Description: The binary length of 0. (Contributed by AV, 20-May-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | blen0 | ⊢ ( #b ‘ 0 ) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | c0ex | ⊢ 0 ∈ V | |
2 | blenval | ⊢ ( 0 ∈ V → ( #b ‘ 0 ) = if ( 0 = 0 , 1 , ( ( ⌊ ‘ ( 2 logb ( abs ‘ 0 ) ) ) + 1 ) ) ) | |
3 | 1 2 | ax-mp | ⊢ ( #b ‘ 0 ) = if ( 0 = 0 , 1 , ( ( ⌊ ‘ ( 2 logb ( abs ‘ 0 ) ) ) + 1 ) ) |
4 | eqid | ⊢ 0 = 0 | |
5 | 4 | iftruei | ⊢ if ( 0 = 0 , 1 , ( ( ⌊ ‘ ( 2 logb ( abs ‘ 0 ) ) ) + 1 ) ) = 1 |
6 | 3 5 | eqtri | ⊢ ( #b ‘ 0 ) = 1 |