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	⊢ ( ℤ≥ ‘ 𝑀 ) ⊆ ℝ

Proof

Step	Hyp	Ref	Expression
1		uzssz	⊢ ( ℤ≥ ‘ 𝑀 ) ⊆ ℤ
2		zssre	⊢ ℤ ⊆ ℝ
3	1 2	sstri	⊢ ( ℤ≥ ‘ 𝑀 ) ⊆ ℝ