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Theorems · Theorem · global analysis

extDeriv_smul

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : ℕ} {x : E} (c : 𝕜)
  (ω : E → E [⋀^Fin n]→L[𝕜] F), extDeriv (c • ω) x = c • extDeriv ω x
Defined in
Mathlib.Analysis.Calculus.DifferentialForm.Basic
Cited by
1 results in Mathlib
Foundations
Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

extDeriv_fun_smul · cited by 0extDeriv_fun_smulNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldSet.univ · cited by 3945Set.univContinuousAlternatingMap · cited by 292ContinuousAlternatingMapextDerivWithin · cited by 23extDerivWithinextDeriv · cited by 14extDerivextDerivWithin_smul · cited by 2extDerivWithin_smulextDeriv_smulCITED BYCITES

Cites8

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Cited by1

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