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Proof step 14 from proof is-aligned-still-space (previous step)

m < n, n * n1 < (n1 * m0 * n + n1 * m) % (n * n1) + n1 ⊦ (n1 * m0 * n + n1 * m) % (n * n1) = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
n * n1 < (n1 * m) % (n * n1) + n1, m < n ⊦ (n1 * m) % (n * n1) = 0, n1 = 0

Rule argument

Additional information

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