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Proof step 144 from proof fix-bits2bytes-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 145:
⊦ m0 ≤ m → (m - m0) * n = m * n - m0 * n
Proof step 146:
n0 ≤ n, # bits = n0 * 8, n0 < n ⊦ bits = [], mklist(i2b(0), n - n0) = bits2bytes(mklist(false, (n - n0) * 8)), n = n0, bits.first, ((n - n0) * 8) % 8 = 0 ∧ n ≠ n0 + 1

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