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Proof step 23 from proof RSA-decrypt-ij-vars (previous step)

gcd(i2, (i - 1) * (i0 - 1)) = 1, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, (i - 1) * (i0 - 1) | abs(i2 * i3 - 1), i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 < j, 0 < i0, 0 < i3, 0 ≤ i2 ⊦ 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 24:
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, (i - 1) * (i0 - 1) | i2 * i3 - 1 ⊦ j = 0, i3 = 0, i = i0, j = j ^ (i2 * i3) |%| (i * i0)

Rule argument

Additional information

Used simplifier rules: div-abs-02: ⊦ i | abs(j) ↔ i | j; from specification int-gcd