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 | ⊢ ( 1 ..^ 𝑁 ) ⊆ ( 0 ..^ 𝑁 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1eluzge0 | ⊢ 1 ∈ ( ℤ_{≥} ‘ 0 ) | |
2 | fzoss1 | ⊢ ( 1 ∈ ( ℤ_{≥} ‘ 0 ) → ( 1 ..^ 𝑁 ) ⊆ ( 0 ..^ 𝑁 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 1 ..^ 𝑁 ) ⊆ ( 0 ..^ 𝑁 ) |