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Proof step 41 from proof two-even (previous step)

2 * i = j1 ^2 + j2 ^2 ⊦ (j1 + j2) % 2 = 0, (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 42:
⊦ i % 2 ≠ 0 ↔ (∃ i0. i = 2 * i0 + 1)
Proof step 43:
2 * i = j1 ^2 + j2 ^2 ⊦ ∀ i0. j1 + j2 ≠ 2 * i0 + 1, (j1 - j2) % 2 = 0, i = ((j1 - j2) / 2)^2 + ((j1 + j2) / 2)^2

Rule argument

spec: int-div inst: name: even-not-ex seq: ⊦ i % 2 ≠ 0 ↔ (∃ i0. i = 2 * i0 + 1) subst: [i] → [j1 + j2] flags: rewrite

Additional information

Used terms: j1 + j2