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Proof step 14 from proof int2bytes-rec-neg-06 (previous step)

0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ 2 ^ (i * 8) = 0, int2bytes(j0) = int2bytes((j0 * 2 ^ (i * 8) + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8))

User applied rule cut formula

And obtained the following new goals

Proof step 15:
j0 * 2 ^ (i * 8) + 1 - 2 ^ (i * 8) = (1 - 2 ^ (i * 8)) + j0 * 2 ^ (i * 8), 0 < i, j0 * 2 ^ (i * 8) + 2 ^ (i * 8 - 1) < 0 ⊦ 2 ^ (i * 8) = 0, int2bytes(j0) = int2bytes((j0 * 2 ^ (i * 8) + 1 - 2 ^ (i * 8)) / 2 ^ (i * 8))

Rule argument

fma: j0 * 2 ^ (i * 8) + 1 - 2 ^ (i * 8) = (1 - 2 ^ (i * 8)) + j0 * 2 ^ (i * 8)

Additional information

Used simplifier rules: ⊦ i + (j - i0) = i + j - i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i - j = i0 ↔ i = i0 + j;% ⊦ i + (j - i) = j;% ⊦ i + j = i + i0 ↔ j = i0; Used formulas: j0 * 2 ^ (i * 8) + 1 - 2 ^ (i * 8) = (1 - 2 ^ (i * 8)) + j0 * 2 ^ (i * 8)