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Proof step 7 from proof intshiftrsign-2pot-neg-02 (previous step)

0 ≤ j, i0 < 2 ^ j + j0, i0 < j, i0 ≤ 0, 0 < 2 ^ j + j0, j0 < 0, i0 * 2 ^ j + j0 < 0, 0 < j, j < 32 ⊦ i0 = 1 + ((i0 * 2 ^ j + j0) + 1 - 2 ^ j) / 2 ^ j, j0 = 0

User applied rule cut formula

And obtained the following new goals

Proof step 8:
(i0 * 2 ^ j + j0) + 1 - 2 ^ j = 2 ^ j * (i0 - 1) + j0 + 1, 0 ≤ j, i0 < 2 ^ j + j0, i0 < j, i0 ≤ 0, 0 < 2 ^ j + j0, j0 < 0, i0 * 2 ^ j + j0 < 0, 0 < j, j < 32 ⊦ i0 = 1 + ((i0 * 2 ^ j + j0) + 1 - 2 ^ j) / 2 ^ j, j0 = 0

Rule argument

fma: (i0 * 2 ^ j + j0) + 1 - 2 ^ j = 2 ^ j * (i0 - 1) + j0 + 1

Additional information

Used simplifier rules: ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i * j + i = i * (j + 1);% ⊦ i + (j - i) = j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i + j = i + i0 ↔ j = i0; Used formulas: (i0 * 2 ^ j + j0) + 1 - 2 ^ j = 2 ^ j * (i0 - 1) + j0 + 1