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Proof step 1 from proof prefix-notin (conclusion)

⊦ a ∈ x ∧ ¬ a ∈ y → ¬ x ⊑ y

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: prefix-in-02: ⊦ a ∈ x ∧ x ⊑ y → a ∈ y;