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Proof step 18 from proof div-est-num (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult 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, i0, j2, i1, j1]

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: j, i0, j2, i1, j1