Theorems · Theorem · approximation theory
Asymptotics.IsBigO.const_mul_left
∀ {α : Type u_1} {F : Type u_4} {R : Type u_13} [inst : Norm F] [inst_1 : SeminormedRing R] {g : α → F} {l : Filter α}
{f : α → R}, f =O[l] g → ∀ (c' : R), (fun x => c' * f x) =O[l] g- Defined in
- Mathlib.Analysis.Asymptotics.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormSeminormedRing
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
- Normstatement and proof · cited by 512
- Asymptotics.IsBigOstatement and proof · cited by 506
- SeminormedRingstatement and proof · cited by 446
- Asymptotics.IsBigOWithproof · cited by 187
- Asymptotics.IsBigOWith.isBigOproof · cited by 40
- Asymptotics.IsBigO.isBigOWithproof · cited by 21
- Asymptotics.IsBigOWith.const_mul_leftproof · cited by 1
Cited by16
Results whose statement or proof uses this declaration.
- Complex.tsum_exp_neg_quadraticproof · cited by 3
- HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principalproof · cited by 3
- NormedRing.inverse_add_norm_diff_nth_orderproof · cited by 2
- ContinuousLinearMap.bilinear_hasTemperateGrowthproof · cited by 2
- FormalMultilinearSeries.taylorComp_sub_taylorComp_isBigOproof · cited by 2
- HurwitzKernelBounds.isBigO_atTop_F_nat_oneproof · cited by 2
- WeakFEPair.hf_zero'proof · cited by 1
- Real.isBigO_logb_const_mul_log_atTopproof · cited by 1
- Chebyshev.integral_one_div_log_sq_isBigOproof · cited by 1
- UpperHalfPlane.IsBoundedAtImInfty.slashproof · cited by 1
- Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleOproof · cited by 1
- Polynomial.isBigO_cobounded_of_degree_leproof · cited by 0