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Proof step 27 from proof enc-invert (previous step)

maxenc(m) * maxenc(m) + maxenc(m) = 2 * n0, maxenc(m) * maxenc(m) < (maxenc(m) + 2) * maxenc(m) + 2, 2 * n0 < (maxenc(m) + 2) * maxenc(m) + maxenc(m) + 2, 2 * n0 ≤ (maxenc(m) + 2) * maxenc(m) + maxenc(m), m * 2 ≤ (maxenc(m) + 2) * maxenc(m) + maxenc(m), maxenc(m) + n0 < m, 2 * m < (maxenc(m) + 2) * maxenc(m) + maxenc(m) + 2, n0 ≤ m ⊦ m = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 29:
maxenc(m) * maxenc(m) + maxenc(m) = 2 * n0, maxenc(m) * maxenc(m) < (maxenc(m) * maxenc(m) + maxenc(m) * 2) + 2, 2 * n0 < (maxenc(m) * maxenc(m) + maxenc(m) * 2) + maxenc(m) + 2, 2 * n0 ≤ (maxenc(m) * maxenc(m) + maxenc(m) * 2) + maxenc(m), m * 2 ≤ (maxenc(m) * maxenc(m) + maxenc(m) * 2) + maxenc(m), maxenc(m) + n0 < m, 2 * m < (maxenc(m) * maxenc(m) + maxenc(m) * 2) + maxenc(m) + 2, n0 ≤ m ⊦ m = 0

Rule argument

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