Theorems · Theorem · approximation theory
Asymptotics.IsBigO.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'}, f₁ =O[l] g → f₂ =O[l] g → (fun x => f₁ x - f₂ x) =O[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 107 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
- sub_eq_add_negproof · cited by 1,023
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- Asymptotics.IsBigO.addproof · cited by 21
- Asymptotics.IsBigO.neg_leftproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- PhragmenLindelof.isBigO_sub_exp_rpowproof · cited by 5
- Asymptotics.IsBigO.sub_iff_leftproof · cited by 2
- Asymptotics.IsBigO.congr_of_subproof · cited by 2
- PhragmenLindelof.isBigO_sub_exp_expproof · cited by 2
- WeakFEPair.hf_zero'proof · cited by 1
- Function.locallyFinsuppWithin.logCounting_single_isBigO_logproof · cited by 1
- Asymptotics.IsBigO.sub_iff_rightproof · cited by 0
- Asymptotics.IsBigO.add_iff_leftproof · cited by 0
- Asymptotics.IsBigO.add_iff_rightproof · cited by 0