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Proof step 12 from proof inject-n2s (previous step)

n→s(m / 10) = n→s(n / 10), n→s(m % 10) = n→s(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 apply induction

And obtained the following new goals

Proof step 13:
m / 10 = n / 10, n→s(m / 10) = n→s(n / 10), n→s(m % 10) = n→s(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

subst: [n, m1] → [n / 10, m / 10]

Additional information

Used simplifier rules: ⊦ ¬ m < n ↔ n ≤ m;%m0 ≠ 0 ⊦ n ≤ m / m0 ↔ n * m0 ≤ m;% ⊦ n ≠ 0 → (m * n ≤ n ↔ m ≤ 1);% ⊦ m0 * m * n = (m0 * m) * n;% ⊦ m * n = n * m; Used terms: n / 10, m / 10