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Proof step 4 from proof intempty-02 (previous step)

∀ a. ¬ a ∈ list2set(x) ∨ ¬ a ∈ s, a ∈ s, a ∈ x ⊦ s = ∅, # s = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
a ∈ s, a ∈ x, ∀ a0. ¬ a0 ∈ s ∨ ¬ a0 ∈ x ⊦ s = ∅, # s = 0

Rule argument

Additional information

Used simplifier rules: in: ⊦ a ∈ list2set(x) ↔ a ∈ x;