English
If h is conformal at x, then there exists c > 0 with the inner-product relation as above.
Русский
Если h конформно в точке x, существует c > 0 с указанным relation между скалярными произведениями.
LaTeX
$$$ \exists c>0, \forall u,v, \langle f'(x)u, f'(x)v \rangle = c \langle u,v \rangle $$$
Lean4
/-- The conformal factor of a conformal map at some point `x`. Some authors refer to this function
as the characteristic function of the conformal map. -/
def conformalFactorAt {f : E → F} {x : E} (h : ConformalAt f x) : ℝ :=
Classical.choose (conformalAt_iff'.mp h)