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Proof step 8 from proof div-ls-same (previous step)

1 < j, 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 ⊦ i0 * j + j0 < i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ¬ i < j ↔ j ≤ i
Proof step 10:
1 < j, 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 ⊦ ¬ i0 ≤ i0 * j + j0

Rule argument

spec: int-abs inst: name: lels seq: ⊦ ¬ i < j ↔ j ≤ i subst: [j, i] → [i0, i0 * j + j0] flags: rewrite

Additional information

Used terms: i0, i0 * j + j0