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Proof step 12 from proof fermat-for-rsa (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mod inst: name: fermat-2-mod seq: ⊦ prime(j) ∧ gcd(j, i) = 1 → i ^ (j - 1) |%| j = 1 subst: [j, i] → [j, i ^ i1] flags: rewrite, current

Additional information

Used simplifier rules: mod-mod: ⊦ 0 < j → (i |%| j) |%| j = i |%| j;%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i ^ i1