sequentialFunctor_initial_aux — Mathlib

English

The sequentialFunctor J is Final.

Русский

Последовательный функтор J является финальным.

LaTeX

$$$ (\\text{sequentialFunctor } J).\\text{Final} $$$

Lean4

theorem sequentialFunctor_initial_aux (j : J) : ∃ (n : ℕ), sequentialFunctor_obj J n ≤ j :=
  by
  obtain ⟨m, h⟩ := (exists_surjective_nat _).choose_spec j
  refine ⟨m + 1, ?_⟩
  simpa only [h] using
    leOfHom
      (IsCofilteredOrEmpty.cone_objs ((exists_surjective_nat _).choose m)
          (sequentialFunctor_obj J m)).choose_spec.choose

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