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Proof step 10 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 ⊦ (i * j1 + i1 * j2) / j ≤ (i * (j - 1) + i1 * (j - 1)) / j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%dist-rmerge: ⊦ i * j + i * j0 = i * (j + j0); from specification int-mult