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Proof step 51 from proof fix-bits2bytes (previous step)

n = m0 + 1 ∧ n ≠ 0, m0 - m = 0, 8 = n1 + n0, # bits = m * 8 + n0, n0 < 8, # bits2bytes(bits) < n, # bits ≤ 8 * m0, m < n ⊦ n * 8 = # bits, n0 = 0, n1 = 0, bits = [], mklist(i2b(0), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(false, n1) + bits), bits.first

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
# bits = m * 8 + n0, 8 = n1 + n0, # bits ≤ 8 * m, # bits2bytes(bits) ≤ m, n0 < 8 ⊦ (i2b(0) ' + mklist(i2b(0), m - # bits2bytes(bits))) + bits2bytes(bits) = bits2bytes(mklist(false, n1) + bits), bits = [], n1 = 0, n0 = 0, 8 * m + 8 = # bits, bits.first

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m;% ⊦ m ≤ n → (n - m = 0 ↔ n = m);% ⊦ (bytes + bytes0) + bytes1 = bytes + bytes0 + bytes1;% ⊦ mklist(by, n) + by ' = by ' + mklist(by, n);% ⊦ mklist(by, 1) = by ';% ⊦ mklist(by, m + n) = mklist(by, m) + mklist(by, n);% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ m < n + 1 ↔ ¬ n < m;% ⊦ m + 1 ≠ 0;% ⊦ m * n = n * m;% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m * (n + 1) = m * n + m;