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Proof step 1 from proof div2-even (conclusion)

⊦ n / 2 + n / 2 = n ↔ even(n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
2 * n / 2 = n ⊦ ∃ m. 2 * m = n

Rule argument

Additional information

Used simplifier rules: Even: ⊦ even(n) ↔ (∃ m. m + m = n);%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ (2 * m) / 2 = m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + m = 2 * m; (s)