Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.triangle
∀ {α : Type u_1} {F : Type u_4} {E' : Type u_6} [inst : Norm F] [inst_1 : SeminormedAddCommGroup E'] {g : α → F}
{l : Filter α} {f₁ f₂ f₃ : α → E'},
(fun x => f₁ x - f₂ x) =o[l] g → (fun x => f₂ x - f₃ x) =o[l] g → (fun x => f₁ x - f₃ x) =o[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormSeminormedAddCommGroup
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.
- Filterstatement and proof · cited by 8,121
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Normstatement and proof · cited by 512
- Asymptotics.IsLittleOstatement and proof · cited by 375
- sub_add_sub_cancelproof · cited by 56
- Asymptotics.IsLittleO.addproof · cited by 17
- Asymptotics.IsLittleO.congr_leftproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- Asymptotics.IsEquivalent.transproof · cited by 5