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Proof step 18 from proof fermat-for-rsa (previous step)

0 ≤ i, 2 < j, prime(j), 0 < j, 0 ≤ i1, j | i ^ 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-fac inst: name: prime-divides-pot-01 seq: ⊦ prime(i) ∧ 0 < j → (i | i0 ^ j ↔ i | i0) subst: [j, i0, i] → [i1, i, j] flags: rewrite

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%gcd-one-01: ⊦ gcd(i, 1) = 1; from specification int-gcd Used terms: i1, i, j