This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem dvdsfi

Description: A natural number has finitely many divisors. (Contributed by Jim Kingdon, 9-Oct-2025)

		Ref	Expression
	Assertion	dvdsfi	$⊢ N \in ℕ \to \{x \in ℕ \| x ∥ N\} \in Fin$

Step	Hyp	Ref	Expression
1		fzfid	$⊢ N \in ℕ \to (1 \dots N) \in Fin$
2		dvdsssfz1	$⊢ N \in ℕ \to \{x \in ℕ \| x ∥ N\} \subseteq (1 \dots N)$
3	1 2	ssfid	$⊢ N \in ℕ \to \{x \in ℕ \| x ∥ N\} \in Fin$