\displaystyle
\exists$otvoreni interval $I \subseteq R$ t.d. $\exists \varphi : I \rightarrow R $ t.d. $ F(x, \varphi(x); c_0)=0 ~ ~ \forall x \in I \Rightarrow \\
$specijalno: $\exists h>0 $ t.d. $ [x_0-h/2, x_0+h/2] \subseteq I \Rightarrow\\ g(t):=(x_0-h/2+ t \cdot h, \varphi(x_0-h/2+ t \cdot h)) : [0,1] \rightarrow R^2 $ jest t.d. $ (F \circ g)=0 \\$ t.j. $ f(g(t))=c_0 ~ ~\forall t \in [0,1]