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Theorems · Theorem · order theory

Filter.tendsto_neg_atBot_atTop

∀ {G : Type u_2} [inst : AddCommGroup G] [inst_1 : PartialOrder G] [IsOrderedAddMonoid G],
  Filter.Tendsto Neg.neg Filter.atBot Filter.atTop
Defined in
Mathlib.Order.Filter.AtTopBot.Group
Cited by
22 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroupPartialOrderIsOrderedAddMonoid

Around this declaration

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

Real.tendsto_exp_atBot · cited by 13Real.tendsto_exp_atBotFilter.tendsto_abs_atBot_atTop · cited by 7Filter.tendsto_abs_atBot_…cexp_neg_quadratic_isLittleO_abs_rpow_cocompact · cited by 2cexp_neg_quadratic_isLitt…not_differentiableWithinAt_of_deriv_tendsto_atBot_Iio · cited by 2not_differentiableWithinA…not_differentiableWithinAt_of_deriv_tendsto_atBot_Ioi · cited by 2not_differentiableWithinA…Polynomial.abs_tendsto_atBot · cited by 2Polynomial.abs_tendsto_at…Filter.Tendsto.atBot_mul_pos · cited by 2Tendsto.atBot_mul_posHasDerivAt.lhopital_zero_atBot_on_Iio · cited by 2HasDerivAt.lhopital_zero_…Asymptotics.IsEquivalent.tendsto_atBot · cited by 2IsEquivalent.tendsto_atBotReal.tendsto_sigmoid_atBot · cited by 1Real.tendsto_sigmoid_atBotPolynomial.isEquivalent_atBot_lead · cited by 1Polynomial.isEquivalent_a…Filter.Tendsto.atBot_mul_atTop₀ · cited by 1Tendsto.atBot_mul_atTop₀isBigO_norm_Icc_restrict_atBot · cited by 1isBigO_norm_Icc_restrict_…MeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Iic · cited by 1MeasureTheory.tendsto_lim…Filter.Tendsto.atBot_mul_neg · cited by 1Tendsto.atBot_mul_negAddCommGroup · cited by 12871AddCommGroupPartialOrder · cited by 6410PartialOrderFilter.Tendsto · cited by 3814Filter.TendstoFilter.atTop · cited by 2405Filter.atTopIsOrderedAddMonoid · cited by 1659IsOrderedAddMonoidFilter.atBot · cited by 512Filter.atBotFilter.tendsto_neg_atTop_atBot · cited by 18Filter.tendsto_neg_atTop_…Filter.tendsto_neg_atBot_atTopCITED BYCITES

Cites7

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Cited by22

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