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Proof step 3 from proof even-add (previous step)

(i + j) % 2 = 0 ⊦ i % 2 = 0 ∧ j % 2 = 0, i % 2 ≠ 0 ∧ j % 2 ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 5:
2 ≠ 0, ∃ j0. i + j = j0 * 2 ⊦ i % 2 = 0 ∧ j % 2 = 0, i % 2 ≠ 0 ∧ j % 2 ≠ 0

Rule argument

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

Additional information

Used terms: 2, i + j