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Proof step 13 from proof prime-divides-pot (previous step)

i * j = i0 ^ i1 * i0, prime(i), 0 ≤ i1, i | i0 ^ i1 ⊦ gcd(i, i0 ^ i1) = 1, i | i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-fac inst: name: prime-divides-pot-01 seq: ⊦ prime(i) ∧ 0 < j → (i | i0 ^ j ↔ i | i0) subst: [j, i0, i] → [i1, i0, i] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%Pot-zero: ⊦ j ^ 0 = 1; from specification int-pot%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%gcd-one-01: ⊦ gcd(i, 1) = 1; from specification int-gcd Used terms: i1, i0, i