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Proof step 3 from proof cons-01 (previous step)

disj(x, y), disj(a ' + x, y), a ∈ y ⊦

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 4:
disj(a ' + x, a0 + y0), disj(x, a0 + y0), a ∈ a0 + y0, ∀ x, a. ¬(disj(x, y0) ∧ disj(a ' + x, y0) ∧ a ∈ y0) ⊦

Rule argument

term: y

Additional information

Used simplifier rules: list freely generated by [], +;;% ⊦ ¬ a ∈ []; (s)