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Proof step 6 from proof div-mult-nle-est (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ i < j → (j ≤ i ↔ false); (as)%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 ≤ i → abs(i) = i; (s) Used terms: i, i1, j0, i0