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Proof step 4 from proof modmod-mult-09 (previous step)

j < 0 ⊦ (i % j * i0) % j = (i * i0) % j

User applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: (i % j * i0) % j = (i % ~ j * i0) % ~ j

Additional information

Used simplifier rules: mod-neg: j ≠ 0 ⊦ i % ~ j = i % j; Used formulas: (i % j * i0) % j = (i % ~ j * i0) % ~ j