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Proof step 10 from proof del-two (previous step)

a0 = b, a2 ∈ s, a1 ∈ s, a3 ∈ s, a4 ∈ s, ∀ a4. a4 = b ∨ a4 = a ∨ ¬ a4 ∈ s ⊦ a1 = b, a2 = a, a0 ∈ s

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
a4 ∈ s, a3 ∈ s, a1 ∈ s, a2 ∈ s, ∀ a0. a0 = a ∨ ¬ a0 ∈ s ⊦ a2 = a, b ∈ s

Rule argument

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