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Proof step 2 from proof square-nle-02 (previous step)

i ≤ 0, 0 ≤ j, ((j + 1) * (j + 2)) / 2 ≤ i + j ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 3:
i ≤ 0, 0 ≤ j, ((j + 1) * (j + 2)) / 2 ≤ i + j ⊦ ((j + 1) * (j + 2)) / 2 ≤ j

Rule argument

fma: ((j + 1) * (j + 2)) / 2 ≤ j

Additional information

Used simplifier rules: square-nle-01: ⊦ 0 ≤ j → ¬ ((j + 1) * (j + 2)) / 2 ≤ j;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: ((j + 1) * (j + 2)) / 2 ≤ j