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Proof step 1 from proof size-three-01 (conclusion)

⊦ a ∈ s ∧ b ∈ s ∧ c ∈ s ∧ a ≠ b ∧ a ≠ c ∧ b ≠ c → 3 ≤ # s

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# s < 3, c ∈ s, b ∈ s, a ∈ s ⊦ a = b, a = c, b = c

Rule argument

Additional information

Used simplifier rules: ne-01: ⊦ a ∈ s → s ≠ ∅;%ne-02: ⊦ a ∈ s → (s = ∅ ↔ false);%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%lels-01: ⊦ ¬ m ≤ n ↔ n < m; from specification nat