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Proof step 19 from proof eq1 (previous step)

n0 % m + 1 = m, m * (m + n0) / m + m ≤ n0 + 1, ∀ m. (n0 + m) / m * m ≤ n0 → m = 0 ⊦ m = 0

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 3 terms: m

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%le-one: ⊦ m ≤ n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m * n + n ≤ m1 * n ↔ m + 1 ≤ m1 ∨ n = 0; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ ¬ n < n; (s) Used terms: m