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Proof step 7 from proof div-ls-mone (previous step)

i0 * j + j0 < j, i0 * j + j0 < 0, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, 0 < j, abs(j0) < j, (i0 * j + j0) + 1 < j ⊦ i0 < ~1 ↔ (i0 * j + j0) + 2 * j ≤ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ j < 0 → abs(j) = 0 - j
Proof step 9:
¬ j0 < 0, i0 * j + j0 < j, i0 * j + j0 < 0, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, 0 < j, abs(j0) < j, (i0 * j + j0) + 1 < j ⊦ i0 < ~1 ↔ (i0 * j + j0) + 2 * j ≤ 0
Proof step 19:
j0 < 0, i0 * j + j0 < j, i0 * j + j0 < 0, i0 < j, i0 ≤ 0, j0 < j, j0 ≤ 0, 0 < j, 0 - j0 < j, (i0 * j + j0) + 1 < j ⊦ i0 < ~1 ↔ (i0 * j + j0) + 2 * j ≤ 0

Rule argument

spec: int-abs inst: name: Abs-neg seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j0] flags: rewrite

Additional information

Used terms: j0