Theorems · Theorem · real analysis
ContDiff.mul
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {n : WithTop ℕ∞} {𝔸 : Type u_3} [inst_3 : NormedRing 𝔸] [inst_4 : NormedAlgebra 𝕜 𝔸]
{f g : E → 𝔸}, ContDiff 𝕜 n f → ContDiff 𝕜 n g → ContDiff 𝕜 n fun x => f x * g xThe product of two C^n functions is C^n.
- Cited by
- 8 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
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- ContDiffstatement and proof · cited by 352
- ContDiff.compproof · cited by 48
- ContDiff.prodMkproof · cited by 11
- contDiff_mulproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- Complex.contDiff_cosproof · cited by 9
- Complex.contDiff_sinproof · cited by 9
- ContDiff.div_constproof · cited by 8
- Manifold.exists_lt_locally_constant_of_riemannianEDist_ltproof · cited by 3
- differentiableAt_iteratedDerivWithin_cexpproof · cited by 2
- Real.contDiff_rpow_const_of_leproof · cited by 1
- Polynomial.contDiff_aevalproof · cited by 0
- Function.Periodic.contDiff_qParamproof · cited by 0