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Proof step 1 from proof div2-even (conclusion) (back to tree)

⊦ n / 2 + n / 2 = n ↔ even(n)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information

Proof step 2 from proof div2-even (previous step) (back to tree)

¬(n / 2 + n / 2 = n ↔ even(n)) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: Even: ⊦ even(n) ↔ (∃ m. m + m = n); 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) 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)

Proof step 3 from proof div2-even (previous step) (back to tree)

2 * n / 2 = n ⊦ ∃ m. 2 * m = n

User applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: n / 2 abort: F discard: T computed: T

Additional information

Used terms: n / 2

Proof Tree for div2-even (View conclusion)

The following image shows the proof tree of sequent calculus. The proved goal is at the bottom. You can click on the nodes to view additional rules. See here for details on colors in a proof tree.

the proof tree