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Proof step 6 from proof unsub-union-01 (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 7:
a ∈ s1, a ∈ s2, a1 ∈ s2, ∀ a. a ∈ s1 ∨ a ∈ s2 → a ∈ s ⊦ (a ∈ s1 → a ∈ s) ∧ (a0 ∈ s2 → a0 ∈ s)
Proof step 13:
a ∈ s2, a1 ∈ s2, ∀ a. a ∈ s1 ∨ a ∈ s2 → a ∈ s ⊦ a ∈ s1, (a ∈ s1 → a ∈ s) ∧ (a0 ∈ s2 → a0 ∈ s)

Rule argument

fma: a ∈ s1

Additional information

Used formulas: a ∈ s1