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Proof step 24 from proof enc-invert (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat name: ls-03 seq: n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0 subst: [m, n0, n] → [maxenc(m), n0, m] 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 + 2) / 2 = m / 2 + 1; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss) Used terms: maxenc(m), n0, m