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Proof step 5 from proof unsub-union-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
a ∈ s2, a1 ∈ s2, ∀ a. a ∈ s1 ∨ a ∈ s2 → a ∈ s ⊦ (a ∈ s1 → a ∈ s) ∧ (a0 ∈ s2 → a0 ∈ s)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ∈ ∅; (s)% ⊦ s1 = s2 ↔ (∀ a. a ∈ s1 ↔ a ∈ s2); (s)%ne-01: ⊦ a ∈ s → s ≠ ∅; (forward) from specification set-basic