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Proof step 14 from proof divi-same (previous step)

n = n3 + m0 ∧ m0 ≤ n, m0 < n, m * n1 = dist(n0, m0), m * n2 = n3, m0 < n ⊦ n = 0, m | dist(n, n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
m * n1 = dist(n0, m0) ⊦ m * n2 + m0 = 0, m = 0, n2 = 0, m | dist(m * n2 + m0, n0)

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%zero-01: ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%l-01: ⊦ m < m + n ↔ n ≠ 0; from specification nat-basic2%lels-03: ⊦ m < n → m ≤ n; from specification nat