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Proof step 18 from proof inject-n2s (previous step)

10 ≤ n / 10 * 10 + n % 10, 10 ≤ n, ∀ m1, n1. m1 < n / 10 * 10 + n % 10 → n→s(m1) = n→s(n1) → m1 = n1 ⊦ n / 10 * 10 + n % 10 = n, n / 10 * 10 + n % 10 = 0, n = 0

User applied rule insert elim lemma

And closed the goal!

Rule argument

spec: nat-div inst: name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [n, 10, m, n0] flags:

Additional information

Used simplifier rules: ⊦ m * n = n * m;% ⊦ m + n = n + m;%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: n, 10, m, n0