Theorems · Theorem · order theory
Filter.tendsto_neg_atTop_atBot
∀ {G : Type u_2} [inst : AddCommGroup G] [inst_1 : PartialOrder G] [IsOrderedAddMonoid G],
Filter.Tendsto Neg.neg Filter.atTop Filter.atBot- Defined in
- Mathlib.Order.Filter.AtTopBot.Group
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- OrderIso.negproof · cited by 27
- OrderIso.tendsto_atTopproof · cited by 3
Cited by18
Results whose statement or proof uses this declaration.
- Filter.tendsto_neg_atBot_atTopproof · cited by 22
- Filter.Tendsto.atTop_mul_negproof · cited by 3
- Filter.Tendsto.atBot_mul_posproof · cited by 2
- HasDerivAt.lhopital_zero_atBot_on_Iioproof · cited by 2
- Asymptotics.IsEquivalent.tendsto_atBotproof · cited by 2
- Finset.tendsto_Icc_neg_atTop_atTopproof · cited by 1
- GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_Iproof · cited by 1
- Real.tendsto_sigmoid_atTopproof · cited by 1
- Finset.tendsto_Ico_neg_atTop_atTopproof · cited by 1
- Finset.tendsto_Ioc_neg_atTop_atTopproof · cited by 1
- Finset.tendsto_Ioo_neg_atTop_atTopproof · cited by 1
- GaussianFourier.tendsto_verticalIntegralproof · cited by 1