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Proof step 7 from proof mod-zero-one (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 8:
i % j < j, i0 % j < j, 0 ≤ i, 0 ≤ i0, 0 < j, 1 < (i % j + i0 % j) / j, 0 < (i % j + i0 % j) / j ⊦ (i % j + i0 % j) / j = 1

Rule argument

fma: i % j < j

Additional information

Used simplifier rules: mod-less-01: ⊦ 0 < j → i % j < j; Used formulas: i % j < j