Theorems · Theorem · real analysis
differentiableOn_inverse
∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {R : Type u_5} [inst_1 : NormedRing R] [HasSummableGeomSeries R]
[inst_3 : NormedAlgebra 𝕜 R], DifferentiableOn 𝕜 Ring.inverse {x | IsUnit x}- Defined in
- Mathlib.Analysis.Calculus.FDeriv.Mul
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Set.ofPredstatement and proof · cited by 6,101
- IsUnitstatement and proof · cited by 1,602
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- DifferentiableOnstatement · cited by 419
- Ring.inversestatement · cited by 160
- HasSummableGeomSeriesstatement and proof · cited by 60
- differentiableWithinAt_inverseproof · cited by 1
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