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Proof step 11 from proof is-aligned-still-space (previous step)

n * n1 < (n2 * n1) % (n * n1) + n1, ∃ m0, m1. n2 = m0 * n + m1 ∧ m1 < n ⊦ (n2 * n1) % (n * n1) = 0, n = 0, n1 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
n * n1 < ((m0 * n + m) * n1) % (n * n1) + n1, m < n ⊦ ((m0 * n + m) * n1) % (n * n1) = 0, n1 = 0

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)