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Proof step 2 from proof pos-get (previous step)

n < # x ⊦ pos(x[n], x) = n, x = [], dups(x)

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: x

Additional information

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