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Proof step 3 from proof firstN-in (previous step)

a ∈ firstn(n, x), n ≤ # x ⊦ a ∈ x

User applied rule structural induction

And obtained the following new goals

Proof step 4:
a ∈ firstn(n, a0 + x0), n ≤ #(a0 + x0), ∀ a, n. a ∈ firstn(n, x0) ∧ n ≤ # x0 → a ∈ x0 ⊦ a ∈ a0 + x0

Rule argument

indvar: x

Additional information

Used simplifier rules: firstN-zero: ⊦ firstn(0, x) = [];%list freely generated by [], +;;% ⊦ # [] = 0; (s)% ⊦ m ≤ 0 ↔ m = 0; (s)% ⊦ ¬ a ∈ []; (s)