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Proof step 18 from proof alignup-le (previous step)

m1 % n = 0, n * m0 / n + n < m1, n * m0 / n + n < m0, m1 ≤ m0 ⊦ m0 % n = 0, n = 0

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: nat-div name: Divdef seq: ⊦ n ≠ 0 → m / n * n ≤ m ∧ m < (m / n)+1 * n subst: [n, m] → [n, m0]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m / n * n ≤ m; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m +1 = m + 1; (s)% ⊦ m * (n + 1) = m * n + m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → ¬ n < m; (s) Used terms: n, m0