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Proof step 2 from proof modmod-mult-09 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
0 < j ⊦ (i % j * i0) % j = (i * i0) % j
Proof step 4:
⊦ (i % j * i0) % j = (i * i0) % j, j = 0, 0 < j

Rule argument

spec: <toplevel> name: modmod-mult-07 seq: 0 < j ⊦ (i % j * i0) % j = (i * i0) % j subst: [i0, j, i] → [i0, j, i] flags: <all paths>

Additional information

Used terms: i0, j, i