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Proof step 2 from proof size-three-01 (previous step)

a ∈ s, b ∈ s, c ∈ s ⊦ a = c, a = b, b = c, 3 ≤ # s

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# s < 3, a ∈ s, b ∈ s, c ∈ s ⊦ a = c, a = b, 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-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)