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

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

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ y, n0. x0 + y to n0 + # x0 = x0 + (y to n0) ∨ n0 + # x0 = 0 ∨ n0 = 0 ⊦ (a + x0) + y to n0 + #(a + x0) = (a + x0) + (y to n0), n0 + #(a + x0) = 0, n0 = 0

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%size-01: ⊦ # [] = 0; from specification list-data%add-base: ⊦ n + 0 = n; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2