Theorems · Theorem · approximation theory
Asymptotics.IsBigOWith.weaken
∀ {α : Type u_1} {E : Type u_3} {F' : Type u_7} [inst : Norm E] [inst_1 : SeminormedAddCommGroup F'] {c c' : ℝ}
{f : α → E} {g' : α → F'} {l : Filter α}, Asymptotics.IsBigOWith c l f g' → c ≤ c' → Asymptotics.IsBigOWith c' l f g'- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 113 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.
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
- Set.ofPredproof · cited by 6,101
- Norm.normproof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- norm_nonnegproof · cited by 725
- Normstatement and proof · cited by 512
- Filter.mem_of_supersetproof · cited by 308
- mul_le_mul_of_nonneg_rightproof · cited by 301
- Asymptotics.IsBigOWithstatement and proof · cited by 187
- Asymptotics.IsBigOWith.boundproof · cited by 17
- Asymptotics.IsBigOWith.of_boundproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- Asymptotics.IsBigOWith.exists_posproof · cited by 2
- Asymptotics.IsBigOWith.of_powproof · cited by 2
- Asymptotics.IsBigOWith.prod_leftproof · cited by 1
- Asymptotics.IsBigOWith.sup'proof · cited by 1
- Asymptotics.isBigO_iff_eventually_isBigOWithproof · cited by 1