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Proof step 8 from proof unsub-union-01 (previous step)

a1 ∈ s2, a ∈ s2, a ∈ s1, a2 ∈ s1, ∀ a. a ∈ s1 ∨ a ∈ s2 → a ∈ s ⊦ a ∈ s ∧ (a0 ∈ s2 → a0 ∈ s)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 9:
a ∈ s, a1 ∈ s2, a ∈ s2, a ∈ s1, a2 ∈ s1, ∀ a. a ∈ s1 ∨ a ∈ s2 → a ∈ s ⊦ a ∈ s ∧ (a0 ∈ s2 → a0 ∈ s)
Proof step 11:
a1 ∈ s2, a ∈ s2, a ∈ s1, a2 ∈ s1, ∀ a. a ∈ s1 ∨ a ∈ s2 → a ∈ s ⊦ a ∈ s, a ∈ s ∧ (a0 ∈ s2 → a0 ∈ s)

Rule argument

fma: a ∈ s

Additional information

Used formulas: a ∈ s