[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 1 from proof otwo-03 (conclusion) (back to tree)

⊦ ¬ odd(2)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information

Proof step 2 from proof otwo-03 (previous step) (back to tree)

odd(2) ⊦

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel>, name:oex, seq: ⊦ odd(n) ↔ (∃ m. n = m + m + 1), subst:[n] → [2]

Additional information

Used simplifier rules: oex: ⊦ odd(n) ↔ (∃ m. n = m + m + 1); ⊦ m + m = 2 * m; (s) n0 < n ⊦ (* n) = m0 + (* n0) ↔ n - n0 = m0; (s) ⊦ 2 * m ≠ 1; (s) mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult mult-c: ⊦ m * n = n * m; from specification nat-mult a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic c: ⊦ m + n = n + m; from specification nat-basic Used terms: 2

Proof step 3 from proof otwo-03 (previous step) (back to tree)

⊦ odd(n) ↔ (∃ m. n = m + m + 1)

Lemma oex

Proof Tree for otwo-03 (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