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Proof step 8 from proof une-01 (previous step)

¬ a ∈ s1 ∧ ¬ a ∈ s2, ∀ a. ¬ a ∈ s1 ∧ ¬ a ∈ s2 ⊦ a ∈ s2, ¬ a ∈ s1 ∧ ¬ a0 ∈ s2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
a0 ∈ s2, a1 ∈ s2, ∀ a. ¬ a ∈ s1 ∧ ¬ a ∈ s2 ⊦ a ∈ s1, a ∈ s2

Rule argument

Additional information

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