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Proof step 4 from proof square-interval (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
0 ≤ j0, 0 ≤ j, 0 ≤ i, j0 ≤ j, (j * (j + 1)) / 2 + j0 < ((i + 1) * (i + 2)) / 2, (i * (i + 1)) / 2 ≤ (j * (j + 1)) / 2 + j0 ⊦ i = j, i * (i + 1) ≤ j * (j + 1) + 2 * j0 ∧ j * (j + 1) + 2 * j0 < (i + 1) * (i + 2)

Proof step 4 from proof square-interval (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information