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Proof step 8 from proof bits2bytes-rec-01 (previous step)

# bits = m * 8 + n ∧ n < 8 ∧ 8 ≠ 0, 8 < # bits ⊦ n = 0, bits2bytes(firstn(n, bits) + restn(n, bits)) = bits2bytes(firstn(n, bits)) + bits2bytes(restn(n, bits)), bits = [], (# bits - n) % 8 = 0 ∧ restn(n, bits) ≠ []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
# bits = m * 8 + n, n + 1 < # bits, n < 8, 8 < # bits, n < # bits ⊦ n = 0, bits2bytes(firstn(n, bits) + restn(n, bits)) = bits2bytes(firstn(n, bits)) + bits2bytes(restn(n, bits)), bits = [], m * 8 = 1, m = 0, (# bits - n) % 8 = 0 ∧ restn(n, bits) ≠ []

Rule argument

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0;% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1);% ⊦ m + n < m + n0 ↔ n < n0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m +1 = m + 1;% ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward)% ⊦ m < n → n ≠ 0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)