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Proof step 2 from proof get-append-less (previous step)

n < # x ⊦ (x + y)[n] = x[n], x = []

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ n, y. n < # x0 → (x0 + y)[n] = x0[n] ∨ x0 = [], n < #(a + x0) ⊦ ((a + x0) + y)[n] = (a + x0)[n], a + x0 = []

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;