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Proof step 5 from proof square-ls-02 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: j + j * j ≤ j + i * i

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)%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