Theorem uzssre

Description: An upper set of integers is a subset of the reals. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Assertion	uzssre	$$⊢{\mathbb{Z}}_{\ge M}\subseteq ℝ$$

Proof

Step	Hyp	Ref	Expression
1		uzssz	$$⊢{\mathbb{Z}}_{\ge M}\subseteq \mathbb{Z}$$
2		zssre	$$⊢\mathbb{Z}\subseteq ℝ$$
3	1 2	sstri	$$⊢{\mathbb{Z}}_{\ge M}\subseteq ℝ$$