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Proof step 10 from proof intu-empty (previous step)

a ∈ s, a0 ∈ s, ∀ a. ¬ a ∈ s ∨ ¬ a ∈ s0, ∀ a. ¬ a ∈ s ∨ ¬ a ∈ s1, a ∈ s0 ∨ a ∈ s1 ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 11:
a0 ∈ s, a ∈ s, a ∈ s0, ∀ a. ¬ a ∈ s ∨ ¬ a ∈ s1, ∀ a. ¬ a ∈ s ∨ ¬ a ∈ s0 ⊦
Proof step 13:
a0 ∈ s, a ∈ s, a ∈ s1, ∀ a. ¬ a ∈ s ∨ ¬ a ∈ s1, ∀ a. ¬ a ∈ s ∨ ¬ a ∈ s0 ⊦

Rule argument

pos: left 5

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