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Proof step 9 from proof mod-zero-one (previous step)

i0 % j < j, 0 < j, 1 < (i % j + i0 % j) / j, 0 < (i % j + i0 % j) / j, i % j < j, 0 ≤ i, 0 ≤ i0 ⊦ (i % j + i0 % j) / j = 1

User applied rule cut formula

And obtained the following new goals

Proof step 10:
i % j < j, 0 < (i % j + i0 % j) / j, 1 < (i % j + i0 % j) / j, 0 < j, i0 % j < j, i0 % j + i % j < j + j, 0 ≤ i0, 0 ≤ i ⊦ (i % j + i0 % j) / j = 1
Proof step 16:
i % j < j, 0 < (i % j + i0 % j) / j, 1 < (i % j + i0 % j) / j, 0 < j, i0 % j < j, 0 ≤ i0, 0 ≤ i ⊦ (i % j + i0 % j) / j = 1, i0 % j + i % j < j + j

Rule argument

fma: i0 % j + i % j < j + j

Additional information

Used formulas: i0 % j + i % j < j + j