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Proof step 14 from proof max-snd-nls (previous step)

(maxenc(m) + (maxenc(m) * maxenc(m) + maxenc(m)) / 2) * 2 < (maxenc(m) + 2) * maxenc(m) + maxenc(m), m ≤ ((maxenc(m) + 2) * maxenc(m) + maxenc(m)) / 2, (maxenc(m) * maxenc(m) + maxenc(m)) / 2 ≤ m, maxenc(m) + (maxenc(m) * maxenc(m) + maxenc(m)) / 2 < m ⊦ maxenc(m) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 16:
2 * maxenc(m) + 2 * (maxenc(m) * maxenc(m) + maxenc(m)) / 2 < (maxenc(m) + 2) * maxenc(m) + maxenc(m), m ≤ ((maxenc(m) + 2) * maxenc(m) + maxenc(m)) / 2, (maxenc(m) * maxenc(m) + maxenc(m)) / 2 ≤ m, maxenc(m) + (maxenc(m) * maxenc(m) + maxenc(m)) / 2 < m ⊦ maxenc(m) = 0

Rule argument

spec: nat-mult inst: name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [m0, n, m] → [2, (maxenc(m) * maxenc(m) + maxenc(m)) / 2, maxenc(m)] flags: rewrite

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: 2, (maxenc(m) * maxenc(m) + maxenc(m)) / 2, maxenc(m)