∀ {G : Type u_1} [inst : AddGroup G] {α : Type u_2} [inst_1 : AddAction G α] {a : α} {n : ℕ}
  (x : Fin n ↪ ↥(SubAddAction.ofStabilizer G a)),
  SubAddAction.ofStabilizer.snoc x =
    Fin.Embedding.snoc (x.trans (Function.Embedding.subtype fun x => x ∈ SubAddAction.ofStabilizer G a)) ⋯