Theorems · Theorem · real analysis
derivWithin_const_mul_field
∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {x : 𝕜} {s : Set 𝕜} {𝕜' : Type u_2} [inst_1 : NormedDivisionRing 𝕜']
[inst_2 : NormedAlgebra 𝕜 𝕜'] {v : 𝕜 → 𝕜'} (u : 𝕜'), derivWithin (fun y => u * v y) s x = u * derivWithin v s xA variant of derivWithin_const_mul without differentiability assumption when the scalar
multiplication is by division ring elements.
- Defined in
- Mathlib.Analysis.Calculus.Deriv.Mul
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- NormedAlgebrastatement and proof · cited by 1,165
- NormedDivisionRingstatement and proof · cited by 360
- derivWithinstatement · cited by 258
- derivWithin_const_smul_fieldproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- deriv_const_mul_fieldproof · cited by 5