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Proof step 21 from proof square-le-04 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i + i * i ≤ i + j * j

Additional information

Used simplifier rules: square-le: ⊦ i * i ≤ j * j ↔ abs(i) ≤ abs(j);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%lep-02: ⊦ i + j ≤ i + j0 ↔ j ≤ j0; from specification int-abs%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels-04: ⊦ 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: i + i * i ≤ i + j * j