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Proof step 5 from proof lemon2pot-01 (previous step)

2 ^ n→i(m * n0 - 1) < 2 ^ n→i(m * n - 1), (m * n0 - 1) + 1 < m * n, 2 ^ n→i(m * n0 - 1) < j, n ≤ n0, j ≤ 2 ^ n→i(m * n - 1) ⊦ m = 0, n = 0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m * n0, m0]

Additional information

Used simplifier rules: ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0; (ws)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m0 * m < m0 * n ↔ m0 ≠ 0 ∧ m < n; (ws)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s)% ⊦ m ≤ 0 ↔ m = 0; (s)%n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m * n0, m0