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Proof step 11 from proof square-le-04 (previous step)

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

User applied rule cut formula

And obtained the following new goals

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

Rule argument

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

Additional information

Used simplifier rules: ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%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