∀ {X : Type u_3} {Y : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [inst_2 : T2Space Y]
  {f f_1 : X → Y} (e_f : f = f_1) (hf : Continuous f) (a a_1 : T2Quotient X),
  a = a_1 → T2Quotient.lift hf a = T2Quotient.lift ⋯ a_1