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Proof step 11 from proof div-sum-ls (previous step)

j1 < j, j2 < j, i + i1 ≤ (i * j1 + i1 * j2) / j, 0 ≤ i, 0 ≤ i1, 0 < i + i1, 0 < j1, 0 < j2, 0 < j, 1 < j, 0 < (i * j1 + i1 * j2) / j, ((j - 1) * (i1 + i)) / j < (i * j1 + i1 * j2) / j ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: ls-02 seq: 0 < i0, i / i0 < j / i0 ⊦ i < j subst: [i0, i, j] → [j, (j - 1) * (i1 + i), i * j1 + i1 * j2] flags: current, []

Additional information

Used terms: j, (j - 1) * (i1 + i), i * j1 + i1 * j2