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Proof step 7 from proof even-add (previous step)

⊦ i % 2 = 0 ∧ j % 2 = 0 ∨ i % 2 ≠ 0 ∧ j % 2 ≠ 0 ↔ i % 2 = 0 ∧ even(j) ∨ odd(i) ∧ odd(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ even(i) ↔ i % 2 = 0
Proof step 9:
⊦ i % 2 = 0 ∧ j % 2 = 0 ∨ i % 2 ≠ 0 ∧ j % 2 ≠ 0 ↔ i % 2 = 0 ∧ j % 2 = 0 ∨ odd(i) ∧ odd(j)

Rule argument

spec: inst: name: even-def-mod seq: ⊦ even(i) ↔ i % 2 = 0 subst: [i] → [j] flags: rewrite, current

Additional information

Used terms: j