ArithmeticGeometric

📁 Source: Mathlib/Analysis/SpecificLimits/ArithmeticGeometric.lean

Statistics

Metric	Count
Definitions arithGeom	1
Theorems arithGeom_eq, arithGeom_eq', arithGeom_eq_add_sum, arithGeom_same_eq_mul_div, arithGeom_same_eq_mul_div', arithGeom_same_eq_sum, arithGeom_strictMono, arithGeom_succ, arithGeom_zero, arithGeom_zero_eq_mul_div, arithGeom_zero_eq_mul_div', arithGeom_zero_eq_sum, div_lt_arithGeom, tendsto_arithGeom_atTop_of_one_lt, tendsto_arithGeom_nhds_of_lt_one	15
Total	16

(root)

Definitions

Name	Category	Theorems
arithGeom 📖	CompOp	15 math math: arithGeom_succ, arithGeom_eq', arithGeom_eq_add_sum, arithGeom_zero_eq_mul_div', arithGeom_same_eq_mul_div', arithGeom_zero, tendsto_arithGeom_nhds_of_lt_one, tendsto_arithGeom_atTop_of_one_lt, arithGeom_eq, arithGeom_zero_eq_sum, arithGeom_same_eq_mul_div, div_lt_arithGeom, arithGeom_same_eq_sum, arithGeom_zero_eq_mul_div, arithGeom_strictMono

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
arithGeom_eq 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Distrib.toAdd Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing Field.toDivisionRing DivInvMonoid.toDiv DivisionRing.toDivInvMonoid AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne	—	pow_zero one_mul sub_add_cancel arithGeom.eq_def
arithGeom_eq' 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Distrib.toAdd Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing Field.toDivisionRing DivInvMonoid.toDiv DivisionRing.toDivInvMonoid AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne	—	arithGeom_eq
arithGeom_eq_add_sum 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring CommSemiring.toSemiring Distrib.toAdd Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero Finset.sum NonUnitalNonAssocSemiring.toAddCommMonoid Finset.range	—	pow_zero one_mul MulZeroClass.mul_zero add_zero arithGeom_succ mul_add Distrib.leftDistribClass mul_assoc add_comm pow_add pow_one add_assoc Finset.sum_range_succ' Finset.mul_sum mul_one Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.pow_one_cast
arithGeom_same_eq_mul_div 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Distrib.toAdd DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne	—	arithGeom_same_eq_mul_div' neg_sub div_neg mul_neg neg_div neg_neg
arithGeom_same_eq_mul_div' 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Distrib.toAdd DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	—	arithGeom_eq Mathlib.Tactic.FieldSimp.eq_eq_cancel_eq IsCancelMulZero.toIsLeftCancelMulZero instIsCancelMulZero Mathlib.Tactic.FieldSimp.eq_mul_of_eq_eq_eq_mul Mathlib.Tactic.FieldSimp.subst_add Mathlib.Tactic.FieldSimp.NF.mul_eq_eval Mathlib.Tactic.FieldSimp.NF.atom_eq_eval Mathlib.Tactic.FieldSimp.subst_sub Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval_cons_neg sub_ne_zero Mathlib.Tactic.FieldSimp.NF.eval_cons_mul_eval one_mul Mathlib.Tactic.FieldSimp.eq_div_of_eq_one_of_subst Mathlib.Tactic.FieldSimp.NF.cons_eq_div_of_eq_div div_one Mathlib.Tactic.FieldSimp.NF.eval_cons Mathlib.Tactic.FieldSimp.zpow'_one Mathlib.Tactic.FieldSimp.NF.div_eq_eval Mathlib.Tactic.FieldSimp.NF.one_eq_eval Mathlib.Tactic.FieldSimp.NF.eval_mul_eval_cons Mathlib.Tactic.FieldSimp.NF.div_eq_eval₃ Mathlib.Tactic.FieldSimp.NF.mul_eq_eval₃ mul_one Mathlib.Tactic.FieldSimp.NF.div_eq_eval₁ Mathlib.Tactic.FieldSimp.NF.cons_ne_zero one_ne_zero NeZero.one GroupWithZero.toNontrivial Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.cast_pos Mathlib.Meta.NormNum.isNat_ofNat Nat.cast_one Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.pow_one_cast
arithGeom_same_eq_sum 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring CommSemiring.toSemiring Distrib.toAdd Finset.sum NonUnitalNonAssocSemiring.toAddCommMonoid Finset.range Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero	—	arithGeom_eq_add_sum Finset.sum_range_succ mul_add Distrib.leftDistribClass add_comm mul_comm
arithGeom_strictMono 📖	mathematical	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing Field.toDivisionRing DivInvMonoid.toDiv DivisionRing.toDivInvMonoid SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup	StrictMono Nat.instPreorder arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Distrib.toAdd	—	strictMono_nat_of_lt_succ div_lt_arithGeom lt_trans Mathlib.Meta.Positivity.pos_of_isNat IsStrictOrderedRing.toIsOrderedRing IsSimpleRing.instNontrivial DivisionRing.isSimpleRing Mathlib.Meta.NormNum.isNat_ofNat Nat.cast_one LT.lt.ne' arithGeom_succ lt_of_not_ge Mathlib.Tactic.Linarith.lt_irrefl Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.cast_pos Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.add_pf_add_overlap_zero Mathlib.Tactic.Ring.add_overlap_pf_zero Mathlib.Meta.NormNum.IsInt.to_isNat Mathlib.Meta.NormNum.isInt_add Mathlib.Tactic.Ring.cast_zero Nat.cast_zero Mathlib.Tactic.Linarith.add_lt_of_neg_of_le Mathlib.Tactic.Linarith.sub_neg_of_lt div_lt_iff_of_neg PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono sub_neg IsRightCancelAdd.addRightStrictMono_of_addRightMono AddRightCancelSemigroup.toIsRightCancelAdd covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono IsOrderedRing.toIsOrderedAddMonoid Mathlib.Tactic.Linarith.sub_nonpos_of_le
arithGeom_succ 📖	mathematical	—	arithGeom	—	—
arithGeom_zero 📖	mathematical	—	arithGeom	—	—
arithGeom_zero_eq_mul_div 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Distrib.toAdd MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne	—	arithGeom_zero_eq_mul_div' neg_sub div_neg mul_neg neg_div neg_neg
arithGeom_zero_eq_mul_div' 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Distrib.toAdd MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	—	arithGeom_eq Mathlib.Tactic.Ring.of_eq Mathlib.Tactic.Ring.add_congr Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.sub_congr Mathlib.Tactic.Ring.cast_zero Mathlib.Meta.NormNum.isNat_ofNat Nat.cast_zero Mathlib.Tactic.Ring.div_congr Mathlib.Tactic.Ring.cast_pos Nat.cast_one Mathlib.Tactic.Ring.sub_pf Mathlib.Tactic.Ring.neg_add Mathlib.Tactic.Ring.neg_mul Mathlib.Tactic.Ring.neg_one_mul Mathlib.Meta.NormNum.IsInt.to_raw_eq Mathlib.Meta.NormNum.isInt_mul Mathlib.Meta.NormNum.IsInt.of_raw Mathlib.Meta.NormNum.IsNat.to_isInt Mathlib.Meta.NormNum.IsNat.of_raw Mathlib.Tactic.Ring.neg_zero Mathlib.Tactic.Ring.add_pf_add_lt Mathlib.Tactic.Ring.add_pf_zero_add Mathlib.Tactic.Ring.div_pf Mathlib.Tactic.Ring.atom_pf' Mathlib.Tactic.Ring.add_pf_add_gt Mathlib.Tactic.Ring.mul_one
arithGeom_zero_eq_sum 📖	mathematical	—	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring CommSemiring.toSemiring Distrib.toAdd MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass Finset.sum NonUnitalNonAssocSemiring.toAddCommMonoid Finset.range Monoid.toNatPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero	—	arithGeom_eq_add_sum MulZeroClass.mul_zero zero_add
div_lt_arithGeom 📖	mathematical	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing DivInvMonoid.toDiv DivisionRing.toDivInvMonoid Field.toDivisionRing SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup Ring.toAddGroupWithOne DivisionRing.toRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne	arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib Distrib.toAdd	—	add_lt_add_left IsRightCancelAdd.addRightStrictMono_of_addRightMono AddRightCancelSemigroup.toIsRightCancelAdd covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono IsOrderedRing.toIsOrderedAddMonoid IsStrictOrderedRing.toIsOrderedRing mul_lt_mul_of_pos_left IsStrictOrderedRing.toPosMulStrictMono
tendsto_arithGeom_atTop_of_one_lt 📖	mathematical	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing Field.toDivisionRing DivInvMonoid.toDiv DivisionRing.toDivInvMonoid SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup	Filter.Tendsto arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Distrib.toAdd Filter.atTop Nat.instPreorder	—	arithGeom_eq' LT.lt.ne' Filter.tendsto_atTop_add_const_right IsOrderedRing.toIsOrderedAddMonoid IsStrictOrderedRing.toIsOrderedRing Filter.Tendsto.atTop_mul_const sub_pos IsRightCancelAdd.addRightStrictMono_of_addRightMono AddRightCancelSemigroup.toIsRightCancelAdd covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono tendsto_pow_atTop_atTop_of_one_lt AddGroup.existsAddOfLE
tendsto_arithGeom_nhds_of_lt_one 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Preorder.toLT AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing Field.toDivisionRing	Filter.Tendsto arithGeom Distrib.toMul NonUnitalNonAssocSemiring.toDistrib Distrib.toAdd Filter.atTop Nat.instPreorder nhds DivInvMonoid.toDiv DivisionRing.toDivInvMonoid SubNegMonoid.toSub AddGroup.toSubNegMonoid AddGroupWithOne.toAddGroup	—	arithGeom_eq' LT.lt.ne zero_add Filter.Tendsto.add IsTopologicalSemiring.toContinuousAdd IsTopologicalRing.toIsTopologicalSemiring IsTopologicalDivisionRing.toIsTopologicalRing IsStrictOrderedRing.toIsTopologicalDivisionRing MulZeroClass.zero_mul Filter.Tendsto.mul_const IsTopologicalSemiring.toContinuousMul tendsto_pow_atTop_nhds_zero_of_lt_one AddGroup.existsAddOfLE tendsto_const_nhds

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