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Proof step 2 from proof unsubsub (previous step)

∀ a. a ∈ s → a ∈ s0, ∀ a. a ∈ s1 → a ∈ s2, a ∈ s ∨ a ∈ s1 ⊦ a ∈ s0, a ∈ s2

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 3:
a ∈ s, ∀ a. a ∈ s → a ∈ s0, ∀ a. a ∈ s1 → a ∈ s2, a ∈ s ∨ a ∈ s1 ⊦ a ∈ s0, a ∈ s2
Proof step 5:
∀ a. a ∈ s → a ∈ s0, ∀ a. a ∈ s1 → a ∈ s2, a ∈ s ∨ a ∈ s1 ⊦ a ∈ s, a ∈ s0, a ∈ s2

Rule argument

fma: a ∈ s

Additional information

Used formulas: a ∈ s