, bot_add, bot_lt_add_iff, bot_mul_bot, bot_mul_coe_of_neg, bot_mul_coe_of_pos, bot_mul_of_neg, bot_mul_of_pos, bot_mul_top, bot_sub, coe_add_top, coe_ennreal_mul_top, coe_mul_bot_of_neg, coe_mul_bot_of_pos, coe_mul_top_of_neg, coe_mul_top_of_pos, coe_neg, coe_real_ereal_eq_coe_toNNReal_sub_coe_toNNReal, coe_sub, coe_sub_bot, coe_zsmul, ge_of_forall_gt_iff_ge, inductionβ‚‚_neg_left, inductionβ‚‚_symm_neg, instNoZeroDivisors, le_add_of_forall_gt, le_neg, le_neg_of_le_neg, le_of_forall_lt_iff_le, le_sub_iff_add_le, left_distrib_of_nonneg, left_distrib_of_nonneg_of_ne_top, lt_neg_comm, lt_neg_of_lt_neg, lt_sub_iff_add_lt, mul_bot_of_neg, mul_bot_of_pos, mul_eq_bot, mul_eq_top, mul_ne_bot, mul_ne_top, mul_neg_iff, mul_nonneg, mul_nonneg_iff, mul_nonpos_iff, mul_pos, mul_pos_iff, mul_top_of_neg, mul_top_of_pos, neg_add, neg_bot, neg_eq_bot_iff, neg_eq_top_iff, neg_eq_zero_iff, neg_le, neg_le_neg_iff, neg_le_of_neg_le, neg_le_zero, neg_lt_comm, neg_lt_neg_iff, neg_lt_of_neg_lt, neg_lt_zero, neg_mul, neg_nonneg, neg_pos, neg_strictAnti, neg_sub, neg_top, nsmul_eq_mul, recENNReal_coe_ennreal, right_distrib_of_nonneg, right_distrib_of_nonneg_of_ne_top, sub_add_cancel, sub_add_cancel_left, sub_add_cancel_right, sub_bot, sub_le_iff_le_add, sub_le_of_le_add, sub_le_of_le_add', sub_le_sub, sub_lt_iff, sub_lt_of_lt_add, sub_lt_of_lt_add', sub_lt_sub_of_lt_of_le, sub_neg, sub_nonneg, sub_nonpos, sub_pos, sub_self, sub_self_le_zero, sub_top, toENNReal_add, toENNReal_add_le, toENNReal_mul, toENNReal_mul', toENNReal_sub, toReal_add, toReal_mul, toReal_neg_eq, toReal_sub, top_add_coe, top_add_iff_ne_bot, top_add_of_ne_bot, top_add_top, top_mul_bot, top_mul_coe_ennreal, top_mul_coe_of_neg, top_mul_coe_of_pos, top_mul_of_neg, top_mul_of_pos, top_mul_top, top_sub, top_sub_bot, top_sub_coe
138
Total147

ENNReal

Theorems

NameKindAssumesProvesValidatesDepends On
toEReal_sub πŸ“–mathematicalENNReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
toEReal
instSub
EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
EReal.instSubNegZeroMonoid
β€”CanLift.prf
canLift
top_sub
EReal.top_sub
NNReal.coe_sub

EReal

Definitions

NameCategoryTheorems
instHasDistribNeg πŸ“–CompOpβ€”
instInvolutiveNeg πŸ“–CompOpβ€”
instNeg πŸ“–CompOp
42 mathmath: neg_nonneg, abs_neg, neg_strictAnti, neg_lt_comm, neg_eq_top_iff, neg_le_neg_iff, coe_neg, sub_add_cancel_left, neg_sub, abs_mul_sign, limsup_neg, ExpGrowth.expGrowthInf_inv, ExpGrowth.expGrowthSup_inv, neg_eq_zero_iff, min_neg_neg, inv_neg, neg_add, LinearGrowth.linearGrowthSup_inv, toReal_neg_eq, coe_coe_sign, neg_lt_zero, le_neg, neg_le_zero, neg_eq_bot_iff, liminf_neg, max_neg_neg, neg_pos, lt_neg_comm, sub_add_cancel_right, sign_mul_inv_abs, sign_mul_abs, sign_neg, neg_le, ENNReal.log_inv, neg_mul, instContinuousNeg, neg_top, sign_mul_inv_abs', neg_bot, exp_neg, neg_lt_neg_iff, LinearGrowth.linearGrowthInf_neg
instSubNegZeroMonoid πŸ“–CompOp
36 mathmath: sub_nonneg, sub_top, sub_lt_sub_of_lt_of_le, top_sub, sub_self, sub_add_cancel_left, neg_sub, top_sub_bot, coe_sub, coe_zsmul, bot_sub, sub_add_cancel, neg_add, add_sub_cancel_left, top_sub_coe, sub_lt_iff, toENNReal_sub, sub_le_of_le_add', sub_nonpos, add_sub_cancel_right, sub_self_le_zero, sub_neg, sub_bot, lt_sub_iff_add_lt, ENNReal.toEReal_sub, sub_le_sub, sub_add_cancel_right, sub_pos, sub_le_iff_le_add, coe_real_ereal_eq_coe_toNNReal_sub_coe_toNNReal, coe_sub_bot, sub_lt_of_lt_add', toReal_sub, sub_lt_of_lt_add, le_sub_iff_add_le, sub_le_of_le_add
neg πŸ“–CompOpβ€”
negOrderIso πŸ“–CompOpβ€”
recENNReal πŸ“–CompOp
1 mathmath: recENNReal_coe_ennreal

Theorems

NameKindAssumesProvesValidatesDepends On
addLECancellable_coe πŸ“–mathematicalβ€”AddLECancellable
EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
Real.toEReal
β€”le_top
bot_le
add_bot
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
AddLeftCancelSemigroup.toIsLeftCancelAdd
contravariant_lt_of_covariant_le
add_bot πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Bot.bot
instBotEReal
β€”WithBot.add_bot
add_eq_bot_iff πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Bot.bot
instBotEReal
β€”WithBot.add_eq_bot
add_le_of_forall_lt πŸ“–β€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”β€”le_of_forall_lt_imp_le_of_dense
instDenselyOrderedEReal
LE.le.trans
LT.lt.le
add_le_of_le_sub πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”neg_neg
sub_le_of_le_add
add_lt_add πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”eq_or_ne
bot_add
LE.le.trans_lt
bot_le
CanLift.prf
canLift
LT.lt.ne_top
add_lt_add_left_coe
add_le_add_left
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoidEReal
le_of_lt
add_lt_add_left_coe πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Real.toEReal
β€”add_comm
add_lt_add_right_coe
add_lt_add_of_lt_of_le πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
Preorder.toLE
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”add_lt_add_of_lt_of_le'
ne_bot_of_le_ne_bot
add_lt_add_of_lt_of_le' πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
Preorder.toLE
Bot.bot
instBotEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”LE.le.eq_or_lt
eq_or_ne
bot_add
CanLift.prf
canLift
add_lt_add_right_coe
add_lt_add
add_lt_add_right_coe πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Real.toEReal
β€”not_le
AddLECancellable.add_le_add_iff_right
AddCommMagma.to_isCommutative
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoidEReal
addLECancellable_coe
LT.lt.not_ge
add_lt_of_lt_sub πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”Mathlib.Tactic.Contrapose.contrapose₁
sub_le_of_le_add
add_lt_top πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Top.top
instTop
β€”add_lt_add
Ne.lt_top
add_ne_bot_iff πŸ“–β€”β€”β€”β€”WithBot.add_ne_bot
add_ne_top πŸ“–β€”β€”β€”β€”lt_top_iff_ne_top
add_lt_top
add_ne_top_iff_ne_top_left πŸ“–β€”β€”β€”β€”bot_add
top_add_of_ne_bot
add_ne_top_iff_ne_top_right πŸ“–β€”β€”β€”β€”add_ne_top_iff_ne_top_left
add_comm
add_ne_top_iff_ne_topβ‚‚ πŸ“–β€”β€”β€”β€”add_top_of_ne_bot
top_add_of_ne_bot
instIsEmptyFalse
add_ne_top
add_ne_top_iff_of_ne_bot_of_ne_top πŸ“–β€”β€”β€”β€”bot_add
top_add_of_ne_bot
add_pos πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”Right.add_pos_of_nonneg_of_pos
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoidEReal
LT.lt.le
add_pos_of_pos_of_nonneg πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
Preorder.toLE
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”Right.add_pos_of_nonneg_of_pos
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoidEReal
add_comm
add_sub_cancel_left πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Real.toEReal
β€”add_comm
add_sub_cancel_right
add_sub_cancel_right πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Real.toEReal
β€”add_sub_cancel_right
add_top_iff_ne_bot πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Top.top
instTop
β€”add_comm
top_add_iff_ne_bot
add_top_of_ne_bot πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Top.top
instTop
β€”add_comm
top_add_of_ne_bot
bot_add πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Bot.bot
instBotEReal
β€”WithBot.bot_add
bot_lt_add_iff πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
Bot.bot
instBotEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”β€”
bot_mul_bot πŸ“–mathematicalβ€”EReal
instMul
Bot.bot
instBotEReal
Top.top
instTop
β€”β€”
bot_mul_coe_of_neg πŸ“–mathematicalReal
Real.instLT
Real.instZero
EReal
instMul
Bot.bot
instBotEReal
Real.toEReal
Top.top
instTop
β€”LT.lt.not_gt
LT.lt.ne
bot_mul_coe_of_pos πŸ“–mathematicalReal
Real.instLT
Real.instZero
EReal
instMul
Bot.bot
instBotEReal
Real.toEReal
β€”β€”
bot_mul_of_neg πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
Bot.bot
instBotEReal
Top.top
instTop
β€”mul_comm
mul_bot_of_neg
bot_mul_of_pos πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
Bot.bot
instBotEReal
β€”mul_comm
mul_bot_of_pos
bot_mul_top πŸ“–mathematicalβ€”EReal
instMul
Bot.bot
instBotEReal
Top.top
instTop
β€”β€”
bot_sub πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Bot.bot
instBotEReal
β€”bot_add
coe_add_top πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Real.toEReal
Top.top
instTop
β€”β€”
coe_ennreal_mul_top πŸ“–mathematicalβ€”EReal
instMul
ENNReal.toEReal
Top.top
instTop
β€”mul_comm
top_mul_coe_ennreal
coe_mul_bot_of_neg πŸ“–mathematicalReal
Real.instLT
Real.instZero
EReal
instMul
Real.toEReal
Bot.bot
instBotEReal
Top.top
instTop
β€”LT.lt.not_gt
LT.lt.ne
coe_mul_bot_of_pos πŸ“–mathematicalReal
Real.instLT
Real.instZero
EReal
instMul
Real.toEReal
Bot.bot
instBotEReal
β€”β€”
coe_mul_top_of_neg πŸ“–mathematicalReal
Real.instLT
Real.instZero
EReal
instMul
Real.toEReal
Top.top
instTop
Bot.bot
instBotEReal
β€”LT.lt.not_gt
LT.lt.ne
coe_mul_top_of_pos πŸ“–mathematicalReal
Real.instLT
Real.instZero
EReal
instMul
Real.toEReal
Top.top
instTop
β€”β€”
coe_neg πŸ“–mathematicalβ€”Real.toEReal
Real
Real.instNeg
EReal
instNeg
β€”β€”
coe_real_ereal_eq_coe_toNNReal_sub_coe_toNNReal πŸ“–mathematicalβ€”Real.toEReal
EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
ENNReal.toEReal
ENNReal.ofNNReal
Real.toNNReal
Real
Real.instNeg
β€”le_total
CanLift.prf
NNReal.canLift
Real.toNNReal_of_nonpos
neg_nonpos
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
NNReal.coe_nonneg
Real.toNNReal_coe
ENNReal.coe_zero
coe_ennreal_zero
sub_zero
coe_nnreal_eq_coe_real
Real.coe_toNNReal
neg_nonneg
zero_sub
coe_neg
neg_neg
coe_sub πŸ“–mathematicalβ€”Real.toEReal
Real
Real.instSub
EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”β€”
coe_sub_bot πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Real.toEReal
Bot.bot
instBotEReal
Top.top
instTop
β€”β€”
coe_zsmul πŸ“–mathematicalβ€”Real.toEReal
Real
SubNegMonoid.toZSMul
AddGroup.toSubNegMonoid
Real.instAddGroup
EReal
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”map_zsmul'
AddMonoidHom.instAddMonoidHomClass
coe_zero
coe_add
coe_neg
ge_of_forall_gt_iff_ge πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
Real.toEReal
β€”WithBot.ge_of_forall_gt_iff_ge
WithTop.denselyOrdered
LinearOrderedSemiField.toDenselyOrdered
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
instNoMaxOrderOfNontrivial
Real.instIsOrderedRing
Real.instNontrivial
WithTop.noMinOrder
instNoMinOrderOfNontrivial
WithTop.forall
instIsEmptyFalse
LE.le.trans
LT.lt.le
inductionβ‚‚_neg_left πŸ“–β€”EReal
instNeg
Top.top
instTop
Real.toEReal
instZeroEReal
Bot.bot
instBotEReal
β€”β€”neg_neg
neg_pos_of_neg
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
inductionβ‚‚
inductionβ‚‚_symm_neg πŸ“–β€”EReal
instNeg
Top.top
instTop
Real.toEReal
instZeroEReal
β€”β€”neg_pos_of_neg
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
neg_neg
inductionβ‚‚_neg_left
instNoZeroDivisors πŸ“–mathematicalβ€”NoZeroDivisors
EReal
instMul
instZeroEReal
β€”Mathlib.Tactic.Contrapose.contrapose₁
lt_or_gt_of_ne
bot_mul_of_neg
bot_mul_of_pos
mul_bot_of_neg
mul_bot_of_pos
IsDomain.to_noZeroDivisors
Real.instIsDomain
mul_top_of_neg
mul_top_of_pos
top_mul_of_neg
top_mul_of_pos
le_add_of_forall_gt πŸ“–β€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”β€”neg_le_neg_iff
neg_add
add_le_of_forall_lt
le_neg_of_le_neg
LT.lt.ne_top
lt_neg_of_lt_neg
le_neg πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”neg_le_neg_iff
neg_neg
le_neg_of_le_neg πŸ“–β€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”β€”le_neg
le_of_forall_lt_iff_le πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
Real.toEReal
β€”WithBot.le_of_forall_lt_iff_le
WithTop.denselyOrdered
LinearOrderedSemiField.toDenselyOrdered
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
instNoMaxOrderOfNontrivial
Real.instIsOrderedRing
Real.instNontrivial
WithTop.noMinOrder
instNoMinOrderOfNontrivial
WithTop.forall
LE.le.trans
LT.lt.le
le_sub_iff_add_le πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”sub_bot
add_bot
AddLECancellable.add_le_add_iff_right
AddCommMagma.to_isCommutative
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoidEReal
addLECancellable_coe
sub_add_cancel
sub_top
bot_le
bot_add
LT.lt.ne
LE.le.trans_lt
Ne.lt_top
add_top_iff_ne_bot
left_distrib_of_nonneg πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”mul_comm
right_distrib_of_nonneg
left_distrib_of_nonneg_of_ne_top πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”LE.le.eq_or_lt'
MulZeroClass.zero_mul
add_zero
CanLift.prf
canLift
LT.lt.ne_bot
add_bot
mul_bot_of_pos
bot_add
mul_top_of_pos
mul_add
Distrib.leftDistribClass
add_top_of_ne_bot
top_add_of_ne_bot
lt_neg_comm πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”neg_lt_neg_iff
neg_neg
lt_neg_of_lt_neg πŸ“–β€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”β€”lt_neg_comm
lt_sub_iff_add_lt πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”lt_iff_lt_of_le_iff_le
sub_le_iff_le_add
mul_bot_of_neg πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
Bot.bot
instBotEReal
Top.top
instTop
β€”coe_mul_bot_of_neg
coe_neg'
not_top_lt
mul_bot_of_pos πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
Bot.bot
instBotEReal
β€”not_lt_bot
coe_mul_bot_of_pos
coe_pos
mul_eq_bot πŸ“–mathematicalβ€”EReal
instMul
Bot.bot
instBotEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
Top.top
instTop
β€”neg_eq_top_iff
neg_mul
mul_eq_top
neg_eq_bot_iff
neg_lt_comm
lt_neg_comm
neg_zero
mul_eq_top πŸ“–mathematicalβ€”EReal
instMul
Top.top
instTop
Bot.bot
instBotEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
β€”inductionβ‚‚_symm
top_mul_coe_of_pos
MulZeroClass.mul_zero
top_mul_coe_of_neg
LT.lt.le
coe_mul_bot_of_pos
coe_ne_top
MulZeroClass.zero_mul
coe_mul_bot_of_neg
mul_ne_bot πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
β€”mul_eq_bot
Mathlib.Tactic.Push.not_and_or_eq
mul_ne_top πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
β€”mul_eq_top
Mathlib.Tactic.Push.not_and_or_eq
mul_neg_iff πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instMul
instZeroEReal
β€”neg_zero
lt_neg_comm
mul_neg
mul_pos_iff
neg_lt_comm
mul_nonneg πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMulβ€”mul_nonneg_iff
mul_nonneg_iff πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
β€”zero_eq_mul
instNoZeroDivisors
lt_trichotomy
mul_nonpos_iff πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instMul
instZeroEReal
β€”neg_zero
le_neg
mul_neg
mul_nonneg_iff
neg_le
mul_pos πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMulβ€”mul_pos_iff
mul_pos_iff πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
β€”inductionβ‚‚_symm
mul_comm
top_mul_coe_of_pos
MulZeroClass.mul_zero
top_mul_coe_of_neg
coe_mul_bot_of_pos
AddGroup.existsAddOfLE
IsStrictOrderedRing.toPosMulStrictMono
Real.instIsStrictOrderedRing
IsStrictOrderedRing.toMulPosStrictMono
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
contravariant_lt_of_covariant_le
MulZeroClass.zero_mul
coe_mul_bot_of_neg
mul_top_of_neg πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
Top.top
instTop
Bot.bot
instBotEReal
β€”coe_mul_top_of_neg
coe_neg'
not_top_lt
mul_top_of_pos πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
Top.top
instTop
β€”not_lt_bot
coe_mul_top_of_pos
coe_pos
neg_add πŸ“–mathematicalβ€”EReal
instNeg
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”coe_add
coe_neg
coe_sub
neg_add'
neg_bot πŸ“–mathematicalβ€”EReal
instNeg
Bot.bot
instBotEReal
Top.top
instTop
β€”β€”
neg_eq_bot_iff πŸ“–mathematicalβ€”EReal
instNeg
Bot.bot
instBotEReal
Top.top
instTop
β€”neg_injective
neg_eq_top_iff πŸ“–mathematicalβ€”EReal
instNeg
Top.top
instTop
Bot.bot
instBotEReal
β€”neg_injective
neg_eq_zero_iff πŸ“–mathematicalβ€”EReal
instNeg
instZeroEReal
β€”neg_injective
neg_zero
neg_le πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”neg_le_neg_iff
neg_neg
neg_le_neg_iff πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”StrictAnti.le_iff_ge
neg_strictAnti
neg_le_of_neg_le πŸ“–β€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”β€”neg_le
neg_le_zero πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
instZeroEReal
β€”neg_le
neg_zero
neg_lt_comm πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”neg_lt_neg_iff
neg_neg
neg_lt_neg_iff πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”StrictAnti.lt_iff_gt
neg_strictAnti
neg_lt_of_neg_lt πŸ“–β€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”β€”neg_lt_comm
neg_lt_zero πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
instZeroEReal
β€”neg_lt_comm
neg_zero
neg_mul πŸ“–mathematicalβ€”EReal
instMul
instNeg
β€”inductionβ‚‚_neg_left
neg_neg
top_mul_coe_of_pos
neg_top
bot_mul_coe_of_pos
MulZeroClass.mul_zero
neg_zero
top_mul_coe_of_neg
bot_mul_coe_of_neg
neg_bot
MulZeroClass.zero_mul
coe_mul_top_of_pos
coe_neg
coe_mul_top_of_neg
neg_neg_of_pos
Real.instIsOrderedAddMonoid
coe_mul_bot_of_pos
coe_mul_bot_of_neg
neg_mul
neg_nonneg πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instNeg
β€”le_neg
neg_zero
neg_pos πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instNeg
β€”lt_neg_comm
neg_zero
neg_strictAnti πŸ“–mathematicalβ€”StrictAnti
EReal
PartialOrder.toPreorder
instPartialOrderEReal
instNeg
β€”WithBot.strictAnti_iff
WithTop.strictAnti_iff
StrictMono.comp_strictAnti
coe_strictMono
neg_lt_neg
Real.instIsOrderedAddMonoid
bot_lt_coe
WithTop.forall
bot_lt_top
coe_lt_top
neg_sub πŸ“–mathematicalβ€”EReal
instNeg
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”sub_eq_add_neg
neg_add
neg_neg
neg_top πŸ“–mathematicalβ€”EReal
instNeg
Top.top
instTop
Bot.bot
instBotEReal
β€”β€”
nsmul_eq_mul πŸ“–mathematicalβ€”EReal
AddMonoid.toNatSMul
instAddMonoidEReal
instMul
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
instAddCommMonoidWithOneEReal
β€”zero_smul
Nat.cast_zero
MulZeroClass.zero_mul
succ_nsmul
Nat.cast_succ
one_mul
right_distrib_of_nonneg
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoidEReal
instZeroLEOneClassEReal
recENNReal_coe_ennreal πŸ“–mathematicalβ€”recENNReal
ENNReal.toEReal
β€”coe_ennreal_nonneg
coe_toENNReal
toENNReal_coe
right_distrib_of_nonneg πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”CanLift.prf
instCanLiftENNRealToERealLeOfNat
add_mul
Distrib.rightDistribClass
mul_neg
coe_ennreal_add
neg_add
coe_ennreal_ne_bot
sub_eq_add_neg
right_distrib_of_nonneg_of_ne_top πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”mul_comm
left_distrib_of_nonneg_of_ne_top
sub_add_cancel πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Real.toEReal
β€”add_comm
add_sub_assoc
add_sub_cancel_left
sub_add_cancel_left πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Real.toEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
instNeg
β€”add_comm
sub_add_cancel_right
sub_add_cancel_right πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Real.toEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
instNeg
β€”sub_add_cancel_right
sub_bot πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Bot.bot
instBotEReal
Top.top
instTop
β€”β€”
sub_le_iff_le_add πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”le_sub_iff_add_le
sub_eq_add_neg
neg_neg
sub_le_of_le_add πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”le_bot_iff
add_bot
bot_sub
sub_le_iff_le_add
coe_ne_bot
coe_ne_top
sub_top
sub_le_of_le_add' πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”sub_le_of_le_add
add_comm
sub_le_sub πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”add_le_add
IsOrderedAddMonoid.toAddLeftMono
instIsOrderedAddMonoidEReal
covariant_swap_add_of_covariant_add
neg_le_neg_iff
sub_lt_iff πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
β€”lt_iff_lt_of_le_iff_le
le_sub_iff_add_le
sub_lt_of_lt_add πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”add_lt_of_lt_sub
sub_eq_add_neg
neg_neg
sub_lt_of_lt_add' πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”sub_lt_of_lt_add
add_comm
sub_lt_sub_of_lt_of_le πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
Preorder.toLE
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”add_lt_add_of_lt_of_le
neg_le_neg_iff
sub_neg πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
instZeroEReal
β€”bot_sub
sub_top
sub_bot
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
top_sub
sub_nonneg πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”bot_sub
sub_top
sub_bot
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
top_sub
sub_nonpos πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
instZeroEReal
β€”bot_sub
sub_top
sub_bot
AddGroup.toOrderedSub
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
zero_add
top_sub
sub_pos πŸ“–mathematicalβ€”EReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
β€”bot_sub
sub_top
sub_bot
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
IsOrderedAddMonoid.toAddLeftMono
Real.instIsOrderedAddMonoid
top_sub
sub_self πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
instZeroEReal
β€”sub_self
sub_self_le_zero πŸ“–mathematicalβ€”EReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
instZeroEReal
β€”bot_sub
sub_self
sub_top
sub_top πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Top.top
instTop
Bot.bot
instBotEReal
β€”add_bot
toENNReal_add πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
toENNReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
ENNReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
β€”ENNReal.ofReal_add
add_top_of_ne_bot
toENNReal_of_ne_top
add_top
top_add_of_ne_bot
top_add
toENNReal_add_le πŸ“–mathematicalβ€”ENNReal
Preorder.toLE
PartialOrder.toPreorder
ENNReal.instPartialOrder
toENNReal
EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
β€”add_bot
toENNReal_of_ne_top
ENNReal.ofReal_zero
add_zero
bot_add
zero_add
ENNReal.instCanonicallyOrderedAdd
add_top
ENNReal.ofReal_add_le
add_top_of_ne_bot
top_add_of_ne_bot
top_add
toENNReal_mul πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
toENNReal
instMul
ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
β€”toENNReal_of_nonpos
toENNReal_of_ne_top
ENNReal.ofReal_zero
MulZeroClass.mul_zero
ENNReal.ofReal_mul
eq_or_lt_of_le
MulZeroClass.zero_mul
mul_top_of_pos
ENNReal.mul_top
lt_trichotomy
top_mul_of_neg
coe_neg'
ENNReal.instNoZeroDivisors
top_mul_of_pos
coe_pos
ENNReal.top_mul
toENNReal_mul' πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
toENNReal
instMul
ENNReal
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
ENNReal.instCommSemiring
β€”mul_comm
toENNReal_mul
mul_comm
toENNReal_sub πŸ“–mathematicalEReal
Preorder.toLE
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
toENNReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
ENNReal
ENNReal.instSub
β€”bot_sub
toENNReal_of_ne_top
ENNReal.ofReal_zero
zero_tsub
ENNReal.instCanonicallyOrderedAdd
ENNReal.instOrderedSub
sub_top
toENNReal_of_nonpos
sub_nonpos
coe_le_coe_iff
tsub_eq_zero_of_le
toENNReal_le_toENNReal
instLawfulBCmpCompare_mathlib
coe_sub
toReal_coe
ENNReal.ofReal_sub
coe_nonneg
ENNReal.sub_top
top_sub
ENNReal.top_sub
tsub_self
toReal_add πŸ“–mathematicalβ€”toReal
EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Real
Real.instAdd
β€”CanLift.prf
canLift
toReal_mul πŸ“–mathematicalβ€”toReal
EReal
instMul
Real
Real.instMul
β€”inductionβ‚‚_symm
mul_comm
mul_comm
MulZeroClass.mul_zero
top_mul_coe_of_pos
MulZeroClass.zero_mul
top_mul_coe_of_neg
coe_mul_bot_of_pos
coe_mul_bot_of_neg
toReal_neg_eq πŸ“–mathematicalβ€”toReal
EReal
instNeg
Real
Real.instNeg
β€”neg_zero
toReal_sub πŸ“–mathematicalβ€”toReal
EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Real
Real.instSub
β€”CanLift.prf
canLift
top_add_coe πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Top.top
instTop
Real.toEReal
β€”β€”
top_add_iff_ne_bot πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Top.top
instTop
β€”bot_ne_top
add_bot
top_add_of_ne_bot
top_add_of_ne_bot πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Top.top
instTop
β€”top_add_coe
top_add_top
top_add_top πŸ“–mathematicalβ€”EReal
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
instAddCommMonoidEReal
Top.top
instTop
β€”β€”
top_mul_bot πŸ“–mathematicalβ€”EReal
instMul
Top.top
instTop
Bot.bot
instBotEReal
β€”β€”
top_mul_coe_ennreal πŸ“–mathematicalβ€”EReal
instMul
Top.top
instTop
ENNReal.toEReal
β€”top_mul_of_pos
coe_ennreal_pos
pos_iff_ne_zero
ENNReal.instCanonicallyOrderedAdd
top_mul_coe_of_neg πŸ“–mathematicalReal
Real.instLT
Real.instZero
EReal
instMul
Top.top
instTop
Real.toEReal
Bot.bot
instBotEReal
β€”LT.lt.not_gt
LT.lt.ne
top_mul_coe_of_pos πŸ“–mathematicalReal
Real.instLT
Real.instZero
EReal
instMul
Top.top
instTop
Real.toEReal
β€”β€”
top_mul_of_neg πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
Top.top
instTop
Bot.bot
instBotEReal
β€”mul_comm
mul_top_of_neg
top_mul_of_pos πŸ“–mathematicalEReal
Preorder.toLT
PartialOrder.toPreorder
instPartialOrderEReal
instZeroEReal
instMul
Top.top
instTop
β€”mul_comm
mul_top_of_pos
top_mul_top πŸ“–mathematicalβ€”EReal
instMul
Top.top
instTop
β€”β€”
top_sub πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Top.top
instTop
β€”β€”
top_sub_bot πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Top.top
instTop
Bot.bot
instBotEReal
β€”β€”
top_sub_coe πŸ“–mathematicalβ€”EReal
SubNegMonoid.toSub
SubNegZeroMonoid.toSubNegMonoid
instSubNegZeroMonoid
Top.top
instTop
Real.toEReal
β€”β€”

Mathlib.Meta.Positivity

Definitions

NameCategoryTheorems
evalERealAdd πŸ“–CompOpβ€”
evalERealMul πŸ“–CompOpβ€”

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