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Proof step 17 from proof enc-invert (previous step)

maxenc(m) * (maxenc(m) + 1) = 2 * n0, m < n0 ⊦ (((maxenc(m) - (m - n0)) + (m - n0)) * ((maxenc(m) - (m - n0)) + (m - n0) + 1)) / 2 + (m - n0) = m, m - n0 ≤ maxenc(m)

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: max-size-01 seq: ⊦ maxenc(m) * (maxenc(m) + 1) ≤ 2 * m ∧ 2 * m < (maxenc(m) + 1) * (maxenc(m) + 2) subst: [m] → [m]

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 ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)%n < n0 ⊦ (* n) ≠ m0 + (* n0); (s)%0 ≠ m ⊦ (* m) * n ≤ m * n0 ↔ n ≤ n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: m