Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.congr_of_sub
∀ {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 : α → E'}, (fun x => f₁ x - f₂ x) =o[l] g → (f₁ =o[l] g ↔ f₂ =o[l] g)- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 112 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.
Cites9
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_cancelproof · cited by 344
- sub_sub_cancelproof · cited by 105
- Asymptotics.IsLittleO.addproof · cited by 17
- Asymptotics.IsLittleO.congr_leftproof · cited by 12
- Asymptotics.IsLittleO.subproof · cited by 9
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.