Theorems · Theorem · order theory
Filter.Tendsto.atTop_of_add_isBoundedUnder_le
∀ {α : Type u_1} {M : Type u_2} [inst : AddCommMonoid M] [inst_1 : Preorder M] [IsOrderedCancelAddMonoid M]
{l : Filter α} {f g : α → M},
Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) l g →
Filter.Tendsto (fun x => f x + g x) l Filter.atTop → Filter.Tendsto f l Filter.atTop- Defined in
- Mathlib.Order.Filter.AtTopBot.Monoid
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Filterstatement and proof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Eventuallyproof · cited by 3,134
- Filter.atTopstatement and proof · cited by 2,405
- le_reflproof · cited by 2,061
- Filter.mapproof · cited by 819
- add_le_addproof · cited by 666
- Filter.Eventually.monoproof · cited by 646
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- Filter.IsBoundedUnderstatement and proof · cited by 247
Cited by3
Results whose statement or proof uses this declaration.
- Filter.tendsto_atTop_add_right_of_le'proof · cited by 3
- Filter.Tendsto.atTop_of_add_le_constproof · cited by 1
- Filter.Tendsto.atBot_of_add_isBoundedUnder_geproof · cited by 0