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Proof step 8 from proof square-nle (previous step)

j * (j + 1) = i0 * 2 + j0, j0 < 2, 0 < j, j0 < j, i0 ≤ j, 0 ≤ j, 2 ≤ j, 0 ≤ i0, 0 ≤ j0 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 9:
j * (j + 1) = i0 * 2 + j0, j0 < j, 0 < j, j0 < 2, j * (j + 1) < (i0 + 1) * 2, 0 ≤ j0, 0 ≤ i0, 2 ≤ j, 0 ≤ j, i0 ≤ j ⊦
Proof step 18:
j * (j + 1) = i0 * 2 + j0, j0 < j, 0 < j, j0 < 2, 0 ≤ j0, 0 ≤ i0, 2 ≤ j, 0 ≤ j, i0 ≤ j ⊦ j * (j + 1) < (i0 + 1) * 2

Rule argument

fma: j * (j + 1) < (i0 + 1) * 2

Additional information

Used formulas: j * (j + 1) < (i0 + 1) * 2