Documentation Verification Report

Defs

📁 Source: Mathlib/Data/NNRat/Defs.lean

Statistics

MetricCount
Definitionsspecialised_high_priority_simp_lemma, coeHom, divNat, gi, instOrderBot, numDenCasesOn, nnabs, toNNRat, instAddCancelCommMonoidNNRat, instCommSemiringNNRat, instInhabitedNNRat, instLinearOrderNNRat, instSubNNRat
13
TheoremsnnratCast_eq, nnratCast_le, nnratCast_lt, nnratCast_ne, abs_coe, add_def, bddAbove_coe, bddBelow_coe, canLift, coe_add, coe_coeHom, coe_divNat, coe_eq_zero, coe_inj, coe_injective, coe_le_coe, coe_lt_coe, coe_max, coe_min, coe_mk, coe_mono, coe_mul, coe_natCast, coe_ne_zero, coe_nonneg, coe_one, coe_pos, coe_pow, coe_sub, coe_zero, coprime_num_den, den_coe, den_mul_eq_num, den_natCast, den_ne_zero, den_ofNat, den_one, den_pos, den_pow, den_zero, divNat_inj, divNat_mul_divNat, divNat_mul_left, divNat_mul_right, divNat_zero, exists, ext, ext_iff, ext_num_den, ext_num_den_iff, forall, instCharZero, instNontrivial, le_def, lt_def, mk_divInt, mk_natCast, mk_zero, mul_def, mul_den_eq_num, natAbs_num_coe, natCast_eq_divNat, ne_iff, nonpos_iff_eq_zero, nsmul_coe, num_coe, num_divNat_den, num_natCast, num_ne_zero, num_ofNat, num_one, num_pos, num_pow, num_zero, sub_def, toNNRat_coe, toNNRat_coe_nat, toNNRat_mono, val_eq_cast, coe_nnabs, coe_toNNRat, instPosMulMono, le_coe_toNNRat, le_toNNRat_iff_coe_le, le_toNNRat_iff_coe_le', lt_toNNRat_iff_coe_lt, toNNRat_add, toNNRat_add_le, toNNRat_eq_zero, toNNRat_le_iff_le_coe, toNNRat_le_toNNRat_iff, toNNRat_lt_iff_lt_coe, toNNRat_lt_toNNRat_iff, toNNRat_lt_toNNRat_iff', toNNRat_lt_toNNRat_iff_of_nonneg, toNNRat_mul, toNNRat_of_nonpos, toNNRat_one, toNNRat_pos, toNNRat_zero
100
Total113

LibraryNote

Definitions

NameCategoryTheorems
specialised_high_priority_simp_lemma 📖CompOp

Mathlib.Tactic.Qify

Theorems

NameKindAssumesProvesValidatesDepends On
nnratCast_eq 📖mathematicalNNRat.cast
Rat.instNNRatCast
nnratCast_le 📖mathematicalNNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
NNRat.cast
Rat.instNNRatCast
NNRat.coe_le_coe
nnratCast_lt 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
NNRat.cast
Rat.instNNRatCast
NNRat.coe_lt_coe
nnratCast_ne 📖NNRat.ne_iff

NNRat

Definitions

NameCategoryTheorems
coeHom 📖CompOp
1 mathmath: coe_coeHom
divNat 📖CompOp
15 mathmath: divNat_mul_left, mul_def, mk_divInt, coe_divNat, divNat_inj, add_def, div_def, inv_def, divNat_zero, divNat_mul_divNat, cast_divNat_of_ne_zero, num_divNat_den, divNat_mul_right, cast_divNat, natCast_eq_divNat
gi 📖CompOp
instOrderBot 📖CompOp
1 mathmath: MvPolynomial.schwartz_zippel_sup_sum
numDenCasesOn 📖CompOp

Theorems

NameKindAssumesProvesValidatesDepends On
abs_coe 📖mathematicalabs
Rat.instLattice
Rat.addGroup
cast
Rat.instNNRatCast
abs_of_nonneg
Rat.instAddLeftMono
add_def 📖mathematicalNNRat
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
divNat
num
den
ext
num_coe
Nat.cast_mul
Nat.cast_add
bddAbove_coe 📖mathematicalBddAbove
Set.image
NNRat
cast
Rat.instNNRatCast
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
LE.le.trans
Set.mem_image_of_mem
le_max_left
bddBelow_coe 📖mathematicalBddBelow
Set.image
NNRat
cast
Rat.instNNRatCast
canLift 📖mathematicalCanLift
NNRat
cast
Rat.instNNRatCast
coe_add 📖mathematicalcast
Rat.instNNRatCast
NNRat
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
coe_coeHom 📖mathematicalDFunLike.coe
RingHom
NNRat
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
Rat.semiring
RingHom.instFunLike
coeHom
cast
Rat.instNNRatCast
coe_divNat 📖mathematicalcast
Rat.instNNRatCast
divNat
coe_eq_zero 📖mathematicalcast
Rat.instNNRatCast
NNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
Nat.cast_zero
coe_inj 📖mathematicalcast
Rat.instNNRatCast
coe_injective 📖mathematicalNNRat
cast
Rat.instNNRatCast
Subtype.coe_injective
coe_le_coe 📖mathematicalcast
Rat.instNNRatCast
NNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
coe_lt_coe 📖mathematicalcast
Rat.instNNRatCast
NNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
coe_max 📖mathematicalcast
Rat.instNNRatCast
NNRat
SemilatticeSup.toMax
Lattice.toSemilatticeSup
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
Rat.instSup
Monotone.map_max
coe_mono
coe_min 📖mathematicalcast
Rat.instNNRatCast
NNRat
SemilatticeInf.toMin
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
Rat.instInf
Monotone.map_min
coe_mono
coe_mk 📖mathematicalcast
Rat.instNNRatCast
coe_mono 📖mathematicalMonotone
NNRat
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
Rat.instPreorder
cast
Rat.instNNRatCast
coe_le_coe
coe_mul 📖mathematicalcast
Rat.instNNRatCast
NNRat
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
coe_natCast 📖mathematicalcast
Rat.instNNRatCast
NNRat
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
coe_ne_zero 📖Iff.not
coe_eq_zero
coe_nonneg 📖mathematicalcast
Rat.instNNRatCast
coe_one 📖mathematicalcast
Rat.instNNRatCast
NNRat
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
coe_pos 📖mathematicalcast
Rat.instNNRatCast
NNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
coe_pow 📖mathematicalcast
Rat.instNNRatCast
NNRat
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiringNNRat
coe_sub 📖mathematicalNNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
cast
Rat.instNNRatCast
instSubNNRat
max_eq_left
le_sub_comm
Rat.instAddLeftMono
sub_zero
coe_zero 📖mathematicalcast
Rat.instNNRatCast
NNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
coprime_num_den 📖mathematicalnum
den
den_coe 📖mathematicalcast
Rat.instNNRatCast
den
den_mul_eq_num 📖mathematicalNNRat
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
den
num
mul_comm
mul_den_eq_num
den_natCast 📖mathematicalden
NNRat
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
den_ne_zero 📖Rat.den_ne_zero
den_ofNat 📖mathematicalden
den_one 📖mathematicalden
NNRat
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
den_pos 📖mathematicalden
den_pow 📖mathematicalden
NNRat
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiringNNRat
Nat.instMonoid
den_zero 📖mathematicalden
NNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
divNat_inj 📖mathematicaldivNatInt.instCharZero
divNat_mul_divNat 📖mathematicalNNRat
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
divNat
ext
Nat.cast_mul
divNat_mul_left 📖mathematicaldivNatext
Nat.cast_mul
Nat.cast_zero
Int.instCharZero
divNat_mul_right 📖mathematicaldivNatext
Nat.cast_mul
Nat.cast_zero
Int.instCharZero
divNat_zero 📖mathematicaldivNat
NNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
Nat.cast_zero
exists 📖
ext 📖cast
Rat.instNNRatCast
ext_iff 📖mathematicalcast
Rat.instNNRatCast
ext
ext_num_den 📖num
den
ext
num_coe
Int.instCharZero
ext_num_den_iff 📖mathematicalnum
den
ext_num_den
forall 📖
instCharZero 📖mathematicalCharZero
NNRat
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
instNontrivial 📖mathematicalNontrivial
NNRat
le_def 📖mathematicalNNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
num
den
coe_le_coe
num_coe
Int.instAddLeftMono
Int.instZeroLEOneClass
Int.instCharZero
lt_def 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
num
den
coe_lt_coe
num_coe
Int.instAddLeftMono
Int.instZeroLEOneClass
Int.instCharZero
mk_divInt 📖mathematicaldivNat
mk_natCast 📖mathematicalNat.cast_nonneg'
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
Rat.commRing
Rat.instPartialOrder
Rat.instAddLeftMono
Rat.instZeroLEOneClass
NNRat
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
Nat.cast_nonneg'
Rat.instAddLeftMono
Rat.instZeroLEOneClass
mk_zero 📖mathematicalle_rfl
Rat.instPreorder
Nonneg.zero
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Rat.commRing
le_rfl
mul_def 📖mathematicalNNRat
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
divNat
num
den
ext
Rat.mul_eq_mkRat
num_coe
Nat.cast_mul
mul_den_eq_num 📖mathematicalNNRat
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
den
num
ext
Int.cast_natCast
den_coe
num_coe
Rat.mul_den_eq_num
natAbs_num_coe 📖mathematicalcast
Rat.instNNRatCast
num
natCast_eq_divNat 📖mathematicalNNRat
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
divNat
num_divNat_den
ne_iff 📖Iff.not
nonpos_iff_eq_zero 📖mathematicalNNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
le_antisymm
nsmul_coe 📖mathematicalcast
Rat.instNNRatCast
NNRat
AddMonoid.toNatSMul
AddMonoidWithOne.toAddMonoid
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
Rat.addMonoid
AddMonoidHom.map_nsmul
num_coe 📖mathematicalcast
Rat.instNNRatCast
num
Int.natCast_natAbs
abs_of_nonneg
Int.instAddLeftMono
num_divNat_den 📖mathematicaldivNat
num
den
ext
Rat.mkRat_num_den'
num_coe
num_natCast 📖mathematicalnum
NNRat
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
num_ne_zero 📖
num_ofNat 📖mathematicalnum
num_one 📖mathematicalnum
NNRat
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
num_pos 📖mathematicalnum
NNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
Iff.not
nonpos_iff_eq_zero
num_pow 📖mathematicalnum
NNRat
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
instCommSemiringNNRat
Nat.instMonoid
num_zero 📖mathematicalnum
NNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
sub_def 📖mathematicalNNRat
instSubNNRat
Rat.toNNRat
cast
Rat.instNNRatCast
toNNRat_coe 📖mathematicalRat.toNNRat
cast
Rat.instNNRatCast
ext
max_eq_left
toNNRat_coe_nat 📖mathematicalRat.toNNRat
NNRat
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
ext
Rat.coe_toNNRat
Rat.instAddLeftMono
Rat.instZeroLEOneClass
toNNRat_mono 📖mathematicalMonotone
NNRat
Rat.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
Rat.toNNRat
max_le_max
le_rfl
val_eq_cast 📖mathematicalcast
Rat.instNNRatCast

Rat

Definitions

NameCategoryTheorems
nnabs 📖CompOp
1 mathmath: coe_nnabs
toNNRat 📖CompOp
28 mathmath: toNNRat_mul, NNRat.toNNRat_sum_of_nonneg, NNRat.toNNRat_coe_nat, toNNRat_lt_toNNRat_iff', toNNRat_div', toNNRat_lt_toNNRat_iff_of_nonneg, toNNRat_div, toNNRat_of_nonpos, toNNRat_pos, NNRat.toNNRat_mono, toNNRat_add_le, NNRat.sub_def, NNRat.toNNRat_prod_of_nonneg, toNNRat_add, toNNRat_inv, NNRat.toNNRat_coe, le_toNNRat_iff_coe_le', toNNRat_le_toNNRat_iff, le_toNNRat_iff_coe_le, toNNRat_le_iff_le_coe, toNNRat_one, toNNRat_lt_iff_lt_coe, lt_toNNRat_iff_coe_lt, toNNRat_zero, le_coe_toNNRat, toNNRat_eq_zero, toNNRat_lt_toNNRat_iff, coe_toNNRat

Theorems

NameKindAssumesProvesValidatesDepends On
coe_nnabs 📖mathematicalNNRat.cast
instNNRatCast
nnabs
abs
instLattice
addGroup
coe_toNNRat 📖mathematicalNNRat.cast
instNNRatCast
toNNRat
max_eq_left
instPosMulMono 📖mathematicalPosMulMono
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
commRing
instPreorder
mul_sub
covariant_swap_add_of_covariant_add
instAddLeftMono
sub_nonneg
le_coe_toNNRat 📖mathematicalNNRat.cast
instNNRatCast
toNNRat
le_max_left
le_toNNRat_iff_coe_le 📖mathematicalNNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
NNRat.cast
instNNRatCast
NNRat.coe_le_coe
coe_toNNRat
le_toNNRat_iff_coe_le' 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
Preorder.toLE
toNNRat
NNRat.cast
instNNRatCast
le_or_gt
le_toNNRat_iff_coe_le
toNNRat_eq_zero
LT.lt.le
LT.lt.not_ge
LT.lt.trans_le
NNRat.coe_nonneg
lt_toNNRat_iff_coe_lt 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
NNRat.cast
instNNRatCast
GaloisConnection.lt_iff_lt
GaloisInsertion.gc
toNNRat_add 📖mathematicaltoNNRat
NNRat
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
NNRat.ext
sup_of_le_left
instAddLeftMono
toNNRat_add_le 📖mathematicalNNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
NNRat.coe_le_coe
max_le
add_le_add
instAddLeftMono
covariant_swap_add_of_covariant_add
le_max_left
NNRat.coe_nonneg
toNNRat_eq_zero 📖mathematicaltoNNRat
NNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
Iff.not
toNNRat_pos
toNNRat_le_iff_le_coe 📖mathematicalNNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
NNRat.cast
instNNRatCast
GaloisInsertion.gc
toNNRat_le_toNNRat_iff 📖mathematicalNNRat
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
sup_of_le_left
toNNRat_lt_iff_lt_coe 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
NNRat.cast
instNNRatCast
NNRat.coe_lt_coe
coe_toNNRat
toNNRat_lt_toNNRat_iff 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
toNNRat_lt_toNNRat_iff'
toNNRat_lt_toNNRat_iff' 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
toNNRat_lt_toNNRat_iff_of_nonneg 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
toNNRat
toNNRat_lt_toNNRat_iff'
LE.le.trans_lt
toNNRat_mul 📖mathematicaltoNNRat
NNRat
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
le_total
NNRat.ext
sup_of_le_left
instPosMulMono
mul_nonpos_of_nonneg_of_nonpos
toNNRat_eq_zero
MulZeroClass.mul_zero
toNNRat_of_nonpos 📖mathematicaltoNNRat
NNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
toNNRat_eq_zero
toNNRat_one 📖mathematicaltoNNRat
NNRat
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
toNNRat_pos 📖mathematicalNNRat
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
instLinearOrderNNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat
toNNRat
toNNRat_zero 📖mathematicaltoNNRat
NNRat
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
CommSemiring.toSemiring
instCommSemiringNNRat

(root)

Definitions

NameCategoryTheorems
instAddCancelCommMonoidNNRat 📖CompOp
instCommSemiringNNRat 📖CompOp
92 mathmath: AddDissociated.randomisation, NNRat.num_pow, Rat.toNNRat_mul, RCLike.norm_expect_le, NNRat.coe_natCast, NNRat.mul_def, Complex.re_balance, NNRat.den_natCast, NNRat.instStarOrderedRing, Complex.im_expect, NNRat.instSMulCommClass', RCLike.ofReal_balance, Ring.choose_eq_smul, NNRat.coe_zero, RCLike.ofReal_comp_balance, RCLike.wInner_cWeight_eq_expect, NNRat.num_pos, NNRat.mul_den_eq_num, NNRat.coe_pos, NNRat.toNNRat_coe_nat, NNRat.cast_multisetProd, instIsStrictOrderedRingNNRat, Complex.re_comp_balance, NNRat.add_def, AddChar.expect_apply_eq_zero_iff_ne_zero, Complex.ofReal_balance, instMulArchimedeanNNRat, NNRat.coe_eq_zero, NNRat.isFractionRing, NNRat.coe_add, NNRat.cast_prod, NNRat.mk_natCast, NNRat.nonpos_iff_eq_zero, binomialSeries_apply, NNRat.num_one, NNRat.instCharZero, NNRat.num_zero, Finset.expect_boole_mul', NNRat.tendsto_algebraMap_inv_atTop_nhds_zero_nat, RCLike.wInner_cWeight_const_left, NNRat.num_natCast, AddChar.expect_eq_zero_iff_ne_zero, Complex.ofReal_comp_balance, NNRat.den_pow, MvPolynomial.schwartz_zippel_sup_sum, Rat.toNNRat_of_nonpos, NNRat.instCanonicallyOrderedAdd, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, Complex.im_balance, Complex.ofReal_expect, Rat.toNNRat_pos, NNRat.instSMulCommClass, Finset.expect_boole_mul, Complex.im_comp_balance, Rat.toNNRat_add_le, NNReal.coe_expect, NNRat.divNat_zero, RCLike.ofReal_expect, NNRat.instOrderedSub, NNRat.divNat_mul_divNat, NNRat.nsmul_coe, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, NNRat.toNNRat_prod_of_nonneg, Rat.toNNRat_add, NNRat.coe_one, RingHomClass.toLinearMapClassNNRat, RCLike.nnnorm_nnqsmul, Rat.toNNRat_one, NNRat.coe_mul, NNRat.den_zero, Complex.re_expect, Rat.toNNRat_zero, MvPolynomial.schwartz_zippel_sum_degreeOf, RCLike.wInner_cWeight_const_right, Finset.expect_div, MeasureTheory.lpNorm_expect_le, Rat.toNNRat_eq_zero, NNRat.coe_pow, Real.compact_inner_le_weight_mul_Lp_of_nonneg, algebraMap.coe_expect, Finset.expect_eq_sum_div_card, AddChar.expect_apply_eq_ite, NNRat.den_mul_eq_num, RCLike.wInner_cWeight_eq_smul_wInner_one, NNRat.den_one, AddChar.expect_eq_ite, Complex.ofReal_choose, NNRat.natCast_eq_divNat, NNRat.num_div_den, RCLike.norm_nnqsmul, Fintype.expect_eq_sum_div_card, NNRat.coe_coeHom
instInhabitedNNRat 📖CompOp
instLinearOrderNNRat 📖CompOp
118 mathmath: NNRat.coe_floor, NNRat.cast_strictMono, NNRat.le_def, Finset.dens_map_le, Finset.addConst_le_inv_dens, Finset.one_le_mulConst_self, NNRat.instStarOrderedRing, NNRat.cast_le, NNRat.floor_coe, Finset.subConst_le_addConst_sq, NNRat.lt_def, MvPolynomial.schwartz_zippel_totalDegree, Finset.mulConst_le_card, NNRat.cast_mono, NNRat.coe_max, NNRat.num_pos, Mathlib.Tactic.Qify.nnratCast_le, Finset.divConst_le_card, Finset.one_le_mulConst, NNRat.floor_cast, NNRat.coe_pos, Finset.divConst_le_mulConst_sq, Finset.pluennecke_ruzsa_inequality_nsmul_add, instIsStrictOrderedRingNNRat, Rat.toNNRat_lt_toNNRat_iff', NNRat.one_le_cast, PosSMulMono.nnrat_of_rat, Finset.dens_le_one, instMulArchimedeanNNRat, NNRat.coe_lt_coe, Finset.addConst_le_subConst_sq, DivisibleHull.instIsStrictOrderedModuleNNRat, NNRat.nonpos_iff_eq_zero, Rat.toNNRat_lt_toNNRat_iff_of_nonneg, NNRat.preimage_cast_Iic, NNRat.natCast_le_cast, NNRat.coe_ceil, NNRat.preimage_cast_Ioi, Finset.nonneg_addConst, Finset.dens_strictMono, NNRat.natCast_lt_cast, NNRat.cast_le_one, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, Finset.addConst_le_card, Finset.one_le_divConst, NNRat.preimage_cast_uIcc, NNRat.preimage_cast_Icc, Finset.dens_biUnion_le, instArchimedeanNNRat, Finset.dens_le_dens_sdiff_add_dens, Finset.dens_lt_dens, Finset.nonneg_addConst_self, MvPolynomial.schwartz_zippel_sup_sum, NNRat.instCanonicallyOrderedAdd, NNRat.coe_le_coe, Finset.pluennecke_ruzsa_inequality_pow_div, Finset.mulConst_le_inv_dens, Rat.toNNRat_pos, NNRat.preimage_cast_Ici, NNRat.ceil_coe, Finset.le_dens_sdiff, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, NNRat.cast_min, NNRat.toNNRat_mono, PosSMulStrictMono.nnrat_of_rat, NNRat.one_lt_cast, Rat.toNNRat_add_le, Finset.subConst_le_card, NNRat.cast_max, LinearOrderedSemifield.toPosSMulStrictMono_rat, Finset.dens_mono, NNRat.instOrderedSub, NNRat.cast_pos, Mathlib.Tactic.Qify.nnratCast_lt, NNRat.ofNat_le_cast, NNRat.ceil_cast, Finset.nonneg_subConst_self, NNRat.coe_mono, NNRat.preimage_cast_Ico, NNRat.cast_nonpos, Finset.one_le_divConst_self, Rat.toNNRat_le_toNNRat_iff, Rat.le_toNNRat_iff_coe_le, Rat.toNNRat_le_iff_le_coe, NNRat.instOrderTopology, Finset.subConst_le_inv_dens, NNRat.preimage_cast_Ioo, Rat.toNNRat_lt_iff_lt_coe, NNRat.cast_lt_one, NNRat.floor_def, NNRat.preimage_cast_Ioc, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, NNRat.cast_lt, Rat.lt_toNNRat_iff_coe_lt, MvPolynomial.schwartz_zippel_sum_degreeOf, NNRat.cast_le_natCast, Finset.pluennecke_ruzsa_inequality_pow_mul, Finset.pluennecke_ruzsa_inequality_nsmul_sub, NNRat.floor_natCast_div_natCast, NNRat.bddAbove_coe, NNRat.cast_lt_natCast, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, Rat.toNNRat_lt_toNNRat_iff, NNRat.coe_min, Finset.dens_union_le, Finset.Nonempty.dens_pos, NNRat.cast_le_ofNat, Finset.dens_le_dens, Finset.divConst_le_inv_dens, NNRat.cast_lt_ofNat, Finset.mulConst_le_divConst_sq, NNRat.preimage_cast_Iio, NNRat.ofNat_lt_cast, NNRat.castOrderEmbedding_apply, NNRat.preimage_cast_uIoc, Finset.dens_pos, Finset.nonneg_subConst, NNRat.cast_lt_zero
instSubNNRat 📖CompOp
6 mathmath: NNRat.coe_sub, NNRat.instContinuousSub, Finset.le_dens_sdiff, NNRat.sub_def, NNRat.instOrderedSub, Finset.dens_sdiff

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