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Proof step 27 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 ⊦ j = 0, i3 = 0, i = i0, j = j ^ (i2 * i3) |%| (i * i0)

User applied rule cut formula

And obtained the following new goals

Proof step 28:
((i - 1) * (i0 - 1)) * i1 < 0, 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 ⊦ j = 0, i3 = 0, i = i0, j = j ^ (i2 * i3) |%| (i * i0)
Proof step 31:
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 ⊦ ((i - 1) * (i0 - 1)) * i1 < 0, j = 0, i3 = 0, i = i0, j = j ^ (i2 * i3) |%| (i * i0)

Rule argument

fma: ((i - 1) * (i0 - 1)) * i1 < 0

Additional information

Used formulas: ((i - 1) * (i0 - 1)) * i1 < 0