∀ {G : Type u_1} [inst : Group G] (X : Action FintypeCat G) [inst_1 : CategoryTheory.PreGaloisCategory.IsConnected X]
  (x : X.V.carrier) [inst_2 : Fintype (G ⧸ MulAction.stabilizer G x)] (σ : G),
  CategoryTheory.CategoryStruct.comp
      ((Action.FintypeCat.ofMulAction G (FintypeCat.of (G ⧸ MulAction.stabilizer G x))).ρ σ)
      (FintypeCat.equivEquivIso
          ((Equiv.Set.univ X.V.carrier).symm.trans
              ((Equiv.setCongr ⋯).trans (MulAction.orbitEquivQuotientStabilizer G x))).symm).hom =
    CategoryTheory.CategoryStruct.comp
      (FintypeCat.equivEquivIso
          ((Equiv.Set.univ X.V.carrier).symm.trans
              ((Equiv.setCongr ⋯).trans (MulAction.orbitEquivQuotientStabilizer G x))).symm).hom
      (X.ρ σ)