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Proof step 5 from proof modmod-mult-03 (previous step)

0 < j0 ⊦ (i % (j * j0)) % j = i % j, j = 0, 0 < j ∧ 0 ≤ i

User applied rule cut formula

And obtained the following new goals

Proof step 6:
j < 0, 0 < j0 ⊦ (i % (j * j0)) % j = i % j, j = 0, 0 < j ∧ 0 ≤ i
Proof step 12:
0 < j0 ⊦ j < 0, (i % (j * j0)) % j = i % j, j = 0, 0 < j ∧ 0 ≤ i

Rule argument

fma: j < 0

Additional information

Used formulas: j < 0