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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Filter.atBotstatement · cited by 512
- Filter.tendsto_neg_atTop_atBotproof · cited by 18
Cited by22
Results whose statement or proof uses this declaration.
- Real.tendsto_exp_atBotproof · cited by 13
- Filter.tendsto_abs_atBot_atTopproof · cited by 7
- cexp_neg_quadratic_isLittleO_abs_rpow_cocompactproof · cited by 2
- not_differentiableWithinAt_of_deriv_tendsto_atBot_Iioproof · cited by 2
- not_differentiableWithinAt_of_deriv_tendsto_atBot_Ioiproof · cited by 2
- Polynomial.abs_tendsto_atBotproof · cited by 2
- Filter.Tendsto.atBot_mul_posproof · cited by 2
- HasDerivAt.lhopital_zero_atBot_on_Iioproof · cited by 2
- Asymptotics.IsEquivalent.tendsto_atBotproof · cited by 2
- Real.tendsto_sigmoid_atBotproof · cited by 1
- Polynomial.isEquivalent_atBot_leadproof · cited by 1
- Filter.Tendsto.atBot_mul_atTop₀proof · cited by 1