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Proof step 7 from proof prime-divides-pot (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ gcd(i, j) = 1 ∧ i * i0 = j * j0 → i | j0
Proof step 9:
¬(gcd(i, i0 ^ i1) = 1 ∧ i * j = i0 ^ i1 * i0), i * j = i0 ^ i1 * i0, prime(i), 0 ≤ i1 ⊦ i | i0

Rule argument

spec: int-gcd inst: name: coprime-divides seq: ⊦ gcd(i, j) = 1 ∧ i * i0 = j * j0 → i | j0 subst: [i, j, i0, j0] → [i, i0 ^ i1, j, i0] flags: rewrite

Additional information

Used terms: i, i0 ^ i1, j, i0