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Proof step 13 from proof RSA-decrypt-ij-vars (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 14:
gcd(i2, (i - 1) * (i0 - 1)) = 1, 0 < i0, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, ≡mod(i2 * i3, 1, (i - 1) * (i0 - 1)), i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 ≤ j, 0 < i3 ⊦ j = 0, i3 = 0, i = i0, j = (j ^ i2 |%| (i * i0)) ^ i3 |%| (i * i0)

Rule argument

fma: j = 0

Additional information

Used simplifier rules: mod-zero-03: ⊦ 0 < j → 0 |%| j = 0;%zero-01: ⊦ 0 < j → 0 ^ j = 0; from specification int-pot Used formulas: j = 0