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Proof step 1 from proof in-01 (conclusion)

⊦ a ∈ x -l b → a ∈ x ∧ a ≠ b

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a ∈ x -l b ⊦ a = b, a ∈ x

Rule argument

Additional information

Used simplifier rules: in-02: ⊦ ¬ a ∈ x -l a;