Theorems · Theorem · real analysis
contDiff_smul_const
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type uF} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {n : WithTop ℕ∞} {A : Type u_4} [inst_3 : NormedRing A] [inst_4 : NormedAlgebra 𝕜 A]
[inst_5 : Module A F] [IsScalarTower 𝕜 A F] [IsBoundedSMul A F] (v : F), ContDiff 𝕜 n fun a => a • vScalar multiplication is smooth (as a function of the scalar variable).
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- IsScalarTowerstatement and proof · cited by 3,896
- WithTopstatement and proof · cited by 3,754
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- ContDiffstatement · cited by 352
- IsBoundedSMulstatement and proof · cited by 329
- ContinuousLinearMap.idproof · cited by 233
Cited by2
Results whose statement or proof uses this declaration.
- ContDiffWithinAt.smul_constproof · cited by 2
- ContDiff.smul_constproof · cited by 0