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Proof step 2 from proof in-01 (previous step)

a ∈ x -l b ⊦ a = b, a ∈ x

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ a, b. a ∈ x0 -l b → a = b ∨ a ∈ x0, a ∈ (a0 + x0) -l b ⊦ a = b, a ∈ a0 + x0

Rule argument

term: x

Additional information

Used simplifier rules: del-e: ⊦ [] -l a = [];%list freely generated by [], +;;%in-empty: ⊦ ¬ a ∈ []; from specification list