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Proof step 1 from proof even-add (conclusion)

⊦ even(m + n) ↔ even(m) ∧ even(n) ∨ odd(m) ∧ odd(n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ (∃ m0. 2 * m0 = m + n) ↔ (∃ m0. 2 * m0 = m) ∧ (∃ m0. 2 * m0 = n) ∨ ¬(∃ m0. 2 * m0 = m) ∧ ¬(∃ m0. 2 * m0 = n)

Rule argument

Additional information

Used simplifier rules: Even: ⊦ even(n) ↔ (∃ m. m + m = n);%Odd: ⊦ odd(n) ↔ ¬ even(n);%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%two-02: ⊦ m + m = 2 * m; from specification nat-mult