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Proof step 20 from proof four-square-mod-zero (previous step)

i2 ^2 + i1 ^2 + (j0 * i)^2 + (j0 * i3)^2 = j0 * j, prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j, j0 | i1, j0 | i2 ⊦ j0 = 1, j = 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ i | j ↔ (∃ i0. i * i0 = j)
Proof step 22:
i2 ^2 + i1 ^2 + (j0 * i)^2 + (j0 * i3)^2 = j0 * j, prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j, j0 | i1, ∃ i0. j0 * i0 = i2 ⊦ j0 = 1, j = 2

Rule argument

spec: int-gcd inst: name: divides seq: ⊦ i | j ↔ (∃ i0. i * i0 = j) subst: [j, i] → [i2, j0] flags: rewrite

Additional information

Used terms: i2, j0