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Proof step 17 from proof div-ls-same (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: ple-04 seq: i ≤ j + i0, j ≤ j0 ⊦ i ≤ j0 + i0 subst: [i, j, i0, j0] → [i0, j0, i0 * j, 0] flags:

Additional information

Used simplifier rules: add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%le-same-03: ⊦ i < 0 → (i ≤ i * j ↔ j ≤ 1); from specification int-mult%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0, j0, i0 * j, 0