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Proof step 17 from proof modmod-mult-07 (previous step)

j ≠ 0 ∧ i < 0, i0 < j, i0 < 0, i + 1 < j, 0 < j, i < 0, i < j, i0 + 1 < j ⊦ (~(~ i % j) * i0) % j = (i * i0) % j, j = 0

User applied rule cut formula

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: mod-neg-01: j ≠ 0 ⊦ ~ i % j = ~(i % j);%neg-02: ⊦ ~ ~ i = i; from specification int-abs%minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%eq-neg: ⊦ i < 0 → (i * j = i * j0 ↔ j = j0); from specification int-mult Used formulas: ~(~ i % j) * i0 = ~ i % j * ~ i0