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Proof step 33 from proof two-even (previous step)

(j1 + j2) % 2 = 0, 2 * i = j1 ^2 + j2 ^2 ⊦ (j1 - j2) % 2 = 0, i = ((j1 - j2) / 2)^2 + ((j1 + j2) / 2)^2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 35:
2 ≠ 0, ∃ j0. j1 + j2 = j0 * 2, 2 * i = j1 ^2 + j2 ^2 ⊦ (j1 - j2) % 2 = 0, i = ((j1 - j2) / 2)^2 + ((j1 + j2) / 2)^2

Rule argument

spec: int-div inst: name: modex seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [2, j1 + j2] flags: rewrite

Additional information

Used terms: 2, j1 + j2