From phma@webjockey.net Thu Dec 19 03:53:51 2002 Return-Path: X-Sender: lojban-out@lojban.org X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_2_3_0); 19 Dec 2002 11:53:50 -0000 Received: (qmail 78429 invoked from network); 19 Dec 2002 11:53:50 -0000 Received: from unknown (66.218.66.216) by m3.grp.scd.yahoo.com with QMQP; 19 Dec 2002 11:53:50 -0000 Received: from unknown (HELO digitalkingdom.org) (204.152.186.175) by mta1.grp.scd.yahoo.com with SMTP; 19 Dec 2002 11:53:50 -0000 Received: from lojban-out by digitalkingdom.org with local (Exim 4.05) id 18OzFO-0004hk-00 for lojban@yahoogroups.com; Thu, 19 Dec 2002 03:53:50 -0800 Received: from digitalkingdom.org ([204.152.186.175] helo=chain) by digitalkingdom.org with esmtp (Exim 4.05) id 18OzFF-0004hR-00; Thu, 19 Dec 2002 03:53:41 -0800 Received: with ECARTIS (v1.0.0; list lojban-list); Thu, 19 Dec 2002 03:53:40 -0800 (PST) Received: from 208-150-110-21-adsl.precisionet.net ([208.150.110.21] helo=neofelis.ixazon.lan) by digitalkingdom.org with esmtp (Exim 4.05) id 18OzF9-0004hC-00 for lojban-list@lojban.org; Thu, 19 Dec 2002 03:53:35 -0800 Received: by neofelis.ixazon.lan (Postfix, from userid 500) id D4B513C478; Thu, 19 Dec 2002 06:52:54 -0500 (EST) Content-Type: text/plain; charset="iso-8859-1" To: lojban-list@lojban.org Subject: [lojban] Lemma and conjecture Date: Thu, 19 Dec 2002 06:52:50 -0500 X-Mailer: KMail [version 1.2] X-Spamtrap: fesmri@ixazon.dynip.com MIME-Version: 1.0 Message-Id: <02121906525001.17068@neofelis> X-archive-position: 3594 X-ecartis-version: Ecartis v1.0.0 Sender: lojban-list-bounce@lojban.org Errors-to: lojban-list-bounce@lojban.org X-original-sender: phma@webjockey.net Precedence: bulk X-list: lojban-list From: Pierre Abbat Reply-To: phma@webjockey.net X-Yahoo-Group-Post: member; u=92712300 Lemma: All brivla contain a consonant followed two letters later, ignoring apostrophes, by a vowel. If a brivla contains 'y', it contains such a consonant after the 'y'. Proof: If a brivla contains no 'y', it contains two adjacent consonants in the first five letters, ignoring apostrophes. Find the first vowel after this consonant cluster. Two letters before it is a consonant. If a brivla contains 'y', there is at least one rafsi after 'y'. Consider the last rafsi. Either it is a CVV or CCV rafsi of a gismu, in which case the first and last letters of the rafsi are the consonant and the vowel two letters later, or it is the final long rafsi of a gismu or fu'ivla, in which case, being identical to the selrafsi, it has such a consonant by the first part. Conjecture: If two lerpoi R and S which both lack 'y' are such that for all i R[i:i+1] is a valid initial consonant pair, valid consonant pair, valid lujvo diphthong, fa'u valid fu'ivla diphthong iff S[i:i+1], and R[i] is a vowel, consonant, fa'u y'ybu iff S[i] is, then R is a valid brivla iff S is, regardless of whether for some i R[i] is 'n', 'r', or 'l' and S[i] isn't. I am trying to prove the conjecture, but having trouble with words like {paske'usazri}, where removing the first rafsi results in {ke'usazri}, which falls apart, while {ke'ursazri}, which is a lujvo, when {pas-} is added becomes {paske'ursazri}, which falls apart. phma