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Proof step 5 from proof inject-n2s (previous step)

¬ m < 10, n→s(m) = n→s(n), ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ m = n

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
n→s(m / 10) + n→s(m % 10) = n→s(n), 10 ≤ m, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦ m = n, m = 0

Rule argument

Additional information

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