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Proof step 11 from proof square-ls-02 (previous step)

0 < j, i < j, i + i * i < i + j * j, j * j + j ≤ i * i + i, 0 ≤ i, 0 ≤ j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 12:
i + i * i < i + j * j, i < j, 0 < j, 0 ≤ j, 0 ≤ i, j * j + j ≤ i * i + i ⊦ j + j * j < i + j * j

Rule argument

fma: j + j * j < i + j * j

Additional information

Used simplifier rules: ⊦ i + j < i + i0 ↔ j < i0; (s)% ⊦ i < j → ¬ j < i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: j + j * j < i + j * j