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Proof step 10 from proof square-le-04 (previous step)

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 11:
j + j * j < j + i * i, j < i, i + i * i ≤ j + j * j, 0 ≤ i, 0 ≤ j, 0 < i ⊦

Rule argument

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

Additional information

Used simplifier rules: square-ls: ⊦ i * i < j * j ↔ abs(i) < abs(j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%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 < j + i * i