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Proof step 2 from proof union-sizele (previous step)

⊦ #(s ∪ s0) ≤ # s ↔ (∀ a. a ∈ s0 → a ∈ s)

User applied rule case distinction

And obtained the following new goals

Proof step 3:
#(s ∪ s0) ≤ # s ⊦ ∀ a. a ∈ s0 → a ∈ s
Proof step 9:
∀ a. a ∈ s0 → a ∈ s ⊦ #(s ∪ s0) ≤ # s

Rule argument

pos: right 1

Additional information