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Theorems · Theorem · real analysis

ContDiff.div

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {f g : E → 𝕜} {n : WithTop ℕ∞},
  ContDiff 𝕜 n f → ContDiff 𝕜 n g → (∀ (x : E), g x ≠ 0) → ContDiff 𝕜 n (f / g)
Defined in
Mathlib.Analysis.Calculus.ContDiff.Operations
Cited by
2 results in Mathlib
Foundations
Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpace
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Around this declaration

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

Real.smoothTransition.contDiff · cited by 3smoothTransition.contDiffContDiff.fun_div · cited by 0ContDiff.fun_divNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldENat · cited by 4985ENatWithTop · cited by 3754WithTopContDiff · cited by 352ContDiffContDiffAt.div · cited by 3ContDiffAt.divContDiff.divCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.