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Proof step 2 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 ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 3:
(i * j1 + i1 * j2) / j ≤ (i * (j - 1) + 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 ⊦
Proof step 10:
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

Rule argument

fma: (i * j1 + i1 * j2) / j ≤ (i * (j - 1) + i1 * (j - 1)) / j

Additional information

Used formulas: (i * j1 + i1 * j2) / j ≤ (i * (j - 1) + i1 * (j - 1)) / j