Subject: Re: [lojban] Lemma and conjecture

From: "Jorge Llambias" <[email-masked]>
Date: Sun, 22 Dec 2002 16:26:45 +0000

la pier cusku di'e

>On Saturday 21 December 2002 22:42, Jorge Llambias wrote:
> > la pier cusku di'e
> > >Is it possible for S1 to be a tosmabru of S3, while S4 is a
> > >slinku'i of S2?
> >
> > S1 was the lujvo beginning with CVVRC, so it can't be a
> > tosmabru of anything. S2 was a corresponding fu'ivla
> > beginning with CVVKC, which can't be a slinku'i.
>
>You have completely missed my point. S1 and S2 begin CVCC, and S3 and S4 
>are
>the same words minus the initial CV. If S1, S2, and S3 are, ignoring the
>tosmabru test, lujvo, while S4 is not, then S2 is valid but S1 is not.

How could S4 not be lujvo if S3 is? Two words beginning with CC
are either both lujvo-form or neither is. Such words cannot be
affected by r-hyphens.

The only words that use r-hyphen are of the form CVVRC...

Therefore, r-hyphen words are never tosmabru, smabru, slinku'i
or paslinku'i. r-hyphen are necessarily CVVC/C... and tosmabru
or paslinku'i could only be CVVCC...

The conjecture says that for a given form, either every exemplar
of the form is a valid brivla, or every exemplar is invalid.

The only forms that could break the conjecture are forms involving
r-hyphens, because every other rule for validity is purely in terms
of forms and does not involve exemplars.

Since forms involving r-hyphens can't participate in tosmabru
or slinku'i failures, all we need to examine are CVVRC... lujvo
forms and their CVVKC... counterparts. It is easy to show that the
conjecture is valid for these forms, and therefore it is valid
for all forms.

mu'o mi'e xorxes

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