Theorems · Theorem · approximation theory
Asymptotics.IsBigOWith.right_le_sub_of_lt_one
∀ {α : Type u_1} {E' : Type u_6} [inst : SeminormedAddCommGroup E'] {c : ℝ} {l : Filter α} {f₁ f₂ : α → E'},
Asymptotics.IsBigOWith c l f₁ f₂ → c < 1 → Asymptotics.IsBigOWith (1 / (1 - c)) l f₂ fun x => f₂ x - f₁ x- Defined in
- Mathlib.Analysis.Asymptotics.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Filterstatement and proof · cited by 8,121
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- mul_oneproof · cited by 3,885
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- mul_commproof · cited by 2,262
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- div_eq_mul_invproof · cited by 715
- one_divproof · cited by 624
- Filter.mem_of_supersetproof · cited by 308
- mul_subproof · cited by 201
Cited by2
Results whose statement or proof uses this declaration.
- Asymptotics.IsBigOWith.right_le_add_of_lt_oneproof · cited by 1
- Asymptotics.IsLittleO.right_isBigO_subproof · cited by 1