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Proof step 108 from proof fix-bits2bytes (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 109:
8 = n1 + n0 ∧ n0 ≤ 8, # bits = m * 8 + n0, n0 < 8, bits.first, # bits2bytes(bits) < n, m * 8 + n0 ≤ 8 * (n - 1), m < n ⊦ bits = [], mklist(i2b(~1), n - # bits2bytes(bits)) + bits2bytes(bits) = bits2bytes(mklist(true, (n - 1 - m) * 8) + mklist(true, n1) + bits), n * 8 = m * 8 + n0, n0 = 0, (n1 + m * 8 + n0) % 8 = 0 ∧ n - 1 - m ≠ 0

Rule argument

seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [8, n0, n1] rotate: T spec: nat inst: name: elim-sub

Additional information

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