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Proof step 8 from proof lemon2pot-02 (previous step)

(m * n0 - 1) + 1 < m * n, 2 ^ n→i(m * n0 - 1) + j0 < j, j ≤ 2 ^ n→i(m * n - 1) + j0, n ≤ n0 ⊦ m = 0, n = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat name: num-02 seq: n ≠ 0 ⊦ (n - 1) + 1 = n subst: [n] → [m * n0] flags: <all paths>

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% ⊦ 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 = 0; (s)% ⊦ m ≤ 0 ↔ m = 0; (s) Used terms: m * n0