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Proof step 22 from proof divi-same (previous step)

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

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: dist-add-01: ⊦ dist(m + n, m0 + n) = dist(m, m0);%dist-mult: ⊦ dist(m * n, m * n0) = m * dist(n, n0);%divi-mult: ⊦ m | m * n0;%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)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → m ≤ n; (s)