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Proof step 7 from proof lemon2pot-02 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
(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

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%n0 ≤ n ⊦ m < n - n0 ↔ m + n0 < n; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0; (ws)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ 0 ≤ n→i(n); (s)