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Proof step 190 from proof int2bytes-rec-neg-05 (previous step)

1 + 8 * i→n(i) = # int2bits(j % 2 ^ (i * 8)), 0 < i, j % 2 ^ (i * 8) < 0, j + 2 ^ (i * 8) < i, j + 2 ^ (i * 8) ≤ 0, j + 2 ^ (i * 8 - 1) < 0, 8 * i→n(i) ≤ 7 ⊦ bits2bytes(int2bits(j % 2 ^ (i * 8)).rest) = bits2bytes(int2bits(j % 2 ^ (i * 8))).rest, j % 2 ^ (i * 8) = 0, int2bits(j % 2 ^ (i * 8)).rest = [], i = 0

User applied rule cut formula

And closed the goal!

Rule argument

fma: 8 * i→n(i) < 8

Additional information

Used simplifier rules: ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ m0 * m < m ↔ m0 = 0 ∧ m ≠ 0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ m * n = n * m;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m0 * m * n = (m0 * m) * n;%0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward)% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) Used formulas: 8 * i→n(i) < 8