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Proof step 17 from proof max-snd-nls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-div inst: name: mult-div seq: ⊦ n % m = 0 ∧ m ≠ 0 → m * n / m = n subst: [n, m] → [maxenc(m) * maxenc(m) + maxenc(m), 2] flags: rewrite

Additional information

Used simplifier rules: square-even-02: ⊦ (m * m + m) % 2 = 0; from specification nat-div%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%two-02: ⊦ m + m = 2 * m; from specification nat-mult%coef-06: ⊦ m * n + m0 * n < m1 * n ↔ ¬ ¬(m + m0 < m1 ∧ n ≠ 0); from specification nat-mult%l: ⊦ m + n < m + n0 ↔ n < n0; from specification nat-basic2 Used terms: maxenc(m) * maxenc(m) + maxenc(m), 2