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Proof step 3 from proof max-size-01 (previous step)

m < ((maxenc(m) + 1) * (maxenc(m) + 2)) / 2, (maxenc(m) * (maxenc(m) + 1)) / 2 ≤ m ⊦ maxenc(m) * (maxenc(m) + 1) ≤ 2 * m ∧ 2 * m < (maxenc(m) + 1) * (maxenc(m) + 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-div name: two-le-03 seq: ⊦ m % 2 = 0 → (m / 2 ≤ n ↔ m ≤ n * 2) subst: [n, m] → [m, maxenc(m) * (maxenc(m) + 1)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m * (n + 1) = m * n + m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ (m * m + m) % 2 = 0; (s)% ⊦ (m + 2) / 2 = m / 2 + 1; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%m0 ≠ 0 ⊦ n ≤ m / m0 ↔ n * m0 ≤ m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s) Used terms: m, maxenc(m) * (maxenc(m) + 1)