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Proof step 25 from proof inject-n2s (previous step)

¬ n < 10, ('0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] ' = n→s(n), m < 10, ∀ 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 26:
('0' ' + '1' ' + '2' ' + '3' ' + '4' ' + '5' ' + '6' ' + '7' ' + '8' ' + '9' ')[m] ' = n→s(n / 10) + n→s(n % 10), m < n, 10 ≤ n, m < 10, ∀ m1, n. m1 < m → n→s(m1) = n→s(n) → m1 = n ⊦

Rule argument

Additional information

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