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Proof step 7 from proof fermat-for-rsa (previous step)

0 ≤ i, 0 < j, 2 < j, prime(j), 0 ≤ i1 * (j - 1) ⊦ (i ^ (i1 * (j - 1)) * i) |%| j = i |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: pot-pot-02 seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j * j0) = (i ^ j) ^ j0 subst: [j0, j, i] → [j - 1, i1, i] flags: rewrite

Additional information

Used simplifier rules: sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-ge-01: ⊦ i < 0 → (0 ≤ i * j ↔ j ≤ 0); from specification int-mult%sub-le: ⊦ i - j ≤ i0 ↔ i ≤ j + i0; from specification int-abs%bet: ⊦ 0 < i → (i ≤ 1 ↔ i = 1); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%sub-eq-01: ⊦ i = j → i - j = 0; from specification int-abs%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%one: ⊦ 1 * i = i; from specification int-mult Used terms: j - 1, i1, i