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Proof step 5 from proof div-sum-ls (previous step)

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

User applied rule simplifier

And obtained the following new goals

Proof step 6:
(i * j1 + i1 * j2) / j ≤ ((i + i1) * (j - 1)) / j, 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 + i1 ≤ ((i + i1) * (j - 1)) / j, 0 < ((i + i1) * (j - 1)) / j ⊦

Rule argument

Additional information

Used simplifier rules: forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs