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Proof step 22 from proof square-le-04 (previous step)

j + j * j < i + i * i, 0 ≤ i, 0 ≤ j, 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;% ⊦ i + j ≤ i + j0 ↔ j ≤ j0; (s)% ⊦ 0 ≤ i → abs(i) = i; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i ≤ j → (j < i ↔ false); (as)%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