Theorems · Theorem · Lie groups
Filter.Tendsto.sub
∀ {G : Type u_1} {α : Type u_2} [inst : TopologicalSpace G] [inst_1 : Sub G] [ContinuousSub G] {f g : α → G}
{l : Filter α} {a b : G},
Filter.Tendsto f l (nhds a) → Filter.Tendsto g l (nhds b) → Filter.Tendsto (fun x => f x - g x) l (nhds (a - b))- Defined in
- Mathlib.Topology.Algebra.Group.Defs
- Cited by
- 68 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Tendsto.compproof · cited by 560
- Continuous.tendstoproof · cited by 206
- ContinuousSubstatement and proof · cited by 48
- Filter.Tendsto.prodMk_nhdsproof · cited by 46
- ContinuousSub.continuous_subproof · cited by 6
Cited by68
Results whose statement or proof uses this declaration.
- MeasureTheory.StronglyMeasurable.subproof · cited by 18
- Filter.Tendsto.sub_constproof · cited by 16
- Filter.Tendsto.const_subproof · cited by 16
- hasSum_geometric_of_lt_oneproof · cited by 14
- tendsto_sub_nhds_zero_iffproof · cited by 12
- ContinuousWithinAt.subproof · cited by 10
- ContinuousAt.subproof · cited by 9
- StieltjesFunction.measure_singletonproof · cited by 6
- hasStrictDerivAt_invproof · cited by 4
- Asymptotics.isEquivalent_const_iff_tendstoproof · cited by 4
- Asymptotics.isEquivalent_iff_exists_eq_mulproof · cited by 4
- Complex.differentiableOn_update_limUnder_of_isLittleOproof · cited by 4