Theorems · Theorem · approximation theory
Asymptotics.IsLittleO.trans_isBigOWith
∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} {G : Type u_5} [inst : Norm E] [inst_1 : Norm F] [inst_2 : Norm G]
{c : ℝ} {f : α → E} {g : α → F} {k : α → G} {l : Filter α},
f =o[l] g → Asymptotics.IsBigOWith c l g k → 0 < c → f =o[l] k- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- Normstatement and proof · cited by 512
- Asymptotics.IsLittleOstatement and proof · cited by 375
- div_posproof · cited by 337
- Asymptotics.IsBigOWithstatement and proof · cited by 187
- div_mul_cancel₀proof · cited by 122
- Asymptotics.IsLittleO_defproof · cited by 19
- Asymptotics.IsBigOWith.transproof · cited by 13
- Asymptotics.IsBigOWith.congr_constproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- Asymptotics.IsLittleO.trans_isBigOproof · cited by 19
- Asymptotics.IsLittleO.transproof · cited by 4
- Asymptotics.IsLittleO.trans_leproof · cited by 2
- Asymptotics.isLittleO_const_iff_isLittleO_oneproof · cited by 1