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<b>let </b><font color="Maroon" title="c1">IPP</font> be  <a href="incproj.html#V9" title="INCPROJ:attr.9">Desarguesian</a> <a href="incproj.html#NM2" title="INCPROJ:NM.2">IncProjSp</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">b1</font>, <font color="Olive" title="b3">a1</font>, <font color="Olive" title="b4">b2</font>, <font color="Olive" title="b5">a2</font>, <font color="Olive" title="b6">b3</font>, <font color="Olive" title="b7">a3</font>, <font color="Olive" title="b8">r</font>, <font color="Olive" title="b9">s</font>, <font color="Olive" title="b10">t</font> being  <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><br/> for <font color="Olive" title="b11">C1</font>, <font color="Olive" title="b12">C2</font>, <font color="Olive" title="b13">C3</font>, <font color="Olive" title="b14">A1</font>, <font color="Olive" title="b15">A2</font>, <font color="Olive" title="b16">A3</font>, <font color="Olive" title="b17">B1</font>, <font color="Olive" title="b18">B2</font>, <font color="Olive" title="b19">B3</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">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="b1">o</font>,<font color="Olive" title="b2">b1</font>,<font color="Olive" title="b3">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="b11">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="b1">o</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b4">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="b12">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="b1">o</font>,<font color="Olive" title="b7">a3</font>,<font color="Olive" title="b6">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="b13">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="b7">a3</font>,<font color="Olive" title="b5">a2</font>,<font color="Olive" title="b10">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="b14">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="b7">a3</font>,<font color="Olive" title="b8">r</font>,<font color="Olive" title="b3">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="b15">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">a2</font>,<font color="Olive" title="b9">s</font>,<font color="Olive" title="b3">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">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="b10">t</font>,<font color="Olive" title="b4">b2</font>,<font color="Olive" title="b6">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="b17">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="b2">b1</font>,<font color="Olive" title="b8">r</font>,<font color="Olive" title="b6">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">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="b2">b1</font>,<font color="Olive" title="b9">s</font>,<font color="Olive" title="b4">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="b19">B3</font> &amp; <font color="Olive" title="b11">C1</font>,<font color="Olive" title="b12">C2</font>,<font color="Olive" title="b13">C3</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a>  &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">a3</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b1</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b2</font> &amp; <font color="Olive" title="b5">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b2</font> holds <br/> ex <font color="Olive" title="b20">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">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="b8">r</font>,<font color="Olive" title="b9">s</font>,<font color="Olive" title="b10">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="b20">O</font></span><br/><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">b1</font>, <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">b2</font>, <font color="Maroon" title="c6">a2</font>, <font color="Maroon" title="c7">b3</font>, <font color="Maroon" title="c8">a3</font>, <font color="Maroon" title="c9">r</font>, <font color="Maroon" title="c10">s</font>, <font color="Maroon" title="c11">t</font> be   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C1</font>, <font color="Olive" title="b2">C2</font>, <font color="Olive" title="b3">C3</font>, <font color="Olive" title="b4">A1</font>, <font color="Olive" title="b5">A2</font>, <font color="Olive" title="b6">A3</font>, <font color="Olive" title="b7">B1</font>, <font color="Olive" title="b8">B2</font>, <font color="Olive" title="b9">B3</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>  st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">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="b1">C1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c5">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="b2">C2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c7">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="b3">C3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c11">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="b4">A1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c4">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="b5">A2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c4">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="b6">A3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">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="b7">B1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c7">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="b8">B2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c5">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="b9">B3</font> &amp; <font color="Olive" title="b1">C1</font>,<font color="Olive" title="b2">C2</font>,<font color="Olive" title="b3">C3</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> holds <br/> ex <font color="Olive" title="b10">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b10">O</font></span><br/><b>let </b><font color="Maroon" title="c12">C1</font>, <font color="Maroon" title="c13">C2</font>, <font color="Maroon" title="c14">C3</font>, <font color="Maroon" title="c15">A1</font>, <font color="Maroon" title="c16">A2</font>, <font color="Maroon" title="c17">A3</font>, <font color="Maroon" title="c18">B1</font>, <font color="Maroon" title="c19">B2</font>, <font color="Maroon" title="c20">B3</font> be   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">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="Maroon" title="c12">C1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c5">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="Maroon" title="c13">C2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c7">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="Maroon" title="c14">C3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c11">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="Maroon" title="c15">A1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c4">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="Maroon" title="c16">A2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c4">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="Maroon" title="c17">A3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">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="Maroon" title="c18">B1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c7">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="Maroon" title="c19">B2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c5">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="Maroon" title="c20">B3</font> &amp; <font color="Maroon" title="c12">C1</font>,<font color="Maroon" title="c13">C2</font>,<font color="Maroon" title="c14">C3</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> implies  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font> )</span><br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E9">A1</font></i>: 
( <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c4">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="Maroon" title="c12">C1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c5">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="Maroon" title="c13">C2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c7">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="Maroon" title="c14">C3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c11">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="Maroon" title="c15">A1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c8">a3</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c4">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="Maroon" title="c16">A2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c6">a2</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c4">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="Maroon" title="c17">A3</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c5">b2</font>,<font color="Maroon" title="c7">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="Maroon" title="c18">B1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c7">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="Maroon" title="c19">B2</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c3">b1</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c5">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="Maroon" title="c20">B3</font> &amp; <font color="Maroon" title="c12">C1</font>,<font color="Maroon" title="c13">C2</font>,<font color="Maroon" title="c14">C3</font> <a href="zfmisc_1.html#R1" title="ZFMISC_1:pred.1">are_mutually_different</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">a3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/>

<a NAME="E2:12"/><b>then </b><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> )
 
<b>by </b><i><a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>;<br/>
<a NAME="E3:12"/><i><font color="Green" title="E11">A3</font></i>: 
( <font color="Maroon" title="c8">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c9">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>;<br/>
<a NAME="E4:12"/><i><font color="Green" title="E12">A4</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> &amp; <font color="Maroon" title="c9">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">B3</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">B3</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">B3</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>;<br/>
<a NAME="E5:12"/><i><font color="Green" title="E13">A5</font></i>: 
( <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c13">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c14">C3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">C1</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/>
<a NAME="E6:12"/><b>then </b><i><font color="Green" title="E14">A6</font></i>: 
( <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">B3</font> &amp; <font color="Maroon" title="c13">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">B3</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/>
<div><i><font color="Green" title="E15">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1"/><i><font color="Green" title="E16">A8</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><i><font color="Green" title="E17">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_1"/><i><font color="Green" title="E18">A10</font></i>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><i><font color="Green" title="E19">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_1_1"/><i><font color="Green" title="E20">A12</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><a NAME="E2:12_1_1_1"/><i><font color="Green" title="E21">A13</font></i>: 
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_1_1"><i><font color="Green" title="E18">A10</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_1_1_1"/>
<font color="Maroon" title="c19">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_1"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_1_1_1"/><b>then </b><i><font color="Green" title="E22">A14</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="#E2:12_1_1_1"><i><font color="Green" title="E21">A13</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_1_1_1"/><i><font color="Green" title="E23">A15</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_1_1_1"><i><font color="Green" title="E20">A12</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_1_1_1"/>
<font color="Maroon" title="c18">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">C2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_1"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_1_1_1"/><b>then </b><i><font color="Green" title="E24">A16</font></i>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="#E4:12_1_1_1"><i><font color="Green" title="E22">A14</font></i></a>, <a class="txt" href="#E5:12_1_1_1"><i><font color="Green" title="E23">A15</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon" title="c21">O</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E9:12_1_1_1"/><i><font color="Green" title="E25">A17</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font></span><br/><b>thus </b><a NAME="E10:12_1_1_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font>
 <b>by </b><i><a class="txt" href="#E7:12_1_1_1"><i><font color="Green" title="E24">A16</font></i></a>, <a class="txt" href="#E9:12_1_1_1"><i><font color="Green" title="E25">A17</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_1_2"/><i><font color="Green" title="E20">A18</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">C2</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">C2</font></span><br/><a NAME="E2:12_1_1_2"/><i><font color="Green" title="E21">A19</font></i>: 
<font color="Maroon" title="c13">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">B1</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_1"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_1_1_2"/><i><font color="Green" title="E22">A20</font></i>: 
<font color="Maroon" title="c13">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">A3</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_1_1"><i><font color="Green" title="E18">A10</font></i></a>, <a class="txt" href="#E1:12_1_1_2"><i><font color="Green" title="E20">A18</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_1_1_2"/><i><font color="Green" title="E23">A21</font></i>: 
<font color="Maroon" title="c19">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_1"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_1_1_2"/>
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_1_1"><i><font color="Green" title="E18">A10</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_1_1_2"/><b>then </b><i><font color="Green" title="E24">A22</font></i>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="#E4:12_1_1_2"><i><font color="Green" title="E23">A21</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon" title="c21">C2</font> = <font color="Maroon" title="c13">C2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">C2</font></span><br/><b>thus </b><a NAME="E7:12_1_1_2"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">C2</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E2:12_1_1_2"><i><font color="Green" title="E21">A19</font></i></a>, <a class="txt" href="#E3:12_1_1_2"><i><font color="Green" title="E22">A20</font></i></a>, <a class="txt" href="#E6:12_1_1_2"><i><font color="Green" title="E24">A22</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_1_1"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E2:12_1_1"><i><font color="Green" title="E19">A11</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_2"/><i><font color="Green" title="E18">A23</font></i>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">o</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1"><b>now </b></a><div class="add"><div><i><font color="Green" title="E19">A24</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_2_1_1"/><i><font color="Green" title="E20">A25</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">B2</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">B2</font></span><br/><a NAME="E2:12_1_2_1_1"/><b>then </b>
<font color="Maroon" title="c12">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">A3</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_1_2"><i><font color="Green" title="E18">A23</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_1_2_1_1"/><b>then </b><i><font color="Green" title="E21">A26</font></i>: 
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E6:12"><i><font color="Green" title="E14">A6</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_1_2_1_1"/><i><font color="Green" title="E22">A27</font></i>: 
<font color="Maroon" title="c18">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">C2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_1"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_1_2_1_1"/>
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_1_2_1_1"><i><font color="Green" title="E20">A25</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_1_2_1_1"/><b>then </b><i><font color="Green" title="E23">A28</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c11">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="Maroon" title="c19">B2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="txt" href="#E3:12_1_2_1_1"><i><font color="Green" title="E21">A26</font></i></a>, <a class="txt" href="#E4:12_1_2_1_1"><i><font color="Green" title="E22">A27</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon" title="c21">B2</font> = <font color="Maroon" title="c19">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B2</font></span><br/><b>thus </b><a NAME="E7:12_1_2_1_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B2</font>
 <b>by </b><i><a class="txt" href="#E6:12_1_2_1_1"><i><font color="Green" title="E23">A28</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_1_2_1_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">A3</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">A3</font></span><br/><a NAME="E2:12_1_2_1_2"/><i><font color="Green" title="E20">A29</font></i>: 
<font color="Maroon" title="c19">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_1"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_1_2_1_2"/><i><font color="Green" title="E21">A30</font></i>: 
<font color="Maroon" title="c18">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">C2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_1"><i><font color="Green" title="E16">A8</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_1_2_1_2"/><i><font color="Green" title="E22">A31</font></i>: 
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">C1</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_1_2_1_2"/><i><font color="Green" title="E23">A32</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">C2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_1_2_1_2"/>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E2:12_1_2_1_2"><i><font color="Green" title="E20">A29</font></i></a>, <a class="txt" href="#E4:12_1_2_1_2"><i><font color="Green" title="E22">A31</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_1_2_1_2"/><b>then </b><i><font color="Green" title="E24">A33</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c9">r</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="Maroon" title="c17">A3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E3:12_1_2_1_2"><i><font color="Green" title="E21">A30</font></i></a>, <a class="txt" href="#E5:12_1_2_1_2"><i><font color="Green" title="E23">A32</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon" title="c21">A3</font> = <font color="Maroon" title="c17">A3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">A3</font></span><br/><b>thus </b><a NAME="E8:12_1_2_1_2"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">A3</font>
 <b>by </b><i><a class="txt" href="#E7:12_1_2_1_2"><i><font color="Green" title="E24">A33</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:12_1_2_1"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E1:12_1_2_1"><i><font color="Green" title="E19">A24</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E3:12_1_2"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_1"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E2:12_1"><i><font color="Green" title="E17">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E16">A34</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2"/><i><font color="Green" title="E17">A35</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><i><font color="Green" title="E18">A36</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><a NAME="E2:12_2_1"/><b>then </b><i><font color="Green" title="E19">A37</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_2_1"/><i><font color="Green" title="E20">A38</font></i>: 
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_2"><i><font color="Green" title="E17">A35</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_2_1"/><i><font color="Green" title="E21">A39</font></i>: 
<font color="Maroon" title="c19">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_2_1"/><i><font color="Green" title="E22">A40</font></i>: 
<font color="Maroon" title="c18">B1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_2_1"/>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E3:12_2_1"><i><font color="Green" title="E20">A38</font></i></a>, <a class="txt" href="#E4:12_2_1"><i><font color="Green" title="E21">A39</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_2_1"/><b>then </b><i><font color="Green" title="E23">A41</font></i>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E2:12_2_1"><i><font color="Green" title="E19">A37</font></i></a>, <a class="txt" href="#E5:12_2_1"><i><font color="Green" title="E22">A40</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon" title="c21">O</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E9:12_2_1"/><i><font color="Green" title="E24">A42</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font></span><br/><b>thus </b><a NAME="E10:12_2_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font>
 <b>by </b><i><a class="txt" href="#E7:12_2_1"><i><font color="Green" title="E23">A41</font></i></a>, <a class="txt" href="#E9:12_2_1"><i><font color="Green" title="E24">A42</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2_2"/><i><font color="Green" title="E19">A43</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><i><font color="Green" title="E20">A44</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2_2_1"/><i><font color="Green" title="E21">A45</font></i>: 
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><a NAME="E2:12_2_2_1"/><i><font color="Green" title="E22">A46</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">B1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_2_2_1_1"/>
( <font color="Maroon" title="c13">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">o</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_2_2_1"><i><font color="Green" title="E21">A45</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E2:12_2_2_1_1"/>
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">B1</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:12_2_2_1"/><i><font color="Green" title="E23">A47</font></i>: 
<font color="Maroon" title="c19">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_2_2_1"/>
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_2"><i><font color="Green" title="E17">A35</font></i></a>, <a class="txt" href="#E1:12_2_2_1"><i><font color="Green" title="E21">A45</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_2_2_1"/><b>then </b>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E3:12_2_2_1"><i><font color="Green" title="E23">A47</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_2_2_1"/><b>then </b><i><font color="Green" title="E24">A48</font></i>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_2_2_1"><i><font color="Green" title="E21">A45</font></i></a>, <a class="txt" href="#E2:12_2_2_1"><i><font color="Green" title="E22">A46</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon" title="c21">O</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E8:12_2_2_1"/><i><font color="Green" title="E25">A49</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font></span><br/><b>thus </b><a NAME="E9:12_2_2_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font>
 <b>by </b><i><a class="txt" href="#E6:12_2_2_1"><i><font color="Green" title="E24">A48</font></i></a>, <a class="txt" href="#E8:12_2_2_1"><i><font color="Green" title="E25">A49</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_2_2_2"/>
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">B1</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">B1</font></span><br/><a NAME="E2:12_2_2_2"/><i><font color="Green" title="E21">A50</font></i>: 
<font color="Maroon" title="c17">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">C2</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_2"><i><font color="Green" title="E17">A35</font></i></a>, <a class="txt" href="#E1:12_2_2"><i><font color="Green" title="E19">A43</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_2_2_2"/><i><font color="Green" title="E22">A51</font></i>: 
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_2"><i><font color="Green" title="E17">A35</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_2_2_2"/><i><font color="Green" title="E23">A52</font></i>: 
<font color="Maroon" title="c20">B3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">C2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_2_2_2"/><i><font color="Green" title="E24">A53</font></i>: 
<font color="Maroon" title="c19">B2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_2_2_2"/>
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E2:12_2_2_2"><i><font color="Green" title="E21">A50</font></i></a>, <a class="txt" href="#E4:12_2_2_2"><i><font color="Green" title="E23">A52</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_2_2_2"/><b>then </b><i><font color="Green" title="E25">A54</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c11">t</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c9">r</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="Maroon" title="c18">B1</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E3:12_2_2_2"><i><font color="Green" title="E22">A51</font></i></a>, <a class="txt" href="#E5:12_2_2_2"><i><font color="Green" title="E24">A53</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon" title="c21">B1</font> = <font color="Maroon" title="c18">B1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B1</font></span><br/><b>thus </b><a NAME="E8:12_2_2_2"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B1</font>
 <b>by </b><i><a class="txt" href="#E7:12_2_2_2"><i><font color="Green" title="E25">A54</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_2_2"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E2:12_2_2"><i><font color="Green" title="E20">A44</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_2"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E2:12_2"><i><font color="Green" title="E18">A36</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E17">A55</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3"/><i><font color="Green" title="E18">A56</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><i><font color="Green" title="E19">A57</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_1"/><i><font color="Green" title="E20">A58</font></i>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><i><font color="Green" title="E21">A59</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_1_1"/><i><font color="Green" title="E22">A60</font></i>: 
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">B2</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">B2</font></span><br/><a NAME="E2:12_3_1_1"/><i><font color="Green" title="E23">A61</font></i>: 
<font color="Maroon" title="c17">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">B3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_3_1_1_1"/>
( <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">B3</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_3_1"><i><font color="Green" title="E20">A58</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E2:12_3_1_1_1"/>
<font color="Maroon" title="c17">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">B3</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:12_3_1_1"/><i><font color="Green" title="E24">A62</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">B1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:12_3_1_1_2"/>
( <font color="Maroon" title="c13">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_3_1_1"><i><font color="Green" title="E22">A60</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E2:12_3_1_1_2"/>
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">B1</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:12_3_1_1"/>
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b1</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_3_1"><i><font color="Green" title="E20">A58</font></i></a>, <a class="txt" href="#E2:12_3_1_1"><i><font color="Green" title="E23">A61</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_3_1_1"/><b>then </b><i><font color="Green" title="E25">A63</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c11">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="Maroon" title="c19">B2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_3_1_1"><i><font color="Green" title="E22">A60</font></i></a>, <a class="txt" href="#E3:12_3_1_1"><i><font color="Green" title="E24">A62</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon" title="c21">B2</font> = <font color="Maroon" title="c19">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B2</font></span><br/><b>thus </b><a NAME="E6:12_3_1_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B2</font>
 <b>by </b><i><a class="txt" href="#E5:12_3_1_1"><i><font color="Green" title="E25">A63</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_1_2"/><i><font color="Green" title="E22">A64</font></i>: 
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><a NAME="E2:12_3_1_2"/><i><font color="Green" title="E23">A65</font></i>: 
<font color="Maroon" title="c17">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_3"><i><font color="Green" title="E18">A56</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_3_1_2"/><i><font color="Green" title="E24">A66</font></i>: 
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">B2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_1_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_3_1_2_1"/>
( <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_3_1"><i><font color="Green" title="E20">A58</font></i></a>, <a class="txt" href="#E1:12_3_1_2"><i><font color="Green" title="E22">A64</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E2:12_3_1_2_1"/>
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">B2</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:12_3_1_2"/><i><font color="Green" title="E25">A67</font></i>: 
<font color="Maroon" title="c20">B3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">C1</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_3_1_2"/>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b1</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_3_1"><i><font color="Green" title="E20">A58</font></i></a>, <a class="txt" href="#E3:12_3_1_2"><i><font color="Green" title="E24">A66</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_3_1_2"/><b>then </b><i><font color="Green" title="E26">A68</font></i>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_3_1"><i><font color="Green" title="E20">A58</font></i></a>, <a class="txt" href="#E2:12_3_1_2"><i><font color="Green" title="E23">A65</font></i></a>, <a class="txt" href="#E4:12_3_1_2"><i><font color="Green" title="E25">A67</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon" title="c21">O</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E8:12_3_1_2"/><i><font color="Green" title="E27">A69</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font></span><br/><b>thus </b><a NAME="E9:12_3_1_2"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font>
 <b>by </b><i><a class="txt" href="#E6:12_3_1_2"><i><font color="Green" title="E26">A68</font></i></a>, <a class="txt" href="#E8:12_3_1_2"><i><font color="Green" title="E27">A69</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_3_1"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E2:12_3_1"><i><font color="Green" title="E21">A59</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_2"/><i><font color="Green" title="E20">A70</font></i>: 
<font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><i><font color="Green" title="E21">A71</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_2_1"/><i><font color="Green" title="E22">A72</font></i>: 
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="incsp_1.html#U2" title="INCSP_1:sel.2">Lines</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><a NAME="E2:12_3_2_1"/><b>then </b><i><font color="Green" title="E23">A73</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_3"><i><font color="Green" title="E18">A56</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_3_2_1"/><i><font color="Green" title="E24">A74</font></i>: 
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">B2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:12_3_2_1_1"/>
( <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> )
 
<b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_3_2"><i><font color="Green" title="E20">A70</font></i></a>, <a class="txt" href="#E1:12_3_2_1"><i><font color="Green" title="E22">A72</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E2:12_3_2_1_1"/>
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">B2</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:12_3_2_1"/><i><font color="Green" title="E25">A75</font></i>: 
<font color="Maroon" title="c18">B1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_3_2_1"/>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_3_2_1"><i><font color="Green" title="E22">A72</font></i></a>, <a class="txt" href="#E3:12_3_2_1"><i><font color="Green" title="E24">A74</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_3_2_1"/><b>then </b><i><font color="Green" title="E26">A76</font></i>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E2:12_3_2_1"><i><font color="Green" title="E23">A73</font></i></a>, <a class="txt" href="#E4:12_3_2_1"><i><font color="Green" title="E25">A75</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon" title="c21">O</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="incsp_1.html#U2" title="INCSP_1:sel.2">Lines</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E8:12_3_2_1"/><i><font color="Green" title="E27">A77</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font></span><br/><b>thus </b><a NAME="E9:12_3_2_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font>
 <b>by </b><i><a class="txt" href="#E6:12_3_2_1"><i><font color="Green" title="E26">A76</font></i></a>, <a class="txt" href="#E8:12_3_2_1"><i><font color="Green" title="E27">A77</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_3_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_3_2_2"/>
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">B2</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">B2</font></span><br/><a NAME="E2:12_3_2_2"/><i><font color="Green" title="E22">A78</font></i>: 
<font color="Maroon" title="c17">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_3"><i><font color="Green" title="E18">A56</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E3:12_3_2_2"/><i><font color="Green" title="E23">A79</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E1:12_3"><i><font color="Green" title="E18">A56</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E4:12_3_2_2"/><i><font color="Green" title="E24">A80</font></i>: 
<font color="Maroon" title="c20">B3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">C1</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_3_2_2"/><i><font color="Green" title="E25">A81</font></i>: 
<font color="Maroon" title="c18">B1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E5:12"><i><font color="Green" title="E13">A5</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E6:12_3_2_2"/>
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E2:12_3_2_2"><i><font color="Green" title="E22">A78</font></i></a>, <a class="txt" href="#E4:12_3_2_2"><i><font color="Green" title="E24">A80</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_3_2_2"/><b>then </b><i><font color="Green" title="E26">A82</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c11">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="Maroon" title="c19">B2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E3:12_3_2_2"><i><font color="Green" title="E23">A79</font></i></a>, <a class="txt" href="#E5:12_3_2_2"><i><font color="Green" title="E25">A81</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon" title="c21">B2</font> = <font color="Maroon" title="c19">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B2</font></span><br/><b>thus </b><a NAME="E8:12_3_2_2"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B2</font>
 <b>by </b><i><a class="txt" href="#E7:12_3_2_2"><i><font color="Green" title="E26">A82</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_3_2"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E2:12_3_2"><i><font color="Green" title="E21">A71</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_3"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E2:12_3"><i><font color="Green" title="E19">A57</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E18">A83</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_4"/><i><font color="Green" title="E19">A84</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><div><i><font color="Green" title="E20">A85</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_4_1"/><i><font color="Green" title="E21">A86</font></i>: 
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">B2</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">B2</font></span><br/><a NAME="E2:12_4_1"/><b>then </b>
( <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c13">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> )
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/><a NAME="E3:12_4_1"/><b>then </b><i><font color="Green" title="E22">A87</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">B1</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>;<br/><a NAME="E4:12_4_1"/>
( <font color="Maroon" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">o</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">B3</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">B3</font> )
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_4"><i><font color="Green" title="E19">A84</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/><a NAME="E5:12_4_1"/><b>then </b><i><font color="Green" title="E23">A88</font></i>: 
<font color="Maroon" title="c17">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">B3</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>;<br/><a NAME="E6:12_4_1"/>
<font color="Maroon" title="c11">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_4_1"><i><font color="Green" title="E21">A86</font></i></a>, <a class="txt" href="#E3:12_4_1"><i><font color="Green" title="E22">A87</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_4_1"/><b>then </b><i><font color="Green" title="E24">A89</font></i>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c11">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="Maroon" title="c19">B2</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_4"><i><font color="Green" title="E19">A84</font></i></a>, <a class="txt" href="#E5:12_4_1"><i><font color="Green" title="E23">A88</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>take </b><font color="Maroon" title="c21">B2</font> = <font color="Maroon" title="c19">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B2</font></span><br/><b>thus </b><a NAME="E8:12_4_1"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c21">B2</font>
 <b>by </b><i><a class="txt" href="#E7:12_4_1"><i><font color="Green" title="E24">A89</font></i></a>, <a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_4_2"/><i><font color="Green" title="E21">A90</font></i>: 
<font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><a NAME="E2:12_4_2"/>
( <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">B3</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c20">B3</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c17">A3</font> )
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_4"><i><font color="Green" title="E19">A84</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/><a NAME="E3:12_4_2"/><b>then </b>
<font color="Maroon" title="c17">A3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">B3</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>;<br/><a NAME="E4:12_4_2"/><b>then </b><i><font color="Green" title="E22">A91</font></i>: 
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_4"><i><font color="Green" title="E19">A84</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E5:12_4_2"/>
( <font color="Maroon" title="c8">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">o</font> &amp; <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> )
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_4"><i><font color="Green" title="E19">A84</font></i></a>, <a class="txt" href="#E1:12_4_2"><i><font color="Green" title="E21">A90</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/><a NAME="E6:12_4_2"/><b>then </b>
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">B2</font>
 <b>by </b><i><a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>;<br/><a NAME="E7:12_4_2"/><b>then </b><i><font color="Green" title="E23">A92</font></i>: 
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_4"><i><font color="Green" title="E19">A84</font></i></a>, <a class="txt" href="#E4:12_4_2"><i><font color="Green" title="E22">A91</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon" title="c21">O</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E9:12_4_2"/><i><font color="Green" title="E24">A93</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font></span><br/><b>thus </b><a NAME="E10:12_4_2"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font>
 <b>by </b><i><a class="txt" href="#E7:12_4_2"><i><font color="Green" title="E23">A92</font></i></a>, <a class="txt" href="#E9:12_4_2"><i><font color="Green" title="E24">A93</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:12_4"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E2:12_4"><i><font color="Green" title="E20">A85</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:12_5"/><i><font color="Green" title="E19">A94</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a2</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c8">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="incsp_1.html#U2" title="INCSP_1:sel.2">Lines</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font></span><br/><a NAME="E2:12_5"/><b>then </b><i><font color="Green" title="E20">A95</font></i>: 
( <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> &amp; <font color="Maroon" title="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> &amp; <font color="Maroon" title="c4">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b1</font> &amp; <font color="Maroon" title="c12">C1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c9">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c16">A2</font> &amp; <font color="Maroon" title="c9">r</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> )
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/><a NAME="E3:12_5"/><i><font color="Green" title="E21">A96</font></i>: 
( <font color="Maroon" title="c13">C2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b3</font> &amp; <font color="Maroon" title="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c5">b2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c7">b3</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">C3</font> &amp; <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> &amp; <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">B1</font> )
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E1:12_5"><i><font color="Green" title="E19">A94</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></i>;<br/><a NAME="E4:12_5"/><i><font color="Green" title="E22">A97</font></i>: 
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">B2</font>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E10">A2</font></i></a>, <a class="txt" href="#E2:12_5"><i><font color="Green" title="E20">A95</font></i></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>;<br/><a NAME="E5:12_5"/><i><font color="Green" title="E23">A98</font></i>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">B1</font>
 <b>by </b><i><a class="txt" href="#E3:12_5"><i><font color="Green" title="E21">A96</font></i></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></i>;<br/><a NAME="E6:12_5"/>
<font color="Maroon" title="c7">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r</font>
 <b>by </b><i><a class="txt" href="#E3:12"><i><font color="Green" title="E11">A3</font></i></a>, <a class="txt" href="#E4:12"><i><font color="Green" title="E12">A4</font></i></a>, <a class="txt" href="#E1:12_5"><i><font color="Green" title="E19">A94</font></i></a>, <a class="txt" href="#E4:12_5"><i><font color="Green" title="E22">A97</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><a NAME="E7:12_5"/><b>then </b><i><font color="Green" title="E24">A99</font></i>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <b>by </b><i><a class="txt" href="#E3:12_5"><i><font color="Green" title="E21">A96</font></i></a>, <a class="txt" href="#E5:12_5"><i><font color="Green" title="E23">A98</font></i></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></i>;<br/><b>consider </b><font color="Maroon" title="c21">O</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="incsp_1.html#U2" title="INCSP_1:sel.2">Lines</a> of <font color="Maroon" title="c1">IPP</font><b> such that </b><br/><a NAME="E9:12_5"/><i><font color="Green" title="E25">A100</font></i>: 
( <font color="Maroon" title="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> &amp; <font color="Maroon" title="c10">s</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c21">O</font> )
 <b>by </b><i><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></i>;<br/><b>take </b><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font></span><br/><b>thus </b><a NAME="E10:12_5"/>
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="Maroon" title="c22">O</font>
 <b>by </b><i><a class="txt" href="#E7:12_5"><i><font color="Green" title="E24">A99</font></i></a>, <a class="txt" href="#E9:12_5"><i><font color="Green" title="E25">A100</font></i></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:12"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c9">r</font>,<font color="Maroon" title="c10">s</font>,<font color="Maroon" title="c11">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="b1">O</font>
 <b>by </b><i><a class="txt" href="#E1:12"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E7:12"><i><font color="Green" title="E15">A7</font></i></a>, <a class="txt" href="#E8:12"><i><font color="Green" title="E16">A34</font></i></a>, <a class="txt" href="#E9:12"><i><font color="Green" title="E17">A55</font></i></a>, <a class="txt" href="#E10:12"><i><font color="Green" title="E18">A83</font></i></a>, <a class="ref" href="incproj.html#D19" title="INCPROJ:def.19">INCPROJ:def 19</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
