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Proof step 29 from proof int2bits-neg-03 (previous step)

~1 = 2 ^ i * 2 + j, n→i(# int2bits(~ j)) = i + 1, 0 ≤ i, 0 ≤ 2 ^ i, j + 1 < 2 ^ i, 0 < 2 ^ i + j, j < 0, j < 2 ^ i, 1 < 2 ^ i, 0 < 2 ^ i, j < i ⊦

User applied rule cut formula

And closed the goal!

Rule argument

fma: j = ~(2 ^ i * 2) - 1

Additional information

Used simplifier rules: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0;% ⊦ ~ i = j ↔ i + j = 0;% ⊦ i * j = j * i;% ⊦ ~ i - j = ~(i + j);% ⊦ i + ~ j = i - j;% ⊦ i - j + i = ~ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ ~ ~ i = i;% ⊦ ~ i < j ↔ 0 < j + i;% ⊦ (* i0) * i + i = (i0 + 1) * i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ 0 ≤ j1 ∧ j1 < j → (i0 * j + j1 < j ↔ i0 ≤ 0); Used formulas: j = ~(2 ^ i * 2) - 1