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	⊢ ( 𝑀 ..^ 𝑁 ) ⊆ ( ℤ≥ ‘ 𝑀 )

Proof

Step	Hyp	Ref	Expression
1		fzossfz	⊢ ( 𝑀 ..^ 𝑁 ) ⊆ ( 𝑀 ... 𝑁 )
2		fzssuz	⊢ ( 𝑀 ... 𝑁 ) ⊆ ( ℤ≥ ‘ 𝑀 )
3	1 2	sstri	⊢ ( 𝑀 ..^ 𝑁 ) ⊆ ( ℤ≥ ‘ 𝑀 )