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Proof step 9 from proof is-aligned-still-space (previous step)

n0 < (n2 * n1) % n0 + n1, ∃ n2. n0 = n2 * n1 ⊦ (n2 * n1) % n0 = 0, n0 = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
n * n1 < (n2 * n1) % (n * n1) + n1 ⊦ (n2 * n1) % (n * n1) = 0, n = 0, n1 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (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% ⊦ m ≠ 0 → (m * n = 0 ↔ n = 0); (s)