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Proof step 13 from proof une-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
a ∈ s1, a0 ∈ s1, ∀ a. ¬ a ∈ s2, ∀ a. ¬ a ∈ s1 ⊦ a ∈ s2

Rule argument

Additional information

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