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Proof step 9 from proof int2bytes-first-zerobyte-01 (previous step)

n→i(# int2bits(j)) = i0 * 8 + j0, i0 < 0, 0 ≤ j0, 0 ≤ j, j0 < 8 ⊦ j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j)

User applied rule cut formula

And obtained the following new goals

Proof step 10:
8 * 0 > i0 * 8 + j0, n→i(# int2bits(j)) = i0 * 8 + j0, i0 < 0, 0 ≤ j0, 0 ≤ j, j0 < 8 ⊦ j0 = 1 ↔ (∃ i. ¬ i < 0 ∧ ¬ j < 2 ^ (8 * i - 1) ∧ ¬ 2 ^ (8 * i) ≤ j)

Rule argument

fma: 8 * 0 > i0 * 8 + j0

Additional information

Used simplifier rules: ⊦ i > j ↔ j < i;% ⊦ i < 0 ∧ j0 < j ∧ 0 ≤ j → i * j + j0 < 0;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used formulas: 8 * 0 > i0 * 8 + j0