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Proof step 5 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 ⊦ i0 ≤ i0 * j + j0 ↔ i0 * j + j0 = 0 ∨ j = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ j ≤ (* i1) * j + i ↔ 0 ≤ (i1 - 1) * j + i
Proof step 7:
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

Rule argument

spec: int-mult inst: name: numle-12 seq: ⊦ j ≤ (* i1) * j + i ↔ 0 ≤ (i1 - 1) * j + i subst: [i, i1, j] → [j0, j, i0] flags: rewrite

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j0, j, i0