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Proof step 12 from proof square-le-04 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 13:
j + j * j < j + i * i, j < i, 0 < i, 0 ≤ i, 0 ≤ j, i + i * i ≤ j + j * j ⊦ i + i * i < j + i * i

Rule argument

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

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