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Proof step 191 from proof fix-bits2bytes-01 (previous step)

# bits = m * 8 + n0, 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 = m * 8 + n0, n0 = 0, ((8 - n0) + m * 8 + n0) % 8 = 0 ∧ (n - 1 - m) * 8 ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 192:
⊦ m + n = n + m
Proof step 193:
# 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, ((8 - n0) + n0 + m * 8) % 8 = 0 ∧ (n - 1 - m) * 8 ≠ 0

Rule argument

seq: ⊦ m + n = n + m subst: [n, m] → [n0, m * 8] rotate: F spec: nat-basic2 inst: name: c

Additional information

Used terms: n0, m * 8