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Proof step 9 from proof RSA-decrypt-ij-vars (previous step)

¬ 0 < (i - 1) * (i0 - 1), gcd(i2, (i - 1) * (i0 - 1)) = 1, i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 ≤ j, 0 < i0, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, (i - 1) * (i0 - 1) | 1 ⊦ i = i0, j = 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
gcd(i2, (i - 1) * (i0 - 1)) = 1, (i - 1) * (i0 - 1) < i, (i - 1) * (i0 - 1) < i2, (i - 1) * (i0 - 1) < i0, (i - 1) * (i0 - 1) ≤ 0, (i - 1) * (i0 - 1) | 1, j < i * i0, 0 < i, 0 < i2, 1 < i * i0, 0 < i0, 0 ≤ j, prime(i), prime(i0), 2 < i, 2 < i0, i2 < i * i0, (i - 1) * (i0 - 1) < i * i0 ⊦ j = 1, i = i0

Rule argument

Additional information

Used simplifier rules: transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs