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Proof step 21 from proof fix-bits2bytes-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ n0 < m0 ∧ n ≤ m ∧ n0 ≠ 0 → ¬ m0 * m + n0 ≤ m0 * n
Proof step 23:
¬(n0 < 8 ∧ n ≤ m ∧ n0 ≠ 0), # bits = 8 * m + n0, n ≤ m + 1, 8 * m + n0 ≤ 8 * n, n0 < 8 ⊦ n = 0, bits = [], fix(n, bits2bytes(bits)) = bits2bytes(mklist(bits.first, n * 8 - 8 * m + n0) + bits), n0 = 0

Rule argument

seq: ⊦ n0 < m0 ∧ n ≤ m ∧ n0 ≠ 0 → ¬ m0 * m + n0 ≤ m0 * n subst: [n, n0, m, m0] → [n, n0, m, 8] rotate: F spec: nat-mult inst: name: mod-nle-01

Additional information

Used terms: n, n0, m, 8