Diff for "CutFreeProof"

Differences between revisions 1 and 2

Essentially, a cut-free proof is a proof that does not use a lemma. That is

Given $(A\wedge B\wedge ...)\vdash C$, and $C\vdash (D\vee E\vee ...)$ we can cut $C$ from the proof of $(D\vee E\vee ...)$ when $(A\wedge B\wedge ...) $ is true. Here we consider $C$ to be the lemma in the proof of $(D\vee E\vee ...)$.

The ability to eliminate $C$ in the above is called the cut-elimination theorem.

For more information set [http://en.wikipedia.org/wiki/Cut-elimination Cut-elimination]

-  ⇤ ← Revision 1 as of 2006-08-22 16:28:38 → 
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+   ← Revision 2 as of 2007-04-18 16:12:39 → ⇥
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-Given $(A\wedge B\wedge ...)\vdash C$, and $C\vdash (D\vee E\vee ...)$ we can cut $C$ from the proof of $(D\vee E\vee ...)$ when $(A\wedge B\wedge ...) $ is true. Here we consider $C$ to be the lemma in the prove of $(D\vee E\vee ...)$.
+Given $(A\wedge B\wedge ...)\vdash C$, and $C\vdash (D\vee E\vee ...)$ we can cut $C$ from the proof of $(D\vee E\vee ...)$ when $(A\wedge B\wedge ...) $ is true. Here we consider $C$ to be the lemma in the proof of $(D\vee E\vee ...)$.