Theorems · Theorem · real analysis
HasDerivAt.const_sub
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {x : 𝕜} (c : F),
HasDerivAt f f' x → HasDerivAt (fun x => c - f x) (-f') x- Defined in
- Mathlib.Analysis.Calculus.Deriv.Add
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 170 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- HasDerivAtstatement and proof · cited by 493
- HasDerivAtFilter.const_subproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- Real.hasDerivAt_arccosproof · cited by 2
- Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_rangeproof · cited by 2
- hasDerivAt_circleAverage_herglotzRieszKernel_smulproof · cited by 1
- Complex.betaIntegral_recurrenceproof · cited by 1
- Real.hasDerivAt_Gamma_one_halfproof · cited by 1
- HasDerivAt.comp_const_subproof · cited by 0
- map_add_eq_sum_add_integral_iteratedFDerivproof · cited by 0