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Proof step 15 from proof RSA-decrypt-ij-vars (previous step)

gcd(i2, (i - 1) * (i0 - 1)) = 1, 0 < i3, 0 < i0, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, ≡mod(i2 * i3, 1, (i - 1) * (i0 - 1)), i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 < j ⊦ j = 0, i3 = 0, i = i0, j = (j ^ i2 |%| (i * i0)) ^ i3 |%| (i * i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: mod-pot-pot seq: ⊦ 0 ≤ i0 ∧ 0 < j → (i |%| j) ^ i0 |%| j = i ^ i0 |%| j subst: [i0, j, i] → [i3, i * i0, j ^ i2] flags: rewrite, current

Additional information

Used simplifier rules: lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); 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: i3, i * i0, j ^ i2