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Proof step 14 from proof inject-n2s (previous step)

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

User applied rule apply induction

And obtained the following new goals

Proof step 15:
m % 10 = n % 10, n→s(m % 10) = n→s(n % 10), m / 10 = n / 10, 10 ≤ n, 10 ≤ m, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ n = 0, m = 0, m = n

Rule argument

subst: [n, m1] → [n % 10, m % 10]

Additional information

Used simplifier rules: n2s-rec: ⊦ 10 ≤ n → n→s(n) = n→s(n / 10) + n→s(n % 10);% ⊦ ¬ m < n ↔ n ≤ m;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)%n ≠ 0 ⊦ ¬ n ≤ m % n; Used terms: n % 10, m % 10