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Proof step 4 from proof append-to-gr (previous step)

n = n0 + # x, # x < n, # x ≤ n ⊦ x + y to n = x + (y to n0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ n0 = 0, x + y to n0 + # x = x + (y to n0)

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → m ≤ n; (s)