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Proof step 44 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 - 1) * (i0 - 1)) * i1 + 1) |%| (i * i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
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), ~1 ≤ ((i - 1) * (i0 - 1)) * i1 ⊦ i1 = 0, j = 0, i3 = 0, i = i0, j = j ^ (((i - 1) * (i0 - 1)) * i1 + 1) |%| (i * i0), ≡mod(j ^ (((i - 1) * (i0 - 1)) * i1 + 1), j, i0) ∧ ≡mod(j ^ (((i - 1) * (i0 - 1)) * i1 + 1), j, i)

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%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