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Proof step 150 from proof fix-bits2bytes-01 (previous step)

# bits = n0 * 8, (n * 8 - n0 * 8) % 8 = 0, n0 < n, n0 + 1 < n ⊦ bits = [], mklist(i2b(0), n - n0) = bits2bytes(firstn(8, mklist(false, n * 8 - n0 * 8))) + bits2bytes(restn(8, mklist(false, n * 8 - n0 * 8))), n = n0, bits.first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 151:
⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n
Proof step 152:
n0 ≤ n, # bits = n0 * 8, ((n - n0) * 8) % 8 = 0, n0 < n, n0 + 1 < n ⊦ bits = [], mklist(i2b(0), n - n0) = bits2bytes(firstn(8, mklist(false, (n - n0) * 8))) + bits2bytes(restn(8, mklist(false, (n - n0) * 8))), n = n0, bits.first

Rule argument

seq: ⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n subst: [m0, n, m] → [n0, 8, n] rotate: T spec: nat-mult inst: name: dist-sub

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m; Used terms: n0, 8, n