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Proof step 6 from proof modneqp (previous step)

i1 * j + j1 ≤ i * j + j0, j1 < j, j0 < j, i0 ≤ j, i < i1, 0 ≤ j1, 0 ≤ j0, 0 < j, 0 ≤ i0, 0 ≤ j, 0 ≤ i, 0 < i1, i1 * j + j1 ≤ i * i0 + j0 ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlep-03 seq: j * i + j0 ≤ j * i0 + j1, 0 ≤ j0, j0 < j, abs(j1) < j ⊦ i ≤ i0 subst: [j, i, j0, i0, j1] → [j, i1, j1, i, j0] flags: current, []

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i;%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs Used terms: j, i1, j1, i, j0