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Proof step 15 from proof pot-div3-nls (previous step)

0 < j, 1 < i0, 0 < i0, j ^ (i0 - 1) < j, (j ^ (i0 - 1) * j * j) / 3 < j, 2 ≤ j, 0 ≤ j, 0 ≤ i0 ⊦

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: int-abs name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i0, 1, i]

Additional information

Used simplifier rules: pot-nls: ⊦ 0 < i ∧ 0 < j → ¬ i ^ j < i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ 0 < i ∧ 0 < j → 0 < i + j; (s)% ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i0, 1, i