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Theorems · Theorem · real analysis

differentiableAt_inv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {R : Type u_5} [inst_1 : NormedDivisionRing R]
  [inst_2 : NormedAlgebra 𝕜 R] {x : R}, x ≠ 0 → DifferentiableAt 𝕜 Inv.inv x
Defined in
Mathlib.Analysis.Calculus.FDeriv.Mul
Cited by
7 results in Mathlib
Foundations
Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedDivisionRingNormedAlgebra
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Around this declaration

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

DifferentiableAt.inv · cited by 8DifferentiableAt.invDifferentiableWithinAt.inv · cited by 4DifferentiableWithinAt.invdifferentiableWithinAt_inv · cited by 1differentiableWithinAt_invlogDeriv_eqOn_iff · cited by 0logDeriv_eqOn_iffderivWithin_inv · cited by 0derivWithin_invfderivWithin_inv · cited by 0fderivWithin_invfderivWithin_inv' · cited by 0fderivWithin_inv'NontriviallyNormedField · cited by 8742NontriviallyNormedFieldNormedAlgebra · cited by 1165NormedAlgebraDifferentiableAt · cited by 617DifferentiableAtNormedDivisionRing · cited by 360NormedDivisionRingHasFDerivAt.differentiableAt · cited by 83HasFDerivAt.differentiabl…hasFDerivAt_inv' · cited by 3hasFDerivAt_inv'differentiableAt_invCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.