Talk:Non-Equivalence of Proposition and Negation/Formulation 1

This is not proof by contradiction. Proof by contradiction demonstrates the falsity of a statement by showing that it implies a contradiction. This sequent merely expresses the trivium that a statement that implies the negation of itself is itself a contradiction, and so if anything is an instance of Principle of Non-Contradiction. --prime mover (talk) 22:56, 3 May 2013 (UTC)


 * Please read it more carefully. That is not what it says at all. I never called it PBC, I called it a corollary of that. If you like a different name, go ahead and change it. --Dfeuer (talk) 23:04, 3 May 2013 (UTC)


 * The only other form I was going to put up was $\lnot (p \iff \lnot p)$, which I think gives a very clear picture of what this theorem is saying. --Dfeuer (talk) 23:06, 3 May 2013 (UTC)


 * What I'm saying is please don't put these results as corollaries of others. They don't belong there.


 * I understand what you're saying and it's not so special, it's just stuff which can be proved by application of proof rules.


 * Not special. Just useful. --Dfeuer (talk) 23:46, 3 May 2013 (UTC)

name
The original reason for having a "sequent form" of the existing proofs which have a "sequent form" version was to distinguish them from the "word" form for which those "sequent form" versions existed. The concept was introduced for those rules which are found somewhere in the "basic proof rules" tha may be found in whatever analysis in the literature. Hence not appropriate for any random statement. --prime mover (talk) 08:01, 4 May 2013 (UTC)

Rearrangement
Yes, you are right that putting the premises together made it better. Thanks. --Dfeuer (talk) 12:52, 4 May 2013 (UTC)