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Proof step 1 from proof RSA-decrypt-ij-vars (conclusion)

prime(i), prime(i0), i1 = i * i0, 2 < i, 2 < i0, i ≠ i0, gcd(i2, (i - 1) * (i0 - 1)) = 1, 0 < i2, i2 < i1, ≡mod(i2 * i3, 1, (i - 1) * (i0 - 1)), 0 ≤ i3, j0 = j ^ i2 |%| i1, 0 ≤ j, j < i1 ⊦ j = j0 ^ i3 |%| i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
gcd(i2, (i - 1) * (i0 - 1)) = 1, 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, 0 ≤ i3, 0 < i0, 1 < i * i0 ⊦ i = i0, j = (j ^ i2 |%| (i * i0)) ^ i3 |%| (i * i0)

Rule argument

Additional information

Used simplifier rules: numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs%lel: ⊦ i < i0 ∧ i = i1 → i1 < i0; (forward) from specification oelem[intlista]%numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs