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Proof step 44 from proof int2bytes-len-pos (previous step)

n→i(m) ≤ i + 1, j < 2 ^ (n→i(m) * 8 + n→i(n) - 1), 2 ^ (n→i(m) * 8 + n→i(n) - 2) ≤ j, n < 8, 0 < j, j < 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 2 ^ (8 * i) ≤ j, n→i(m) * 8 + n→i(n) ≤ 8 * (i + 1), 0 ≤ j, 8 * i + 1 < n→i(m) * 8 + n→i(n), 1 < n→i(m) * 8 + n→i(n), 0 < n→i(m) * 8 + n→i(n), 8 * i + 1 < 8 * (i + 1), i ≤ n→i(m) ⊦ m * 8 + n = 0, m = i→n(i), n = 0, n = 1

User applied rule cut formula

And closed the goal!

Rule argument

fma: n→i(m) = i + 1

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m = m + n ↔ n = 0;% ⊦ n→i(m) = n→i(n) + 1 ↔ m = n + 1;% ⊦ i→n(n→i(n)) = n;% ⊦ i ≤ j → (j ≤ i ↔ i = j);% ⊦ i < j + 1 ↔ i ≤ j;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)% ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward)% ⊦ i ≤ j ∧ j < j0 → i < j0; (forward)% ⊦ i + j0 ≤ i0 ∧ j0 ≥ 0 → i ≤ i0;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);%0 ≤ j ⊦ 2 ^ j < 2 ^ j0 ↔ j < j0;% ⊦ i < j - i0 ↔ i + i0 < j;% ⊦ i * j + i0 < i * (j + j1) + j0 ↔ i0 < i * j1 + j0;% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0;%i < 0 ⊦ (* i) < n→i(n);% ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i ≤ j - i0 ↔ i + i0 ≤ j;% ⊦ 1 ≤ i ↔ 0 < i;% ⊦ 1 < 2 ^ i ↔ 0 < i;% ⊦ i * (j + i0) + j1 ≤ i * (j0 + i0) ↔ i * j + j1 ≤ i * j0;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ n→i(n) ≤ 0 ↔ n = 0; Used formulas: n→i(m) = i + 1