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Proof step 4 from proof modmod-mult-07 (previous step)

0 < j ⊦ (i % j * i0) % j = (i * i0) % j, 0 ≤ i ∧ 0 ≤ i0

User applied rule cut formula

And obtained the following new goals

Proof step 5:
i < 0, 0 < j ⊦ (i % j * i0) % j = (i * i0) % j, 0 ≤ i ∧ 0 ≤ i0
Proof step 21:
0 < j ⊦ i < 0, (i % j * i0) % j = (i * i0) % j, 0 ≤ i ∧ 0 ≤ i0

Rule argument

fma: i < 0

Additional information

Used formulas: i < 0