<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="incproj.html#V10" title="INCPROJ:attr.10">Pappian</a> <a onclick="hs(this)" href="javascript:()">INCPROJ:def 14 : <br/></a><span> for <font color="Olive" title="b1">IT</font> being    <a href="incsp_1.html#L1" title="INCSP_1:struct.1">IncProjStr</a>  holds <br/> ( <font color="Olive" title="b1">IT</font> is  <a href="incproj.html#V10" title="INCPROJ:attr.10">Pappian</a>  iff  for <font color="Olive" title="b2">o</font>, <font color="Olive" title="b3">a1</font>, <font color="Olive" title="b4">a2</font>, <font color="Olive" title="b5">a3</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">b2</font>, <font color="Olive" title="b8">b3</font>, <font color="Olive" title="b9">c1</font>, <font color="Olive" title="b10">c2</font>, <font color="Olive" title="b11">c3</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Olive" title="b1">IT</font><br/>  for <font color="Olive" title="b12">A1</font>, <font color="Olive" title="b13">A2</font>, <font color="Olive" title="b14">A3</font>, <font color="Olive" title="b15">B1</font>, <font color="Olive" title="b16">B2</font>, <font color="Olive" title="b17">B3</font>, <font color="Olive" title="b18">C1</font>, <font color="Olive" title="b19">C2</font>, <font color="Olive" title="b20">C3</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Olive" title="b1">IT</font>  st <font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">a1</font>,<font color="Olive" title="b4">a2</font>,<font color="Olive" title="b5">a3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_distinct</a>  &amp; <font color="Olive" title="b2">o</font>,<font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">b2</font>,<font color="Olive" title="b8">b3</font> <a href="zfmisc_1.html#R2" title="ZFMISC_1:pred.2">are_mutually_distinct</a>  &amp; <font color="Olive" title="b14">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b17">B3</font> &amp; <font color="Olive" title="b2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b14">A3</font> &amp; <font color="Olive" title="b2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b17">B3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b4">a2</font>,<font color="Olive" title="b8">b3</font>,<font color="Olive" title="b9">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b12">A1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">a3</font>,<font color="Olive" title="b6">b1</font>,<font color="Olive" title="b10">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b15">B1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b3">a1</font>,<font color="Olive" title="b7">b2</font>,<font color="Olive" title="b11">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b18">C1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b3">a1</font>,<font color="Olive" title="b8">b3</font>,<font color="Olive" title="b10">c2</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b13">A2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b5">a3</font>,<font color="Olive" title="b7">b2</font>,<font color="Olive" title="b9">c1</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b16">B2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b4">a2</font>,<font color="Olive" title="b6">b1</font>,<font color="Olive" title="b11">c3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b19">C2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">b2</font>,<font color="Olive" title="b8">b3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b14">A3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b3">a1</font>,<font color="Olive" title="b4">a2</font>,<font color="Olive" title="b5">a3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b17">B3</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Olive" title="b9">c1</font>,<font color="Olive" title="b10">c2</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Olive" title="b20">C3</font> holds <br/><font color="Olive" title="b11">c3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b20">C3</font> );<br/></span></div>
