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Proof step 7 from proof div-ls-zero (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 < 0 ↔ (i0 * j + j0) + j ≤ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i ≤ j ↔ ¬ j < i
Proof step 9:
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 < 0 ↔ ¬ 0 < (i0 * j + j0) + j

Rule argument

spec: int-abs inst: name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [0, (i0 * j + j0) + j] flags: rewrite

Additional information

Used terms: 0, (i0 * j + j0) + j