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Proof step 59 from proof RSA-decrypt-ij-vars (previous step)

gcd(i2, (i - 1) * (i0 - 1)) = 1, i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 < j, 0 < i0, 0 < i3, 0 ≤ i2, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, 0 < i1, 0 ≤ (i - 1) * (i0 - 1), ≡mod(j ^ (((i - 1) * (i0 - 1)) * i1 + 1), j, i), ≡mod(j ^ (((i - 1) * (i0 - 1)) * i1 + 1), j, i0), ~1 ≤ ((i - 1) * (i0 - 1)) * i1 ⊦ i1 = 0, j = 0, i3 = 0, j = j |%| (i * i0), i = i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: mod-zero seq: ⊦ 0 ≤ i ∧ i < j → i |%| j = i subst: [j, i] → [i * i0, j] flags: rewrite, current

Additional information

Used simplifier rules: lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs Used terms: i * i0, j