Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.neg_left
∀ {α : Type u_1} {F : Type u_4} {E' : Type u_6} [inst : Norm F] [inst_1 : SeminormedAddCommGroup E'] {g : α → F}
{f' : α → E'} {l : Filter α}, f' =o[l] g → (fun x => -f' x) =o[l] gAlias of the reverse direction of Asymptotics.isLittleO_neg_left.
- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 105 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.
Cites5
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 · cited by 375
- Asymptotics.isLittleO_neg_leftproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- Asymptotics.IsLittleO.subproof · cited by 9
- Asymptotics.IsEquivalent.sub_isLittleOproof · cited by 3
- Asymptotics.IsLittleO.symmproof · cited by 2
- isLittleO_log_rpow_nhdsGT_zeroproof · cited by 1
- isBigO_rpow_zero_log_smulproof · cited by 1
- Asymptotics.IsEquivalent.negproof · cited by 1
- Asymptotics.IsBigOWith.sub_isLittleOproof · cited by 0