// Main VL template
#import "../preamble.typ": *

// Fix theorems to be shown the right way in this document
#import "@preview/ctheorems:1.1.3": *
#show: thmrules

// Main settings call
#show: conf.with(
	// May add more flags here in the future
	num: 5,
	type: 0, // 0 normal, 1 exercise
	date: datetime.today().display(),
	//date: datetime(
	//	year: 2025,
	//	month: 5,
	//	day: 1,
	//).display(),
)

= Uebersicht

#theorem[
	Sei $U subset RR^n times RR^n $ offen, $(a,b) in U, f: U -> RR^n $ stetig diffbar mit $f (a,b) =  0$ und $det (partial_(y) f^(i) )_(1 <= i, j <= n) .. (a,b) != 0 $. Dann gibt es eine difbare Funnktion $g: U' ->  U''$ sodass gilt
	$
		f (x,y) =  0 "fuer ein " x in U', y in U'' <=> y =  g (x).
	$
]