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

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: nat-pair inst: name: max-size-01 seq: ⊦ maxenc(m) * (maxenc(m) + 1) ≤ 2 * m ∧ 2 * m < (maxenc(m) + 1) * (maxenc(m) + 2) subst: [m] → [m] flags: current, []

Additional information

Used simplifier rules: rsucc-02: ⊦ m * (n + 1) = m * 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%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%add-num-03: n < n0 ⊦ (* n) ≠ m0 + (* n0); from specification nat%le-num: 0 ≠ m ⊦ (* m) * n ≤ m * n0 ↔ n ≤ n0; from specification nat-mult%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat Used terms: m