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Proof step 9 from proof square-ls (previous step)

m0 * m0 + m0 < m * m + m ↔ m0 < m, 3 * m0 + m0 * m0 < 3 * m + m * m ⊦ m0 < m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
3 * m0 + m0 * m0 < 3 * m + m * m, m * m + m ≤ m0 * m0 + m0, m ≤ m0 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)