conformalFactorAt_pos — Mathlib

English

For h conformal at x and any u,v, the inner product of f'(x)u and f'(x)v equals conformalFactorAt(h) times inner product of u and v.

Русский

Для h конформно в x и любых u,v: ⟪f'(x)u, f'(x)v⟫ = conformalFactorAt(h) · ⟪u,v⟫.

LaTeX

$$$ ⟪f'(x)u, f'(x)v\rangle = (\text{conformalFactorAt}(h)) \cdot ⟪u,v⟫ $$$

Lean4

theorem conformalFactorAt_pos {f : E → F} {x : E} (h : ConformalAt f x) : 0 < conformalFactorAt h :=
  (Classical.choose_spec <| conformalAt_iff'.mp h).1

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