Theorems · Theorem · global analysis

HasMFDerivWithinAt.prod

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s : Set M} {z : M} {F' : Type u_21}
  [inst_6 : NormedCommRing F'] [inst_7 : NormedAlgebra 𝕜 F'] {ι : Type} {t : Finset ι} {f : ι → M → F'}
  {f' : ι → TangentSpace I z →L[𝕜] F'} [inst_8 : DecidableEq ι],
  (∀ i ∈ t, HasMFDerivAt[s] (f i) z (f' i)) →
    HasMFDerivAt[s] (∏ i ∈ t, f i) z (∑ i ∈ t, (∏ j ∈ t.erase i, f j z) • f' i)

Defined in

Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions

Cited by

2 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedCommRingNormedAlgebraDecidableEq