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Proof step 58 from proof RSA-decrypt-ij-vars (previous step)

≡mod(j ^ (((i - 1) * (i0 - 1)) * i1 + 1), j, i) ∧ ≡mod(j ^ (((i - 1) * (i0 - 1)) * i1 + 1), j, i0) ∧ prime(i) ∧ prime(i0) ∧ 0 < j ∧ i ≠ i0 ∧ 0 ≤ ((i - 1) * (i0 - 1)) * i1 + 1, 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, 0 < i1, 0 ≤ (i - 1) * (i0 - 1) ⊦ i1 = 0, j = 0, i3 = 0, i = i0, j = j |%| (i * i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 59:
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, 0 < i1, 0 ≤ (i - 1) * (i0 - 1), ≡mod(j ^ (((i - 1) * (i0 - 1)) * i1 + 1), j, i), ≡mod(j ^ (((i - 1) * (i0 - 1)) * i1 + 1), j, i0), ~1 ≤ ((i - 1) * (i0 - 1)) * i1 ⊦ i1 = 0, j = 0, i3 = 0, j = j |%| (i * i0), i = i0

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs