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Proof step 11 from proof root-is-irrational (previous step)

gcd(i, j0) = 1, i * i = j * j0 * j0, 0 < j0 ⊦ j0 = 0, ∃ i. j = i * i

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 12:
j ≠ 0 ∨ j0 ≠ 0, j * j = i * j0 * j0 ⊦ ∃ i0. i = i0 * i0
Proof step 13:
∃ i0. j = i0 * i0, gcd(i, j0) = 1, i * i = j * j0 * j0, 0 < j0 ⊦ j0 = 0, ∃ i. j = i * i

Rule argument

seq: j ≠ 0 ∨ j0 ≠ 0, j * j = i * j0 * j0 ⊦ ∃ i0. i = i0 * i0 subst: [j, j0, i] → [i, j0, j] rotate: F spec: int-gcd inst: name: square-neq-any

Additional information

Used terms: i, j0, j