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Proof step 16 from proof inject-n2s (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
m = m0 * 10 + n0 ∧ n0 < 10 ∧ 10 ≠ 0, m0 = n / 10, n0 = n % 10, 10 ≤ m, 10 ≤ n, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ m = n, m = 0, n = 0

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] → [m, 10, m0, n0] flags:

Additional information

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