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Proof step 13 from proof alignup-le-is-aligned (previous step)

m % n = 0, m0 = n0 + m0 / n * n, m0 < n * m0 / n + n, m < n * m0 / n + n, m0 ≤ m, m0 / n * n ≤ m0 ⊦ n = 0, n0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
m % n = 0, m0 = n0 + m0 / n * n, n0 < n, m < n * m0 / n + n, m0 < n * m0 / n + n, m0 ≤ m ⊦ n0 = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%n ≠ 0 ⊦ m / n * n ≤ m; (s)