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Proof step 16 from proof mod-div-ls (previous step)

j0 < j, 0 < i1, 0 < j, i0 < i1, i0 < (i0 + i1 * j0) / j, 0 < (i0 + i1 * j0) / j, 0 ≤ i2, 0 ≤ j0, i1 ≤ (i0 + i1 * j0) / j, 0 ≤ i0, i1 ≤ (i1 * (j0 + 1)) / j ⊦ j0 + 1 = j

User applied rule cut formula

And obtained the following new goals

Proof step 17:
0 < (i0 + i1 * j0) / j, i0 < (i0 + i1 * j0) / j, i0 < i1, 0 < j, 0 < i1, j0 < j, i1 ≤ (i1 * (j0 + 1)) / j, 0 ≤ i0, i1 ≤ (i0 + i1 * j0) / j, 0 ≤ j0, 0 ≤ i2 ⊦ j0 + 1 = j, (i1 * (j0 + 1)) / j < i1

Rule argument

fma: (i1 * (j0 + 1)) / j < i1

Additional information

Used simplifier rules: ⊦ i ≤ j → ¬ j < i; (s) Used formulas: (i1 * (j0 + 1)) / j < i1