Theorems · Theorem · approximation theory
Asymptotics.IsBigO.sup
∀ {α : Type u_1} {E : Type u_3} {F' : Type u_7} [inst : Norm E] [inst_1 : SeminormedAddCommGroup F'] {f : α → E}
{g' : α → F'} {l l' : Filter α}, f =O[l] g' → f =O[l'] g' → f =O[l ⊔ l'] g'- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 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.
- Realproof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- Asymptotics.IsBigOWithproof · cited by 187
- Asymptotics.IsBigOWith.isBigOproof · cited by 40
- Asymptotics.IsBigO.isBigOWithproof · cited by 21
- Asymptotics.IsBigOWith.sup'proof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- PhragmenLindelof.quadrant_Iproof · cited by 4
- Asymptotics.isBigO_supproof · cited by 2
- Asymptotics.IsTheta.supproof · cited by 1