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Proof step 57 from proof int2bytes-len-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 58:
⊦ m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → ¬ m * n0 + n2 < m0 * n + n1
Proof step 59:
¬(m < i→n(i) ∧ 8 ≤ 8 ∧ 1 < 8 ∧ n < 8), m * 8 + n ≤ 8 + 8 * i→n(i), j < 0, 1 + i→n(i) * 8 < m * 8 + n, 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 2 ^ (n→i(m) * 8 + n→i(n) - 1), j + 2 ^ (n→i(m) * 8 + n→i(n) - 2) < 0, 0 ≤ 2 ^ (n→i(m) * 8 + n→i(n) - 1) + j, n < 8, j < ~1, 0 ≤ i ⊦ ~1 = i, j + 2 ^ (8 * i) = 0, m = i→n(i), n = 0, 8 * (i + 1) = 1, m = 0 ∧ n = 1

Rule argument

seq: ⊦ m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → ¬ m * n0 + n2 < m0 * n + n1 subst: [n1, n, m0, n2, n0, m] → [n, 8, m, 1, 8, i→n(i)] rotate: F spec: nat-mult inst: name: mod-nls

Additional information

Used simplifier rules: ⊦ m * n = n * m;% ⊦ m + n = n + m; Used terms: n, 8, m, 1, 8, i→n(i)