Theorems · Theorem · approximation theory
Asymptotics.IsBigO.congr
∀ {α : Type u_1} {E : Type u_3} {F : Type u_4} [inst : Norm E] [inst_1 : Norm F] {l : Filter α} {f₁ f₂ : α → E}
{g₁ g₂ : α → F}, f₁ =O[l] g₁ → (∀ (x : α), f₁ x = f₂ x) → (∀ (x : α), g₁ x = g₂ x) → f₂ =O[l] g₂- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 6 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.
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
- Filter.univ_mem'proof · cited by 1,672
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- Asymptotics.IsBigO.congr'proof · cited by 16
Cited by6
Results whose statement or proof uses this declaration.
- Asymptotics.IsBigO.congr_leftproof · cited by 8
- Asymptotics.IsBigO.sub_iff_leftproof · cited by 2
- Asymptotics.IsBigO.sub_iff_rightproof · cited by 0
- Asymptotics.IsBigO.congr_rightproof · cited by 0
- Asymptotics.IsBigO.add_iff_leftproof · cited by 0
- Asymptotics.IsBigO.add_iff_rightproof · cited by 0