Theorem fzo0ss1

Description: Subset relationship for half-open integer ranges with lower bounds 0 and 1. (Contributed by Alexander van der Vekens, 18-Mar-2018)

	Ref	Expression
Assertion	fzo0ss1	$$⊢\left(1..^N\right)\subseteq \left(0..^N\right)$$

Proof

Step	Hyp	Ref	Expression
1		1eluzge0	$$⊢1\in {\mathbb{Z}}_{\ge 0}$$
2		fzoss1	$$⊢1\in {\mathbb{Z}}_{\ge 0}\to \left(1..^N\right)\subseteq \left(0..^N\right)$$
3	1 2	ax-mp	$$⊢\left(1..^N\right)\subseteq \left(0..^N\right)$$