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Proof step 3 from proof square-less (previous step)

m * m < m * n ∧ m * n < n * n → m * m < n * n ⊦ m * m < n * n ↔ m < n

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 1

Additional information

Used simplifier rules: ls-06: ⊦ m < m0 ∧ n < n0 → m * n < m0 * n0;%mult-a: ⊦ m0 * m * n = (m0 * m) * n;%mult-c: ⊦ m * n = n * m;