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Proof step 56 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 < i0, 0 < i3, 0 ≤ i2, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, 0 < i1, 0 ≤ (i - 1) * (i0 - 1), ~1 ≤ ((i - 1) * (i0 - 1)) * i1, 0 ≤ j ^ (((i - 1) * (i0 - 1)) * i1), 0 < j ⊦ i0 = 0, i1 = 0, j = 0, i3 = 0, i = i0, j = (j ^ (((i - 1) * (i0 - 1)) * i1) * j) |%| (i * i0), (j ^ (((i - 1) * (i0 - 1)) * i1) * j) |%| i = j |%| i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: fermat-for-rsa seq: ⊦ prime(j) ∧ j - 1 | i0 ∧ 2 < j ∧ 0 ≤ i ∧ 0 ≤ i0 → (i ^ i0 * i) |%| j = i |%| j subst: [j, i0, i] → [i, ((i - 1) * (i0 - 1)) * i1, j] flags: rewrite, current

Additional information

Used simplifier rules: div-mult: ⊦ i | i * j; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: i, ((i - 1) * (i0 - 1)) * i1, j