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Proof step 2 from proof square-interval (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 3:
j * (j + 1) + 2 * j0 < (i + 1) * (i + 2), j * (j + 1) + 2 * j0 < (j + 1) * (j + 2), i * (i + 1) ≤ j * (j + 1) + 2 * j0, j0 ≤ j, 0 ≤ i, 0 ≤ j0 ⊦ i = j
Proof step 9:
j * (j + 1) + 2 * j0 < (i + 1) * (i + 2), i * (i + 1) ≤ j * (j + 1) + 2 * j0, j0 ≤ j, 0 ≤ i, 0 ≤ j0 ⊦ i = j, j * (j + 1) + 2 * j0 < (j + 1) * (j + 2)

Rule argument

fma: j * (j + 1) + 2 * j0 < (j + 1) * (j + 2)

Additional information

Used formulas: j * (j + 1) + 2 * j0 < (j + 1) * (j + 2)