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Proof step 8 from proof modmod-mult-07 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ~ i * j = ~(i * j)
Proof step 10:
j ≠ 0 ∧ i < 0, i < j, i < 0, 0 < j, i + 1 < j ⊦ ~(~ i % j * i0) % j = (i * i0) % j

Rule argument

spec: int-mult inst: name: minus-left seq: ⊦ ~ i * j = ~(i * j) subst: [j, i] → [i0, ~ i % j] flags: rewrite

Additional information

Used terms: i0, ~ i % j