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Theorems · Theorem · real analysis

ContDiffAt.inv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {x : E} {n : WithTop ℕ∞} {𝕜' : Type u_4} [inst_3 : NormedField 𝕜']
  [inst_4 : NormedAlgebra 𝕜 𝕜'] {f : E → 𝕜'}, ContDiffAt 𝕜 n f x → f x ≠ 0 → ContDiffAt 𝕜 n f⁻¹ x
Defined in
Mathlib.Analysis.Calculus.ContDiff.Operations
Cited by
3 results in Mathlib
Foundations
Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedFieldNormedAlgebra
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ContDiff.inv · cited by 3ContDiff.invOpenPartialHomeomorph.contDiffOn_univUnitBall_symm · cited by 1OpenPartialHomeomorph.con…ContDiffAt.fun_inv · cited by 0ContDiffAt.fun_invNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldENat · cited by 4985ENatWithTop · cited by 3754WithTopNormedAlgebra · cited by 1165NormedAlgebraNormedField · cited by 1084NormedFieldContDiffAt · cited by 262ContDiffAtContDiffWithinAt.inv · cited by 4ContDiffWithinAt.invContDiffAt.invCITED BYCITES

Cites9

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Cited by3

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