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Proof step 1 from proof sqls (conclusion)

⊦ m ≤ n → (m + 1 < n * n ↔ 1 < n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
m ≤ n ⊦ m + 1 < n * n ↔ n ≠ 0 ∧ n ≠ 1

Rule argument

Additional information

Used simplifier rules: one: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); from specification nat-basic1