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Theorems · Theorem · order theory

tendsto_natCast_atTop_atTop

∀ {R : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [IsOrderedRing R] [Archimedean R],
  Filter.Tendsto Nat.cast Filter.atTop Filter.atTop
Defined in
Mathlib.Order.Filter.AtTopBot.Archimedean
Cited by
51 results in Mathlib
Foundations
Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringPartialOrderIsOrderedRingArchimedean

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

summable_pow_mul_jacobiTheta₂_term_bound · cited by 6summable_pow_mul_jacobiTh…Filter.Eventually.natCast_atTop · cited by 6Eventually.natCast_atTopPairReduction.exists_radius_le · cited by 4PairReduction.exists_radi…summable_jacobiTheta₂_term_iff · cited by 4summable_jacobiTheta₂_ter…Asymptotics.isLittleO_sum_range_of_tendsto_zero · cited by 3Asymptotics.isLittleO_sum…Real.tendsto_eulerMascheroniSeq' · cited by 3Real.tendsto_eulerMascher…LiouvilleWith.frequently_lt_rpow_neg · cited by 3LiouvilleWith.frequently_…MeasureTheory.hausdorffMeasure_pi_real · cited by 3MeasureTheory.hausdorffMe…ZetaAsymptotics.termTSum_of_lt · cited by 2ZetaAsymptotics.termTSum_…Real.tendsto_log_nat_add_one_sub_log · cited by 2Real.tendsto_log_nat_add_…Asymptotics.IsBigO.natCast_atTop · cited by 2IsBigO.natCast_atTopReal.tendsto_one_add_div_pow_exp · cited by 2Real.tendsto_one_add_div_…AntitoneOn.integrableOn_Ioi_of_summable_comp_add · cited by 2AntitoneOn.integrableOn_I…tendsto_birkhoffAverage_apply_sub_birkhoffAverage · cited by 2tendsto_birkhoffAverage_a…qExpansion_coeff_isBigO_of_norm_isBigO · cited by 2qExpansion_coeff_isBigO_o…Semiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderFilter.Tendsto · cited by 3814Filter.TendstoFilter.atTop · cited by 2405Filter.atTopIsOrderedRing · cited by 777IsOrderedRingArchimedean · cited by 603ArchimedeanNat.mono_cast · cited by 76Nat.mono_castexists_nat_ge · cited by 20exists_nat_geMonotone.tendsto_atTop_atTop · cited by 13Monotone.tendsto_atTop_at…tendsto_natCast_atTop_atTopCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by51

Results whose statement or proof uses this declaration.