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Proof step 10 from proof modmod-mult-07 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
j ≠ 0 ⊦ ~ i % j = ~(i % j)
Proof step 12:
0 < j, i < 0 ⊦ j = 0, ~((~ i % j * i0) % j) = (i * i0) % j

Rule argument

spec: <toplevel> name: mod-neg-01 seq: j ≠ 0 ⊦ ~ i % j = ~(i % j) subst: [j, i] → [j, ~ i % j * i0] flags: <all paths>

Additional information

Used terms: j, ~ i % j * i0