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Proof step 2 from proof subset (previous step)

a ∈ x, list2set(x) ⊆ s ⊦ a ∈ s

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a, s. a ∈ x0 ∧ list2set(x0) ⊆ s → a ∈ s ⊦ a0 ∈ a + x0 ∧ list2set(a + x0) ⊆ s → a0 ∈ s

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;% ⊦ ¬ a ∈ [];