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Proof step 5 from proof div-mult-nle-est (previous step)

j0 < i, 0 < i, i0 < i1, i1 * i + j0 ≤ i * i0, 0 ≤ i0, 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] → [i, 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: i, i1, j0, i0