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Proof step 16 from proof square-nls (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
j * (j + 1) = i0 * 2 + j0, j0 < 2, i0 < j, 0 < j, 0 ≤ j, 0 ≤ i0, 0 ≤ j0, (i0 + 1) * 2 ≤ i0 * 2 + j0 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)