Theorems · Theorem · real analysis
contDiff_const_smul
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {F : Type uF} [inst_1 : NormedAddCommGroup F]
[inst_2 : NormedSpace 𝕜 F] {n : WithTop ℕ∞} {R : Type u_3} [inst_3 : DistribSMul R F] [SMulCommClass 𝕜 R F]
[ContinuousConstSMul R F] (c : R), ContDiff 𝕜 n fun p => c • pScalar multiplication is smooth (as a function of the vector variable).
- Cited by
- 5 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.
Cites11
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
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- SMulCommClassstatement and proof · cited by 1,927
- ContinuousConstSMulstatement and proof · cited by 832
- ContDiffstatement · cited by 352
- ContinuousLinearMap.idproof · cited by 233
- DistribSMulstatement and proof · cited by 117
- ContinuousLinearMap.contDiffproof · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- ContDiff.const_smulproof · cited by 4
- ContDiffWithinAt.const_smulproof · cited by 2
- MeasureTheory.contDiff_charFunproof · cited by 2
- ContDiffAt.contDiffAt_norm_smulproof · cited by 1
- MeasureTheory.contDiff_charFun'proof · cited by 0