SeminormFromConst

📁 Source: Mathlib/Analysis/Normed/Unbundled/SeminormFromConst.lean

Statistics

Metric	Count
Definitions normFromConst, seminormFromConst, seminormFromConst', seminormFromConst_seq	4
Theorems seminormFromConstRingNormOfField_def, seminormFromConst_apply_c, seminormFromConst_apply_of_isMul, seminormFromConst_bddBelow, seminormFromConst_const_mul, seminormFromConst_def, seminormFromConst_isLimit, seminormFromConst_isMul_of_isMul, seminormFromConst_isNonarchimedean, seminormFromConst_isPowMul, seminormFromConst_le_seminorm, seminormFromConst_one, seminormFromConst_one_le, seminormFromConst_seq_antitone, seminormFromConst_seq_def, seminormFromConst_seq_nonneg, seminormFromConst_seq_one, seminormFromConst_seq_zero, tendsto_seminormFromConst_seq_atTop	19
Total	23

(root)

Definitions

Name	Category	Theorems
normFromConst 📖	CompOp	1 math math: seminormFromConstRingNormOfField_def
seminormFromConst 📖	CompOp	2 math math: seminormFromConst_def, algNormFromConst_def
seminormFromConst' 📖	CompOp	13 math math: seminormFromConst_isMul_of_isMul, seminormFromConst_one_le, seminormFromConst_isNonarchimedean, seminormFromConst_le_seminorm, seminormFromConst_const_mul, seminormFromConst_apply_of_isMul, seminormFromConst_isPowMul, seminormFromConst_one, seminormFromConst_isLimit, seminormFromConst_apply_c, seminormFromConst_def, tendsto_seminormFromConst_seq_atTop, seminormFromConstRingNormOfField_def
seminormFromConst_seq 📖	CompOp	8 math math: seminormFromConst_seq_antitone, seminormFromConst_seq_one, seminormFromConst_isLimit, tendsto_seminormFromConst_seq_atTop, seminormFromConst_bddBelow, seminormFromConst_seq_def, seminormFromConst_seq_zero, seminormFromConst_seq_nonneg

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
seminormFromConstRingNormOfField_def 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne DivisionRing.toRing Field.toDivisionRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero DivisionSemiring.toSemiring Semifield.toDivisionSemiring Field.toSemifield	DFunLike.coe RingNorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Field.toCommRing Real RingNorm.funLike NonUnitalCommRing.toNonUnitalRing normFromConst seminormFromConst'	—	—
seminormFromConst_apply_c 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	seminormFromConst' DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Real RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing	—	mul_comm pow_succ le_add_self Nat.instCanonicallyOrderedAdd mul_div_assoc div_self pow_ne_zero isReduced_of_noZeroDivisors NormMulClass.toNoZeroDivisors NormedDivisionRing.toNormMulClass mul_one tendsto_const_nhds tendsto_nhds_unique TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat tendsto_seminormFromConst_seq_atTop
seminormFromConst_apply_of_isMul 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring Real.instMul	seminormFromConst' DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Real RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing	—	pow_zero mul_one div_one mul_div_assoc div_self pow_ne_zero isReduced_of_noZeroDivisors NormMulClass.toNoZeroDivisors NormedDivisionRing.toNormMulClass tendsto_const_nhds tendsto_nhds_unique TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat tendsto_seminormFromConst_seq_atTop
seminormFromConst_bddBelow 📖	mathematical	—	BddBelow Real Real.instLE Set.range seminormFromConst_seq	—	seminormFromConst_seq_nonneg
seminormFromConst_const_mul 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	seminormFromConst' Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Real Real.instMul	—	Filter.Tendsto.comp tendsto_seminormFromConst_seq_atTop Filter.tendsto_atTop_atTop_of_monotone add_left_mono covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono Nat.instIsOrderedAddMonoid seminormFromConst_apply_c tendsto_nhds_unique TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat Mathlib.Tactic.Ring.div_congr Mathlib.Tactic.Ring.atom_pf' Mathlib.Tactic.Ring.mul_congr Mathlib.Tactic.Ring.atom_pf Mathlib.Tactic.Ring.add_mul Mathlib.Tactic.Ring.mul_add Mathlib.Tactic.Ring.mul_pf_left Mathlib.Tactic.Ring.mul_pf_right Mathlib.Tactic.Ring.one_mul Mathlib.Tactic.Ring.mul_zero Mathlib.Tactic.Ring.add_pf_add_zero Mathlib.Tactic.Ring.zero_mul Mathlib.Tactic.Ring.pow_congr Mathlib.Tactic.Ring.pow_add Mathlib.Tactic.Ring.single_pow Mathlib.Tactic.Ring.mul_pow Mathlib.Tactic.Ring.one_pow Mathlib.Tactic.Ring.pow_zero Mathlib.Tactic.RingNF.mul_assoc_rev Mathlib.Tactic.RingNF.nat_rawCast_1 pow_one mul_one add_zero Mathlib.Tactic.Ring.div_pf Mathlib.Tactic.Ring.inv_single Mathlib.Tactic.Ring.inv_mul Mathlib.Meta.NormNum.IsNat.to_raw_eq Mathlib.Meta.NormNum.IsNNRat.to_isNat Mathlib.Meta.NormNum.isNNRat_inv_pos RCLike.charZero_rclike Mathlib.Meta.NormNum.IsNat.to_isNNRat Mathlib.Meta.NormNum.IsNat.of_raw 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 mul_assoc mul_inv_cancel₀ Filter.Tendsto.mul IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal tendsto_const_nhds
seminormFromConst_def 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Real RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing seminormFromConst seminormFromConst'	—	—
seminormFromConst_isLimit 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	Filter.Tendsto Real seminormFromConst_seq Filter.atTop Nat.instPreorder nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace seminormFromConst'	—	tendsto_seminormFromConst_seq_atTop
seminormFromConst_isMul_of_isMul 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring Real.instMul	seminormFromConst' Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Real Real.instMul	—	seminormFromConst_apply_of_isMul mul_assoc mul_div_assoc Filter.Tendsto.const_mul IsSemitopologicalSemiring.toSeparatelyContinuousMul IsSemitopologicalRing.toIsSemitopologicalSemiring IsTopologicalRing.toIsSemitopologicalRing instIsTopologicalRingReal tendsto_seminormFromConst_seq_atTop tendsto_nhds_unique TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat
seminormFromConst_isNonarchimedean 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring IsNonarchimedean Real.linearOrder Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring	IsNonarchimedean Real Real.linearOrder Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing seminormFromConst'	—	le_of_tendsto_of_tendsto' HasSolidNorm.orderClosedTopology instHasSolidNormReal Real.instIsOrderedAddMonoid Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat tendsto_seminormFromConst_seq_atTop Filter.Tendsto.max add_mul Distrib.rightDistribClass le_max_iff div_le_div_of_nonneg_right MulPosReflectLE.toMulPosReflectLT MulPosStrictMono.toMulPosReflectLE IsStrictOrderedRing.toMulPosStrictMono Real.instIsStrictOrderedRing le_of_lt pow_pos IsStrictOrderedRing.toPosMulStrictMono IsStrictOrderedRing.toZeroLEOneClass lt_of_le_of_ne' NonnegHomClass.apply_nonneg RingSeminormClass.toNonnegHomClass RingSeminorm.ringSeminormClass
seminormFromConst_isPowMul 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring seminormFromConst'	—	Filter.Tendsto.comp tendsto_seminormFromConst_seq_atTop Filter.tendsto_atTop_atTop_of_monotone mul_le_mul_right Nat.instMulLeftMono le_mul_of_one_le_left' covariant_swap_mul_of_covariant_mul tendsto_nhds_unique TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat mul_comm div_pow mul_pow Filter.Tendsto.pow IsTopologicalSemiring.toContinuousMul IsTopologicalRing.toIsTopologicalSemiring instIsTopologicalRingReal
seminormFromConst_le_seminorm 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	Real Real.instLE seminormFromConst' DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing	—	le_of_tendsto instClosedIicTopology HasSolidNorm.orderClosedTopology instHasSolidNormReal Real.instIsOrderedAddMonoid Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat tendsto_seminormFromConst_seq_atTop seminormFromConst_seq.eq_1 div_le_iff₀ MulPosReflectLE.toMulPosReflectLT MulPosStrictMono.toMulPosReflectLE IsStrictOrderedRing.toMulPosStrictMono Real.instIsStrictOrderedRing pow_pos IsStrictOrderedRing.toPosMulStrictMono IsStrictOrderedRing.toZeroLEOneClass lt_of_le_of_ne' NonnegHomClass.apply_nonneg RingSeminormClass.toNonnegHomClass RingSeminorm.ringSeminormClass SubmultiplicativeHomClass.map_mul_le_mul RingSeminormClass.toSubmultiplicativeHomClass
seminormFromConst_one 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	seminormFromConst' AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real Real.instOne	—	tendsto_nhds_unique_of_eventuallyEq TopologicalSpace.t2Space_of_metrizableSpace EMetricSpace.metrizableSpace Filter.atTop_neBot instIsDirectedOrder IsStrictOrderedRing.toIsOrderedRing Nat.instIsStrictOrderedRing instArchimedeanNat tendsto_seminormFromConst_seq_atTop tendsto_const_nhds seminormFromConst_seq_one
seminormFromConst_one_le 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	Real Real.instLE seminormFromConst' AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne	—	le_of_eq seminormFromConst_one
seminormFromConst_seq_antitone 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	Antitone Real Nat.instPreorder Real.instPreorder seminormFromConst_seq	—	pow_add mul_assoc lt_of_le_of_ne NonnegHomClass.apply_nonneg RingSeminormClass.toNonnegHomClass Real.instIsOrderedAddMonoid RingSeminorm.ringSeminormClass le_trans div_le_div_iff_of_pos_right MulPosReflectLE.toMulPosReflectLT MulPosStrictMono.toMulPosReflectLE IsStrictOrderedRing.toMulPosStrictMono Real.instIsStrictOrderedRing pow_pos IsStrictOrderedRing.toPosMulStrictMono Real.instZeroLEOneClass SubmultiplicativeHomClass.map_mul_le_mul RingSeminormClass.toSubmultiplicativeHomClass LE.le.eq_or_lt pow_zero mul_one mul_le_mul_of_nonneg_left IsOrderedRing.toPosMulMono Real.instIsOrderedRing mul_div_assoc div_eq_mul_inv pow_sub₀ mul_comm mul_inv_cancel₀ pow_ne_zero isReduced_of_noZeroDivisors NormMulClass.toNoZeroDivisors NormedDivisionRing.toNormMulClass one_mul le_refl
seminormFromConst_seq_def 📖	mathematical	—	seminormFromConst_seq Real DivInvMonoid.toDiv Real.instDivInvMonoid DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing Distrib.toMul NonUnitalNonAssocSemiring.toDistrib NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring Real.instMonoid	—	—
seminormFromConst_seq_nonneg 📖	mathematical	—	Pi.hasLe Real Real.instLE Pi.instZero Real.instZero seminormFromConst_seq	—	div_nonneg PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing NonnegHomClass.apply_nonneg RingSeminormClass.toNonnegHomClass Real.instIsOrderedAddMonoid RingSeminorm.ringSeminormClass pow_nonneg Real.instZeroLEOneClass IsOrderedRing.toPosMulMono Real.instIsOrderedRing
seminormFromConst_seq_one 📖	mathematical	IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Real RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing	seminormFromConst_seq AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real Real.instOne	—	one_mul div_self pow_ne_zero isReduced_of_noZeroDivisors NormMulClass.toNoZeroDivisors NormedDivisionRing.toNormMulClass
seminormFromConst_seq_zero 📖	mathematical	DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Real RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring Real.instZero	seminormFromConst_seq MulZeroClass.toZero NonUnitalNonAssocSemiring.toMulZeroClass NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing Pi.instZero Real Real.instZero	—	seminormFromConst_seq_def MulZeroClass.zero_mul zero_div Pi.zero_apply
tendsto_seminormFromConst_seq_atTop 📖	mathematical	Real Real.instLE DFunLike.coe RingSeminorm NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing NonUnitalCommRing.toNonUnitalNonAssocCommRing CommRing.toNonUnitalCommRing RingSeminorm.funLike NonUnitalCommRing.toNonUnitalRing AddMonoidWithOne.toOne AddGroupWithOne.toAddMonoidWithOne Ring.toAddGroupWithOne CommRing.toRing Real.instOne IsPowMul Monoid.toPow MonoidWithZero.toMonoid Semiring.toMonoidWithZero CommSemiring.toSemiring CommRing.toCommSemiring	Filter.Tendsto Real seminormFromConst_seq Filter.atTop Nat.instPreorder nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace seminormFromConst'	—	tendsto_atTop_ciInf LinearOrder.infConvergenceClass instOrderTopologyReal seminormFromConst_seq_antitone seminormFromConst_bddBelow

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