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Proof step 5 from proof append-to-gr (previous step)

⊦ n0 = 0, x + y to n0 + # x = x + (y to n0)

User applied rule structural induction

And obtained the following new goals

Proof step 6:
∀ n0, y. n0 = 0 ∨ x0 + y to n0 + # x0 = x0 + (y to n0) ⊦ n0 = 0, (a + x0) + y to n0 + #(a + x0) = (a + x0) + (y to n0)

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;% ⊦ [] + x = x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # [] = 0; (s)% ⊦ 0 + m = m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic