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Proof step 64 from proof int2bytes-len-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n0 < m0 ∧ n ≤ m ∧ n0 ≠ 0 → ¬ m0 * m + n0 ≤ m0 * n subst: [n, n0, m, m0] → [1 + i→n(i), n, m, 8] rotate: F spec: nat-mult inst: name: mod-nle-01

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ m * (n + 1) = m * n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n → (n ≤ m ↔ false);% ⊦ m + 1 ≤ n ↔ m < n;% ⊦ m ≠ n → (¬ m < n ↔ n < m);% ⊦ m < n → ¬ n < m; Used terms: 1 + i→n(i), n, m, 8