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Proof step 11 from proof div-est-num (previous step)

abs(j2) < j, i1 * j + j1 < j, i1 < j, j1 < j, j1 ≤ 0, (i0 * j + j2) + 1 < j, 0 < j, j0 ≤ i0, i0 * j + j2 ≤ i1 * j + j1, i1 < j0, (i1 * j + j1) + 1 < j, abs(j1) < j, j2 ≤ 0, j2 < j, i0 ≤ 0, i0 < j, i1 < 0, j0 ≤ 0, i0 * j + j2 < j, i0 * j + j2 < 0, i1 < i0, j0 < j, i1 + 1 < j ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlep-04 seq: j * i + j0 ≤ j * i0 + j1, j0 ≤ 0, j1 ≤ 0, abs(j0) < j, abs(j1) < j ⊦ i ≤ i0 subst: [j, i, j0, i0, j1] → [j, i0, j2, i1, j1] flags:

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i0, j2, i1, j1