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Proof step 22 from proof modmod-mult-07 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 23:
(i % j * i0) % j = ~(i % j * ~ i0) % j, 0 < j, i0 < 0, 0 ≤ i ⊦ (i % j * i0) % j = (i * i0) % j

Rule argument

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

Additional information

Used simplifier rules: ⊦ ~ i * j = ~(i * j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ ~ ~ i = i; (s) Used formulas: (i % j * i0) % j = ~(i % j * ~ i0) % j