Let $M$ be a real analytic manifold. Let $F$ be an object of the bounded derived category of sheaves on $M$ with real constructible cohomology sheaves. Let $CC(F)$ denote the characteristic cycle of $F$ and $SS(F)$ be its singular support (I follow the terminology and notation of the book “Sheaves on manifolds” by Kashiwara and Schapira). If I understand correctly one has the inclusion: $$supp(CC(F))\subset SS(F)\,\,\,\,\, (1)$$ by formula (9.4.10) in the above book by Kashiwara-Schapira.
Does one have equality in the inclusion (1)?