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Proof step 21 from proof fermat-for-rsa (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i, j] flags: rewrite

Additional information

Used simplifier rules: mod-mult-01: ⊦ 0 < j → (i * j) |%| j = 0;%mod-zero-03: ⊦ 0 < j → 0 |%| j = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%Mult-zero: ⊦ i * 0 = 0; from specification int-mult Used terms: i, j