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Proof step 40 from proof RSA-decrypt-ij-vars (previous step)

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, 0 ≤ i1, ¬ (i - 1) * (i0 - 1) < 0 ∨ i1 = 0 ⊦ i1 = 0, 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 41:
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, 0 < i1, 0 ≤ (i - 1) * (i0 - 1) ⊦ i1 = 0, j = 0, i3 = 0, i = i0, j = j ^ (i2 * i3) |%| (i * i0)

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs