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Proof step 13 from proof pot-div3-nls (previous step)

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

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

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

Additional information

Used simplifier rules: pot-nls: ⊦ 0 < i ∧ 0 < j → ¬ i ^ j < i;%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-02: ⊦ 0 < i ∧ 0 < j → 0 < i + j; from specification int-basic2%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs% ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i0, 1, i