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Proof step 1 from proof three (conclusion)

⊦ m ≠ 0 ∧ n ≠ 0 ∧ m ≠ 1 → (m + n = 3 ↔ m = 2 ∧ n = 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m + n = 3 ⊦ m = 1, n = 0, m = 0, m = 2 ∧ n = 1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1;%c: ⊦ m + n = n + m;