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Proof step 55 from proof RSA-decrypt-ij-vars (previous step)

prime(i0) ∧ i0 - 1 | ((i - 1) * (i0 - 1)) * i1 ∧ 2 < i0 ∧ 0 ≤ j ∧ 0 ≤ ((i - 1) * (i0 - 1)) * i1, gcd(i2, (i - 1) * (i0 - 1)) = 1, i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 < i0, 0 < i3, 0 ≤ i2, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, 0 < i1, 0 ≤ (i - 1) * (i0 - 1), ~1 ≤ ((i - 1) * (i0 - 1)) * i1, 0 < j, 0 ≤ j ^ (((i - 1) * (i0 - 1)) * i1) ⊦ i0 = 0, i1 = 0, j = 0, i3 = 0, i = i0, j = (j ^ (((i - 1) * (i0 - 1)) * i1) * j) |%| (i * i0), j |%| i0 = j |%| i0 ∧ (j ^ (((i - 1) * (i0 - 1)) * i1) * j) |%| i = j |%| i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
gcd(i2, (i - 1) * (i0 - 1)) = 1, i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 < i0, 0 < i3, 0 ≤ i2, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, 0 < i1, 0 ≤ (i - 1) * (i0 - 1), ~1 ≤ ((i - 1) * (i0 - 1)) * i1, 0 ≤ j ^ (((i - 1) * (i0 - 1)) * i1), 0 < j ⊦ i0 = 0, i1 = 0, j = 0, i3 = 0, i = i0, j = (j ^ (((i - 1) * (i0 - 1)) * i1) * j) |%| (i * i0), (j ^ (((i - 1) * (i0 - 1)) * i1) * j) |%| i = j |%| i

Rule argument

Additional information

Used simplifier rules: zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%div-mult: ⊦ i | i * j; from specification int-gcd