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Proof step 50 from proof RSA-decrypt-ij-vars (previous step)

0 < i, gcd(i2, (i - 1) * (i0 - 1)) = 1, i2 < i * i0, 2 < i0, 2 < i, prime(i0), prime(i), 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, 0 < j, 0 ≤ j ^ (((i - 1) * (i0 - 1)) * i1 + 1) ⊦ i1 = 0, j = 0, i3 = 0, i = i0, j = j ^ (((i - 1) * (i0 - 1)) * i1 + 1) |%| (i * i0), i0 = 0, j ^ (((i - 1) * (i0 - 1)) * i1 + 1) |%| i0 = j |%| i0 ∧ j ^ (((i - 1) * (i0 - 1)) * i1 + 1) |%| i = j |%| i

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [((i - 1) * (i0 - 1)) * i1 + 1, j] flags: rewrite

Additional information

Used simplifier rules: numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: ((i - 1) * (i0 - 1)) * i1 + 1, j