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Proof step 7 from proof div-le-same-neg (previous step)

i0 * j + j0 < j, i0 * j + j0 < 0, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, (i0 * j + j0) + 1 < j, 0 < j, abs(j0) < j ⊦ 0 ≤ (j - 1) * i0 + j0 ↔ i0 * j + j0 = 0 ∨ j = 1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
j = i1 + 1, i0 * j + j0 < j, i0 * j + j0 < 0, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, (i0 * j + j0) + 1 < j, 0 < j, abs(j0) < j ⊦ 0 ≤ i1 * i0 + j0 ↔ i0 * j + j0 = 0 ∨ j = 1

Rule argument

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

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: j, 1, i