mem_analyticGroupoid — Mathlib

English

If n/2 < a < n, then (a : ZMod n).valMinAbs = a - n.

Русский

Если n/2 < a < n, то (a : ZMod n).valMinAbs = a - n.

LaTeX

$$$ (ha : n/2 < a) (ha' : a < n) \\Rightarrow (a : \\mathbb{Z}/n\\mathbb{Z}).valMinAbs = a - n$$$

Lean4

/-- `f ∈ analyticGroupoid` iff it and its inverse are analytic within `range I`. -/
theorem mem_analyticGroupoid {I : ModelWithCorners 𝕜 E H} {f : OpenPartialHomeomorph H H} :
    f ∈ analyticGroupoid I ↔
      AnalyticOn 𝕜 (I ∘ f ∘ I.symm) (I.symm ⁻¹' f.source ∩ range I) ∧
        AnalyticOn 𝕜 (I ∘ f.symm ∘ I.symm) (I.symm ⁻¹' f.target ∩ range I) :=
  by rfl

Похожие утверждения