In Definition 4.1.1 of $(\infty,2)$-Categories and the Goodwillie Calculus I, Lurie defines a *weak $\infty$-bicategory* to be a scaled simplicial set that has the extension property with respect to every scaled anodyne morphism. In Theorem 4.2.7, he defines a model structure on $\operatorname{Set}_{\Delta}^{\operatorname{sc}}$, the category of scaled simplical sets, and in Definition 4.2.8 he defines an *$\infty$-bicategory* to be a scaled simplicial set that is a fibrant object in the model category $\operatorname{Set}_{\Delta}^{\operatorname{sc}}$.

Every $\infty$-bicategory is a weak $\infty$-bicategory, because every scaled anodyne morphism is a bicategorical equivalence (Proposition 3.1.13). What about the converse? Is every weak $\infty$-bicategory an $\infty$-bicategory?

EDIT:

I think I now have a proof that, indeed, every weak $\infty$-bicategory is an $\infty$-bicategory. I will post it tomorrow.

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