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Proof step 122 from proof fix-bits2bytes (previous step)

((8 - n0) + m * 8 + n0) % 8 = 0, # bits = m * 8 + n0, m < n, m * 8 + n0 ≤ 8 * (n - 1), (m * 8 + n0) / 8 + 1 < n, bits.first, n0 < 8 ⊦ (m * 8 + n0) % 8 = 0, n - 1 - m = 0, mklist(true, 8 - n0) + bits = [], n0 = 0, n * 8 = m * 8 + n0, mklist(i2b(~1), n - (m * 8 + n0) / 8 + 1) + bits2bytes(bits) = bits2bytes(mklist(true, (n - 1 - m) * 8)) + bits2bytes(mklist(true, 8 - n0) + bits), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 123:
n ≠ 0 ⊦ (n0 + m * n) / n = n0 / n + m
Proof step 124:
8 ≠ 0, ((8 - n0) + m * 8 + n0) % 8 = 0, # bits = m * 8 + n0, m < n, m * 8 + n0 ≤ 8 * (n - 1), (n0 / 8 + m) + 1 < n, bits.first, n0 < 8 ⊦ (m * 8 + n0) % 8 = 0, n - 1 - m = 0, mklist(true, 8 - n0) + bits = [], n0 = 0, n * 8 = m * 8 + n0, mklist(i2b(~1), n - (n0 / 8 + m) + 1) + bits2bytes(bits) = bits2bytes(mklist(true, (n - 1 - m) * 8)) + bits2bytes(mklist(true, 8 - n0) + bits), bits = []

Rule argument

seq: n ≠ 0 ⊦ (n0 + m * n) / n = n0 / n + m subst: [n0, n, m] → [n0, 8, m] rotate: F spec: nat-div inst: name: mult

Additional information

Used simplifier rules: ⊦ m * n = n * m;% ⊦ m + n = n + m; Used terms: n0, 8, m