Let $F:C \rightarrow D$ be a functor between categories. Then $C$ is cofibered in groupoids over $D$ if and only if the induced map $N(F):N(C)\rightarrow N(D)$ is a left fibration of simplicial sets.
In line 1 of proof, Lurie states $N(F)$ is an inner fibration - how does this follow from Prop. 22.214.171.124?
We only know that $N(C)$ and $N(D)$ as objects has LLP for inner horns.