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Proof step 4 from proof equal-add-in (previous step)

b = c, ∀ a1. a1 = a ∨ a1 ∈ s ↔ a1 = b ∨ a1 ∈ s0, ∀ a1. a1 = b ∨ a1 ∈ s0 ↔ a1 = a0 ∨ a1 ≠ c ∧ a1 ∈ s1 ⊦ b = a0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information