Theorems · Theorem · geometry

DifferentiableAt.inversion

∀ {E : Type u_1} {F : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
  [inst_3 : InnerProductSpace ℝ F] {c x : E → F} {R : E → ℝ} {a : E},
  DifferentiableAt ℝ c a →
    DifferentiableAt ℝ R a →
      DifferentiableAt ℝ x a → x a ≠ c a → DifferentiableAt ℝ (fun a => EuclideanGeometry.inversion (c a) (R a) (x a)) a

Defined in

Mathlib.Geometry.Euclidean.Inversion.Calculus

Cited by

1 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupInnerProductSpace