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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E8">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: PROJRED1:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">IPP</font> being   <a href="incproj.html#V9" title="INCPROJ:attr.9">Desarguesian</a>  <a href="incproj.html#NM2" title="INCPROJ:NM.2">IncProjSp</a><br/>  for <font color="Olive" title="b2">o</font>, <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">a1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">a2</font>, <font color="Olive" title="b7">b3</font>, <font color="Olive" title="b8">a3</font>, <font color="Olive" title="b9">r</font>, <font color="Olive" title="b10">s</font>, <font color="Olive" title="b11">t</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Olive" title="b1">IPP</font><br/>  for <font color="Olive" title="b12">C1</font>, <font color="Olive" title="b13">C2</font>, <font color="Olive" title="b14">C3</font>, <font color="Olive" title="b15">A1</font>, <font color="Olive" title="b16">A2</font>, <font color="Olive" title="b17">A3</font>, <font color="Olive" title="b18">B1</font>, <font color="Olive" title="b19">B2</font>, <font color="Olive" title="b20">B3</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Olive" title="b1">IPP</font>  st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b2">o</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">a1</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">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="b2">o</font>,<font color="Olive" title="b6">a2</font>,<font color="Olive" title="b5">b2</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">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="b2">o</font>,<font color="Olive" title="b8">a3</font>,<font color="Olive" title="b7">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">C3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b8">a3</font>,<font color="Olive" title="b6">a2</font>,<font color="Olive" title="b11">t</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">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="b8">a3</font>,<font color="Olive" title="b9">r</font>,<font color="Olive" title="b4">a1</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">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="b6">a2</font>,<font color="Olive" title="b10">s</font>,<font color="Olive" title="b4">a1</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">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="b11">t</font>,<font color="Olive" title="b5">b2</font>,<font color="Olive" title="b7">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="b18">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">b1</font>,<font color="Olive" title="b9">r</font>,<font color="Olive" title="b7">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="b19">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="b3">b1</font>,<font color="Olive" title="b10">s</font>,<font color="Olive" title="b5">b2</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="b20">B3</font> &amp; <font color="Olive" title="b12">C1</font>,<font color="Olive" title="b13">C2</font>,<font color="Olive" title="b14">C3</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_distinct</a>  &amp; <font color="Olive" title="b2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b8">a3</font> &amp; <font color="Olive" title="b2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b1</font> &amp; <font color="Olive" title="b2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">b2</font> &amp; <font color="Olive" title="b6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">b2</font> holds <br/> ex <font color="Olive" title="b21">O</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Olive" title="b1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b9">r</font>,<font color="Olive" title="b10">s</font>,<font color="Olive" title="b11">t</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="b21">O</font></div></div>
