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Proof step 2 from proof sym (previous step)

disj(x, y) ⊦ disj(y, x)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ y. disj(x0, y) → disj(y, x0), disj(a + x0, y) ⊦ disj(y, a + x0)

Rule argument

indvar: x

Additional information

Used simplifier rules: dis-empty: ⊦ disj([], x);%e: ⊦ disj(x, []);%list freely generated by [], +;;