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Proof step 195 from proof fix-bits2bytes-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 196:
⊦ (* m0) * m + m = (m0 + 1) * m
Proof step 197:
n0 ≤ 8, # bits = n0 + m * 8, n0 < 8, bits.first, # bits2bytes(bits) < n, m < n ⊦ mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, (n - 1 - m) * 8) + mklist(true, 8 - n0) + bits), bits = [], n * 8 = n0 + m * 8, n0 = 0, ((m + 1) * 8) % 8 = 0 ∧ (n - 1 - m) * 8 ≠ 0

Rule argument

seq: ⊦ (* m0) * m + m = (m0 + 1) * m subst: [m, m0] → [8, m] rotate: F spec: nat-mult inst: name: succ

Additional information

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