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Proof step 9 from proof coprime-pot (previous step)

gcd(i, j) = 1, i * i0 = j ^ i1 * j, 0 < i, 1 < i, 0 ≤ i1, ∀ j1, i, i0, j. i→n(j1) < i→n(i1 + 1) → i * i0 = j ^ j1 ∧ gcd(i, j) = 1 ∧ 0 < i ∧ 1 < i ∧ 0 < j1 → j = 0 ⊦ j = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 10:
⊦ gcd(i, j) = 1 ∧ i * i0 = j * j0 → i | j0
Proof step 11:
gcd(i, j) = 1 ∧ i * i0 = j * j ^ i1 → i | j ^ i1, gcd(i, j) = 1, i * i0 = j ^ i1 * j, 0 < i, 1 < i, 0 ≤ i1, ∀ j1, i, i0, j. i→n(j1) < i→n(i1 + 1) → i * i0 = j ^ j1 ∧ gcd(i, j) = 1 ∧ 0 < i ∧ 1 < i ∧ 0 < j1 → j = 0 ⊦ j = 0

Rule argument

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

Additional information

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