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Proof step 13 from proof mult-ls-01 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlep-02 seq: j * i + j0 ≤ j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [j, i1, j0, i0] 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: j, i1, j0, i0