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

m < # x ⊦ x = [], x[m] ∈ x

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: x

Additional information

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