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Proof step 2 from proof size-two-06 (previous step)

# s < 2, b ∈ s, a ∈ s ⊦ a = b

Heuristic structural induction applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ b, a. # s0 < 2 ∧ b ∈ s0 ∧ a ∈ s0 → a = b, #(s0 ++ a0) < 2, b ∈ s0 ++ a0, a ∈ s0 ++ a0 ⊦ a = b

Rule argument

term: s

Additional information

Used simplifier rules: gen: ⊦ ;%Size-empty: ⊦ # ∅ = 0;%In-empty: ⊦ ¬ a ∈ ∅;