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Proof step 4 from proof RSA-decrypt-ij-vars (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 6:
gcd(i2, (i - 1) * (i0 - 1)) = 1, i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 0 ≤ j, 0 < i0, 1 < i * i0, 0 < i2, 0 < i, j < i * i0, (i - 1) * (i0 - 1) | abs(0 - 1) ⊦ i = i0, j = 1

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, 0] flags: rewrite, current

Additional information

Used terms: (i - 1) * (i0 - 1), 1, 0