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Proof step 10 from proof fermat-for-rsa (previous step)

0 ≤ i, 2 < j, prime(j), 0 < j, 0 ≤ i1 ⊦ ((i ^ i1) ^ (j - 1) * i) |%| j = i |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 0 < j → (i * i0) |%| j = (i |%| j * i0 |%| j) |%| j
Proof step 12:
0 < j, 0 ≤ i, 2 < j, prime(j), 0 < j, 0 ≤ i1 ⊦ ((i ^ i1) ^ (j - 1) |%| j * i |%| j) |%| j = i |%| j

Rule argument

spec: int-mod inst: name: mod-mult-law seq: ⊦ 0 < j → (i * i0) |%| j = (i |%| j * i0 |%| j) |%| j subst: [j, i0, i] → [j, i, (i ^ i1) ^ (j - 1)] flags: rewrite, current

Additional information

Used terms: j, i, (i ^ i1) ^ (j - 1)