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Proof step 33 from proof bits2bytes-fill (previous step)

# bits = m * 8 + n, n < m * 8 + 7, n < 8, m * 8 + n ≤ 8, n < m * 8 + 8 ⊦ m = 0, i2b(bits2int(bits)) ' = bits2bytes(firstn(8, mklist(bits.first, 8 - n) + bits)) + bits2bytes(restn(n, bits)), n = 0, bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
m2 ≠ 0 ⊦ m2 * m + n ≤ m ↔ (m2 - 1) * m + n = 0

Rule argument

seq: m2 ≠ 0 ⊦ (* m2) * m + n ≤ m ↔ (m2 - 1) * m + n = 0 subst: [n, m, m2] → [n, 8, m] rotate: F spec: nat-mult inst: name: numeral-32

Additional information

Used simplifier rules: ⊦ m + n = 0 ↔ m = 0 ∧ n = 0;%n ≠ 0 ⊦ (* m) * m0 = (* n) ↔ n % m = 0 ∧ m0 = n / m ∧ m ≠ 0;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: n, 8, m