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Proof step 9 from proof ls-01 (previous step)

i2 * j0 + j2 ≤ i1 * j0 + j1, j2 < j0, 0 ≤ i1, j1 < j0, 0 ≤ j1, i1 < i2, i0 ≤ j0, i2 * j0 + j2 ≤ i1 * i0 + j1, j1 < i0, 0 < i0, 0 < j0, 0 ≤ j2, 0 < i2, 0 ≤ i2 ⊦ i0 = 0, j0 = 0

User applied rule insert spec-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] → [j0, i2, 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%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs Used terms: j0, i2, j2, i1, j1