Theorem fzossuz

Description: A half-open integer interval is a subset of an upper set of integers. (Contributed by Glauco Siliprandi, 8-Apr-2021)

	Ref	Expression
Assertion	fzossuz	$$⊢\left(M..^N\right)\subseteq {\mathbb{Z}}_{\ge M}$$

Proof

Step	Hyp	Ref	Expression
1		fzossfz	$$⊢\left(M..^N\right)\subseteq \left(M\dots N\right)$$
2		fzssuz	$$⊢\left(M\dots N\right)\subseteq {\mathbb{Z}}_{\ge M}$$
3	1 2	sstri	$$⊢\left(M..^N\right)\subseteq {\mathbb{Z}}_{\ge M}$$