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Proof step 17 from proof inject-n2s (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
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

Rule argument

Additional information

Used simplifier rules: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward)% ⊦ m + n = n + m;% ⊦ m * n = n * m;%n ≠ 0 ⊦ m % n < n;