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Proof step 21 from proof RSA-decrypt-ij-vars (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 23:
gcd(i2, (i - 1) * (i0 - 1)) = 1, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, (i - 1) * (i0 - 1) | abs(i2 * i3 - 1), i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 < j, 0 < i0, 0 < i3, 0 ≤ i2 ⊦ j = 0, i3 = 0, i = i0, j = j ^ (i2 * i3) |%| (i * i0)

Rule argument

spec: inst: name: congmod-def seq: ⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0) subst: [j, i0, i] → [(i - 1) * (i0 - 1), 1, i2 * i3] flags: rewrite, current

Additional information

Used terms: (i - 1) * (i0 - 1), 1, i2 * i3