Theorems · Theorem · order theory
Filter.tendsto_mabs_atBot_atTop
∀ {G : Type u_2} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G],
Filter.Tendsto mabs Filter.atBot Filter.atTop$\lim_{x\to\infty^{-1}|x|_m=+\infty$
- Defined in
- Mathlib.Order.Filter.AtTopBot.Group
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Filter.Tendstostatement · cited by 3,814
- Filter.atTopstatement · cited by 2,405
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- Filter.atBotstatement · cited by 512
- mabsstatement · cited by 148
- Filter.tendsto_atTop_monoproof · cited by 22
- inv_le_mabsproof · cited by 4
- Filter.tendsto_inv_atBot_atTopproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Filter.comap_mabs_atTopproof · cited by 0