Theorem dvdsfi

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

	Ref	Expression
Assertion	dvdsfi	$$⊢N\in \mathbb{N}\to \left\{x\in \mathbb{N}|x\parallel N\right\}\in \mathrm{Fin}$$

Proof

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