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Proof step 28 from proof RSA-decrypt-ij-vars (previous step)

((i - 1) * (i0 - 1)) * i1 < 0, gcd(i2, (i - 1) * (i0 - 1)) = 1, i2 * i3 = ((i - 1) * (i0 - 1)) * i1 + 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 ⊦ j = 0, i3 = 0, i = i0, j = j ^ (i2 * i3) |%| (i * i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
i2 * i3 = ((i - 1) * (i0 - 1)) * i1 + 1, gcd(i2, (i - 1) * (i0 - 1)) = 1, ((i - 1) * (i0 - 1)) * i1 < i, ((i - 1) * (i0 - 1)) * i1 < i3, ((i - 1) * (i0 - 1)) * i1 < i0, ((i - 1) * (i0 - 1)) * i1 < j, ((i - 1) * (i0 - 1)) * i1 < 0, j < i * i0, 0 < i, 0 < i2, 1 < i * i0, 0 ≤ i2, 0 < i3, 0 < i0, 0 < j, prime(i), prime(i0), 2 < i, 2 < i0, i2 < i * i0, ((i - 1) * (i0 - 1)) * i1 < i * i0 ⊦ j = j ^ (i2 * i3) |%| (i * i0), i = i0, i3 = 0, j = 0

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]