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Proof step 1 from proof in-union (conclusion)

⊦ ¬ a ∈ x → (a ∈ list2set(x) ∪ s ↔ a ∈ s)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: in: ⊦ a ∈ list2set(x) ↔ a ∈ x;% ⊦ s ∪ s0 = s0 ∪ s;% ⊦ (s ∪ s0) ∪ s1 = s ∪ s0 ∪ s1;% ⊦ a ∈ s1 ∪ s2 ↔ a ∈ s1 ∨ a ∈ s2;