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Proof step 19 from proof fix-bits2bytes (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 20:
⊦ m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → ¬ m * n0 + n2 ≤ m0 * n + n1
Proof step 21:
n - 1 < m ∧ 8 ≤ 8 ∧ n0 < 8 ∧ 0 < 8 → ¬ m * 8 + n0 ≤ (n - 1) * 8 + 0, # bits = m * 8 + n0, n ≤ m + 1, m * 8 + n0 ≤ 8 * (n - 1), n0 < 8 ⊦ bits = [], n = 0, fix(n, bits2bytes(bits)) = bits2bytes(fillsgn(n * 8, bits)), n0 = 0

Rule argument

seq: ⊦ m0 < m ∧ n ≤ n0 ∧ n2 < n0 ∧ n1 < n → ¬ m * n0 + n2 ≤ m0 * n + n1 subst: [m0, m, n, n0, n2, n1] → [n - 1, m, 8, 8, n0, 0] rotate: F spec: nat-mult inst: name: mod-nle

Additional information

Used terms: n - 1, m, 8, 8, n0, 0