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Proof step 35 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 ⊦ i1 < 0, ((i - 1) * (i0 - 1)) * 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 36:
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 ⊦ j = 0, i3 = 0, i = i0, j = j ^ (i2 * i3) |%| (i * i0)

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-ls-02: ⊦ 0 ≤ i → (i * j < 0 ↔ ¬ ¬(j < 0 ∧ i ≠ 0)); from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs