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Proof step 193 from proof fix-bits2bytes-01 (previous step)

# 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 194:
⊦ n ≤ n0 → (m + (n0 - n)) + n = m + n0
Proof step 195:
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

Rule argument

seq: ⊦ n ≤ n0 → (m + (n0 - n)) + n = m + n0 subst: [m, n, n0] → [m * 8, n0, 8] rotate: F spec: nat inst: name: sub-add

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < n → ¬ n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m; Used terms: m * 8, n0, 8