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Proof step 4 from proof sym (previous step)

disj(a ' + x0, y), ∀ y. disj(x0, y) → disj(y, x0) ⊦ disj(y, a ' + x0)

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 5:
a ∈ y, disj(a ' + x0, y), ∀ y. disj(x0, y) → disj(y, x0) ⊦ disj(y, a ' + x0)

Rule argument

fma: a ∈ y

Additional information

Used simplifier rules: first-01: ⊦ ¬ a ∈ x → (disj(a ' + y, x) ↔ disj(y, x));%cons-02: ⊦ disj(x, y) → (disj(y, a ' + x) ↔ ¬ a ∈ y);%a: ⊦ (x + y) + z = x + y + z; from specification list Used formulas: a ∈ y