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Proof step 16 from proof fix-bits2bytes-01 (previous step)

# bits ≤ 8 * n, n ≤ # bits / 8 + 1 ⊦ # bits % 8 = 0, fix(n, bits2bytes(bits)) = bits2bytes(mklist(bits.first, n * 8 - # bits) + bits), bits = [], n = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
# bits = m * 8 + n0 ∧ n0 < 8 ∧ 8 ≠ 0, # bits ≤ 8 * n, n ≤ m + 1 ⊦ n0 = 0, fix(n, bits2bytes(bits)) = bits2bytes(mklist(bits.first, n * 8 - # bits) + bits), bits = [], n = 0

Rule argument

seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [# bits, 8, m, n0] rotate: T spec: nat-div inst: name: div-elim

Additional information

Used simplifier rules: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: # bits, 8, m, n0