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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:14"/><span class="lab"><font color="Green" title="E10">A2</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:14"/><span class="lab"><font color="Green" title="E11">A3</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:14"/><span class="lab"><font color="Green" title="E12">A4</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E5:14"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E6:14"/><span class="lab"><font color="Green" title="E14">A6</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E7:14"/><span class="lab"><font color="Green" title="E15">A7</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E8:14"/><span class="lab"><font color="Green" title="E16">A8</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E9:14"/><span class="lab"><font color="Green" title="E17">A9</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E10:14"/><span class="lab"><font color="Green" title="E18">A10</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E11:14"/><span class="lab"><font color="Green" title="E19">A11</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E12:14"/><span class="lab"><font color="Green" title="E20">A12</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E13:14"/><span class="lab"><font color="Green" title="E21">A13</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E14:14"/><span class="lab"><font color="Green" title="E22">A14</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E15:14"/><span class="lab"><font color="Green" title="E23">A15</font></span>: 
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E16:14"/><span class="lab"><font color="Green" title="E24">A16</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E17:14"/><span class="lab"><font color="Green" title="E25">A17</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E18:14"/><span class="lab"><font color="Green" title="E26">A18</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E19:14"/><span class="lab"><font color="Green" title="E27">A19</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E20:14"/><span class="lab"><font color="Green" title="E28">A20</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E21:14"/><span class="lab"><font color="Green" title="E29">A21</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E22:14"/><span class="lab"><font color="Green" title="E30">A22</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E23:14"/><span class="lab"><font color="Green" title="E31">A23</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E24:14"/><span class="lab"><font color="Green" title="E32">A24</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E25:14"/><span class="lab"><font color="Green" title="E33">A25</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E26:14"/><span class="lab"><font color="Green" title="E34">A26</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E27:14"/><span class="lab"><font color="Green" title="E35">A27</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E28:14"/><span class="lab"><font color="Green" title="E36">A28</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E29:14"/><span class="lab"><font color="Green" title="E37">A29</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E38">A30</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14_1"/>
<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>
 <span class="kw">and </span><br/><a NAME="E2:14_1"/>
<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>
 <span class="kw">and </span><br/><a NAME="E3:14_1"/>
<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>
 <span class="kw">and </span><br/><a NAME="E4:14_1"/><span class="lab"><font color="Green" title="E39">A31</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E40">A32</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_1"/><span class="lab"><font color="Green" title="E41">A33</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E3:14_1_1"/><span class="lab"><font color="Green" title="E42">A34</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/><span class="kw">assume </span><a NAME="E4:14_1_1"/><span class="lab"><font color="Green" title="E43">A35</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E5:14_1_1"/><span class="lab"><font color="Green" title="E44">A36</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E6:14_1_1"/><span class="lab"><font color="Green" title="E45">A37</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E7:14_1_1"/><span class="lab"><font color="Green" title="E46">A38</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E8:14_1_1"/><span class="lab"><font color="Green" title="E47">A39</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E9:14_1_1"/><span class="lab"><font color="Green" title="E48">A40</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E10:14_1_1"/><span class="lab"><font color="Green" title="E49">A41</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E11:14_1_1"/><span class="lab"><font color="Green" title="E50">A42</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E12:14_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="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><a NAME="E13:14_1_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E45">A37</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E44">A36</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E46">A38</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E50">A42</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E14:14_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A43</font></span>: 
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E29:14"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E15:14_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="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><a NAME="E16:14_1_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E43">A35</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E49">A41</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E48">A40</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E47">A39</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E41">A33</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E17:14_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E51">A43</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E18:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E42">A34</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_2"/><span class="lab"><font color="Green" title="E41">A44</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E2:14_1_2"/><span class="lab"><font color="Green" title="E42">A45</font></span>: 
( <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="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><a NAME="E3:14_1_2"/><span class="lab"><font color="Green" title="E43">A46</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E4:14_1_2"/><span class="lab"><font color="Green" title="E44">A47</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E5:14_1_2"/><span class="lab"><font color="Green" title="E45">A48</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E6:14_1_2"/><span class="lab"><font color="Green" title="E46">A49</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E7:14_1_2"/><span class="lab"><font color="Green" title="E47">A50</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><span class="kw">assume </span><a NAME="E8:14_1_2"/><span class="lab"><font color="Green" title="E48">A51</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E9:14_1_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E10:14_1_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E8:14_1_2"><span class="lab"><font color="Green" title="E48">A51</font></span></a>, <a class="txt" href="#E2:14_1_2"><span class="lab"><font color="Green" title="E42">A45</font></span></a>, <a class="txt" href="#E3:14_1_2"><span class="lab"><font color="Green" title="E43">A46</font></span></a>, <a class="txt" href="#E7:14_1_2"><span class="lab"><font color="Green" title="E47">A50</font></span></a>, <a class="txt" href="#E6:14_1_2"><span class="lab"><font color="Green" title="E46">A49</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E11:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A52</font></span>: 
<font color="Maroon" title="c11">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E8:14_1_2"><span class="lab"><font color="Green" title="E48">A51</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c21">B2</font> = <font color="Maroon" title="c19">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E12:14_1_2"/><span class="lab"><font color="Green" title="E50">A53</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E13:14_1_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="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><a NAME="E14:14_1_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E44">A47</font></span></a>, <a class="txt" href="#E12:14_1_2"><span class="lab"><font color="Green" title="E50">A53</font></span></a>, <a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E41">A44</font></span></a>, <a class="txt" href="#E5:14_1_2"><span class="lab"><font color="Green" title="E45">A48</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E15:14_1_2"/><span class="kw">then </span>
<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="c21">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E29:14"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E39">A31</font></span></a>, <a class="txt" href="#E11:14_1_2"><span class="lab"><font color="Green" title="E49">A52</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E16:14_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">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E7:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1"><span class="lab"><font color="Green" title="E40">A32</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E31:14"/><span class="lab"><font color="Green" title="E39">A54</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E32:14"/><span class="lab"><font color="Green" title="E40">A55</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/>
<a NAME="E33:14"/><span class="lab"><font color="Green" title="E41">A56</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E34:14"/><span class="lab"><font color="Green" title="E42">A57</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E35:14"/><span class="lab"><font color="Green" title="E43">A58</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E36:14"/><span class="lab"><font color="Green" title="E44">A59</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/>
<a NAME="E37:14"/><span class="lab"><font color="Green" title="E45">A60</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E38:14"/><span class="lab"><font color="Green" title="E46">A61</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E39:14"/><span class="lab"><font color="Green" title="E47">A62</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E40:14"/><span class="lab"><font color="Green" title="E48">A63</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E41:14"/><span class="lab"><font color="Green" title="E49">A64</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<a NAME="E42:14"/><span class="lab"><font color="Green" title="E50">A65</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E51">A66</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14_2"/><span class="lab"><font color="Green" title="E52">A67</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:14_2"/><span class="lab"><font color="Green" title="E53">A68</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:14_2"/><span class="lab"><font color="Green" title="E54">A69</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E55">A70</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_2_1"/><span class="lab"><font color="Green" title="E56">A71</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E57">A72</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_2_1_1"/><span class="lab"><font color="Green" title="E58">A73</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E2:14_2_1_1"/><span class="lab"><font color="Green" title="E59">A74</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E3:14_2_1_1"/><span class="lab"><font color="Green" title="E60">A75</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E4:14_2_1_1"/><span class="lab"><font color="Green" title="E61">A76</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E5:14_2_1_1"/><span class="lab"><font color="Green" title="E62">A77</font></span>: 
( <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="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><span class="kw">assume </span><a NAME="E6:14_2_1_1"/><span class="lab"><font color="Green" title="E63">A78</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c21">B2</font> = <font color="Maroon" title="c19">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E7:14_2_1_1"/><span class="lab"><font color="Green" title="E64">A79</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E8:14_2_1_1"/>
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E1:14_2_1"><span class="lab"><font color="Green" title="E56">A71</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E9:14_2_1_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E5:14_2_1_1"><span class="lab"><font color="Green" title="E62">A77</font></span></a>, <a class="txt" href="#E4:14_2_1_1"><span class="lab"><font color="Green" title="E61">A76</font></span></a>, <a class="txt" href="#E3:14_2_1_1"><span class="lab"><font color="Green" title="E60">A75</font></span></a>, <a class="txt" href="#E7:14_2_1_1"><span class="lab"><font color="Green" title="E64">A79</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E10:14_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A80</font></span>: 
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E29:14"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="txt" href="#E1:14_2_1"><span class="lab"><font color="Green" title="E56">A71</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E11:14_2_1_1"/><span class="lab"><font color="Green" title="E66">A81</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E12:14_2_1_1"/><span class="lab"><font color="Green" title="E67">A82</font></span>: 
( <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="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><a NAME="E13:14_2_1_1"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E6:14_2_1_1"><span class="lab"><font color="Green" title="E63">A78</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E14:14_2_1_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E6:14_2_1_1"><span class="lab"><font color="Green" title="E63">A78</font></span></a>, <a class="txt" href="#E12:14_2_1_1"><span class="lab"><font color="Green" title="E67">A82</font></span></a>, <a class="txt" href="#E11:14_2_1_1"><span class="lab"><font color="Green" title="E66">A81</font></span></a>, <a class="txt" href="#E2:14_2_1_1"><span class="lab"><font color="Green" title="E59">A74</font></span></a>, <a class="txt" href="#E1:14_2_1_1"><span class="lab"><font color="Green" title="E58">A73</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E15:14_2_1_1"/><span class="kw">then </span>
<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="c21">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E6:14_2_1_1"><span class="lab"><font color="Green" title="E63">A78</font></span></a>, <a class="txt" href="#E10:14_2_1_1"><span class="lab"><font color="Green" title="E65">A80</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E16:14_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_2_1_2"/><span class="lab"><font color="Green" title="E58">A83</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E2:14_2_1_2"/><span class="lab"><font color="Green" title="E59">A84</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E3:14_2_1_2"/><span class="lab"><font color="Green" title="E60">A85</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E5:14_2_1_2"/><span class="lab"><font color="Green" title="E61">A86</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/><span class="kw">assume </span><a NAME="E6:14_2_1_2"/><span class="lab"><font color="Green" title="E62">A87</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E7:14_2_1_2"/><span class="lab"><font color="Green" title="E63">A88</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E8:14_2_1_2"/>
( <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="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><a NAME="E9:14_2_1_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E1:14_2_1"><span class="lab"><font color="Green" title="E56">A71</font></span></a>, <a class="txt" href="#E6:14_2_1_2"><span class="lab"><font color="Green" title="E62">A87</font></span></a>, <a class="txt" href="#E1:14_2_1_2"><span class="lab"><font color="Green" title="E58">A83</font></span></a>, <a class="txt" href="#E7:14_2_1_2"><span class="lab"><font color="Green" title="E63">A88</font></span></a>, <a class="txt" href="#E2:14_2_1_2"><span class="lab"><font color="Green" title="E59">A84</font></span></a>, <a class="txt" href="#E3:14_2_1_2"><span class="lab"><font color="Green" title="E60">A85</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E10:14_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A89</font></span>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E1:14_2_1"><span class="lab"><font color="Green" title="E56">A71</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E11:14_2_1_2"/>
( <font color="Maroon" title="c17">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font> &amp; <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E29">A21</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E34:14"><span class="lab"><font color="Green" title="E42">A57</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E42:14"><span class="lab"><font color="Green" title="E50">A65</font></span></a>, <a class="txt" href="#E32:14"><span class="lab"><font color="Green" title="E40">A55</font></span></a>, <a class="txt" href="#E2:14_2"><span class="lab"><font color="Green" title="E53">A68</font></span></a>, <a class="txt" href="#E3:14_2"><span class="lab"><font color="Green" title="E54">A69</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E12:14_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E29:14"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="txt" href="#E1:14_2_1"><span class="lab"><font color="Green" title="E56">A71</font></span></a>, <a class="txt" href="#E10:14_2_1_2"><span class="lab"><font color="Green" title="E64">A89</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E13:14_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="c22">O</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_2_1_2"><span class="lab"><font color="Green" title="E61">A86</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_2_1"><span class="lab"><font color="Green" title="E57">A72</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_2_2"/><span class="lab"><font color="Green" title="E56">A90</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E57">A91</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_2_2_1"/><span class="lab"><font color="Green" title="E58">A92</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="txt" href="#E36:14"><span class="lab"><font color="Green" title="E44">A59</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E2:14_2_2_1"/><span class="lab"><font color="Green" title="E59">A93</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E4:14_2_2_1"/><span class="lab"><font color="Green" title="E60">A94</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/><a NAME="E5:14_2_2_1"/><span class="lab"><font color="Green" title="E61">A95</font></span>: 
( <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="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">C1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><a NAME="E6:14_2_2_1"/><span class="lab"><font color="Green" title="E62">A96</font></span>: 
( <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="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E7:14_2_2_1"/><span class="lab"><font color="Green" title="E63">A97</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><span class="kw">assume </span><a NAME="E8:14_2_2_1"/><span class="lab"><font color="Green" title="E64">A98</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E9:14_2_2_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E10:14_2_2_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E1:14_2_2"><span class="lab"><font color="Green" title="E56">A90</font></span></a>, <a class="txt" href="#E8:14_2_2_1"><span class="lab"><font color="Green" title="E64">A98</font></span></a>, <a class="txt" href="#E5:14_2_2_1"><span class="lab"><font color="Green" title="E61">A95</font></span></a>, <a class="txt" href="#E2:14_2_2_1"><span class="lab"><font color="Green" title="E59">A93</font></span></a>, <a class="txt" href="#E7:14_2_2_1"><span class="lab"><font color="Green" title="E63">A97</font></span></a>, <a class="txt" href="#E6:14_2_2_1"><span class="lab"><font color="Green" title="E62">A96</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E11:14_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A99</font></span>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:14"><span class="lab"><font color="Green" title="E47">A62</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E38:14"><span class="lab"><font color="Green" title="E46">A61</font></span></a>, <a class="txt" href="#E8:14_2_2_1"><span class="lab"><font color="Green" title="E64">A98</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E12:14_2_2_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E40:14"><span class="lab"><font color="Green" title="E48">A63</font></span></a>, <a class="txt" href="#E1:14_2"><span class="lab"><font color="Green" title="E52">A67</font></span></a>, <a class="txt" href="#E3:14_2"><span class="lab"><font color="Green" title="E54">A69</font></span></a>, <a class="txt" href="#E8:14_2_2_1"><span class="lab"><font color="Green" title="E64">A98</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E13:14_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E1:14_2_2_1"><span class="lab"><font color="Green" title="E58">A92</font></span></a>, <a class="txt" href="#E11:14_2_2_1"><span class="lab"><font color="Green" title="E65">A99</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E14:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_2_2_1"><span class="lab"><font color="Green" title="E60">A94</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c21">B2</font> = <font color="Maroon" title="c19">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E2:14_2_2_2"/>
( <font color="Maroon" title="c17">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font> &amp; <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E29">A21</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E34:14"><span class="lab"><font color="Green" title="E42">A57</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E42:14"><span class="lab"><font color="Green" title="E50">A65</font></span></a>, <a class="txt" href="#E32:14"><span class="lab"><font color="Green" title="E40">A55</font></span></a>, <a class="txt" href="#E2:14_2"><span class="lab"><font color="Green" title="E53">A68</font></span></a>, <a class="txt" href="#E3:14_2"><span class="lab"><font color="Green" title="E54">A69</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E3:14_2_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A100</font></span>: 
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="txt" href="#E29:14"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E4:14_2_2_2"/>
( <font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font> &amp; <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E40:14"><span class="lab"><font color="Green" title="E48">A63</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="txt" href="#E36:14"><span class="lab"><font color="Green" title="E44">A59</font></span></a>, <a class="txt" href="#E3:14_2"><span class="lab"><font color="Green" title="E54">A69</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E5:14_2_2_2"/><span class="kw">then </span>
<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="c21">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E3:14_2_2_2"><span class="lab"><font color="Green" title="E58">A100</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E6:14_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">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_2_2"><span class="lab"><font color="Green" title="E57">A91</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E6:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_2"><span class="lab"><font color="Green" title="E55">A70</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E44:14"/><span class="lab"><font color="Green" title="E52">A101</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/>
<a NAME="E45:14"/><span class="lab"><font color="Green" title="E53">A102</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E54">A103</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14_3"/><span class="lab"><font color="Green" title="E55">A104</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:14_3"/><span class="lab"><font color="Green" title="E56">A105</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E57">A106</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_3_1"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E58">A107</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_3_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_3_1_1"/><span class="lab"><font color="Green" title="E59">A108</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E44:14"><span class="lab"><font color="Green" title="E52">A101</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">assume </span><a NAME="E2:14_3_1_1"/><span class="lab"><font color="Green" title="E60">A109</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E3:14_3_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E39:14"><span class="lab"><font color="Green" title="E47">A62</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E1:14_3"><span class="lab"><font color="Green" title="E55">A104</font></span></a>, <a class="txt" href="#E2:14_3"><span class="lab"><font color="Green" title="E56">A105</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E4:14_3_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A110</font></span>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E38:14"><span class="lab"><font color="Green" title="E46">A61</font></span></a>, <a class="txt" href="#E1:14_3_1_1"><span class="lab"><font color="Green" title="E59">A108</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E5:14_3_1_1"/><span class="lab"><font color="Green" title="E62">A111</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E6:14_3_1_1"/><span class="lab"><font color="Green" title="E63">A112</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E7:14_3_1_1"/><span class="lab"><font color="Green" title="E64">A113</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E9:14_3_1_1"/><span class="lab"><font color="Green" title="E65">A114</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/><a NAME="E10:14_3_1_1"/><span class="lab"><font color="Green" title="E66">A115</font></span>: 
( <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="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><span class="kw">take </span><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E11:14_3_1_1"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E2:14_3_1_1"><span class="lab"><font color="Green" title="E60">A109</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E12:14_3_1_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E2:14_3_1_1"><span class="lab"><font color="Green" title="E60">A109</font></span></a>, <a class="txt" href="#E10:14_3_1_1"><span class="lab"><font color="Green" title="E66">A115</font></span></a>, <a class="txt" href="#E6:14_3_1_1"><span class="lab"><font color="Green" title="E63">A112</font></span></a>, <a class="txt" href="#E5:14_3_1_1"><span class="lab"><font color="Green" title="E62">A111</font></span></a>, <a class="txt" href="#E7:14_3_1_1"><span class="lab"><font color="Green" title="E64">A113</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E13:14_3_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E2:14_3_1_1"><span class="lab"><font color="Green" title="E60">A109</font></span></a>, <a class="txt" href="#E4:14_3_1_1"><span class="lab"><font color="Green" title="E61">A110</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E14:14_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="c22">O</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_3_1_1"><span class="lab"><font color="Green" title="E65">A114</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_3_1"/><span class="lab"><font color="Green" title="E59">A116</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="14_3_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_3_1_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c21">B1</font> = <font color="Maroon" title="c18">B1</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E2:14_3_1_2"/>
( <font color="Maroon" title="c17">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">C2</font> &amp; <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E45:14"><span class="lab"><font color="Green" title="E53">A102</font></span></a>, <a class="txt" href="#E34:14"><span class="lab"><font color="Green" title="E42">A57</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E29:14"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="txt" href="#E32:14"><span class="lab"><font color="Green" title="E40">A55</font></span></a>, <a class="txt" href="#E2:14_3"><span class="lab"><font color="Green" title="E56">A105</font></span></a>, <a class="txt" href="#E2:14_3_1"><span class="lab"><font color="Green" title="E59">A116</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E3:14_3_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A117</font></span>: 
<font color="Maroon" title="c10">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="txt" href="#E42:14"><span class="lab"><font color="Green" title="E50">A65</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E4:14_3_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> &amp; <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E39:14"><span class="lab"><font color="Green" title="E47">A62</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E44:14"><span class="lab"><font color="Green" title="E52">A101</font></span></a>, <a class="txt" href="#E2:14_3"><span class="lab"><font color="Green" title="E56">A105</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E5:14_3_1_2"/><span class="kw">then </span>
<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="c21">B1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E38:14"><span class="lab"><font color="Green" title="E46">A61</font></span></a>, <a class="txt" href="#E3:14_3_1_2"><span class="lab"><font color="Green" title="E60">A117</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E6:14_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="c21">B1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_3_1"><span class="lab"><font color="Green" title="E58">A107</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_3_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_3_2"/>
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:14_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A118</font></span>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E40:14"><span class="lab"><font color="Green" title="E48">A63</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E3:14_3_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> &amp; <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E39:14"><span class="lab"><font color="Green" title="E47">A62</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E44:14"><span class="lab"><font color="Green" title="E52">A101</font></span></a>, <a class="txt" href="#E2:14_3"><span class="lab"><font color="Green" title="E56">A105</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E4:14_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A119</font></span>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E38:14"><span class="lab"><font color="Green" title="E46">A61</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E6:14_3_2"/><span class="lab"><font color="Green" title="E60">A120</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E7:14_3_2"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="txt" href="#E36:14"><span class="lab"><font color="Green" title="E44">A59</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E8:14_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E2:14_3_2"><span class="lab"><font color="Green" title="E58">A118</font></span></a>, <a class="txt" href="#E4:14_3_2"><span class="lab"><font color="Green" title="E59">A119</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E9:14_3_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_3_2"><span class="lab"><font color="Green" title="E60">A120</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_3"><span class="lab"><font color="Green" title="E57">A106</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E47:14"/><span class="lab"><font color="Green" title="E55">A121</font></span>: 
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E42:14"><span class="lab"><font color="Green" title="E50">A65</font></span></a>, <a class="txt" href="#E32:14"><span class="lab"><font color="Green" title="E40">A55</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E56">A122</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_4"/><span class="lab"><font color="Green" title="E57">A123</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E58">A124</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_4_1"/><span class="lab"><font color="Green" title="E59">A125</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E60">A126</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_4_1_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:14_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A127</font></span>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E40:14"><span class="lab"><font color="Green" title="E48">A63</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E3:14_4_1_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> &amp; <font color="Maroon" title="c19">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E39:14"><span class="lab"><font color="Green" title="E47">A62</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E38:14"><span class="lab"><font color="Green" title="E46">A61</font></span></a>, <a class="txt" href="#E1:14_4"><span class="lab"><font color="Green" title="E57">A123</font></span></a>, <a class="txt" href="#E1:14_4_1"><span class="lab"><font color="Green" title="E59">A125</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E4:14_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A128</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E44:14"><span class="lab"><font color="Green" title="E52">A101</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E6:14_4_1_1"/><span class="lab"><font color="Green" title="E63">A129</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E7:14_4_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E1:14_4"><span class="lab"><font color="Green" title="E57">A123</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E8:14_4_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E36:14"><span class="lab"><font color="Green" title="E44">A59</font></span></a>, <a class="txt" href="#E4:14_4_1_1"><span class="lab"><font color="Green" title="E62">A128</font></span></a>, <a class="txt" href="#E2:14_4_1_1"><span class="lab"><font color="Green" title="E61">A127</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E9:14_4_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_4_1_1"><span class="lab"><font color="Green" title="E63">A129</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_4_1_2"/>
( <font color="Maroon" title="c19">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font> &amp; <font color="Maroon" title="c16">A2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E39:14"><span class="lab"><font color="Green" title="E47">A62</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E38:14"><span class="lab"><font color="Green" title="E46">A61</font></span></a>, <a class="txt" href="#E1:14_4"><span class="lab"><font color="Green" title="E57">A123</font></span></a>, <a class="txt" href="#E1:14_4_1"><span class="lab"><font color="Green" title="E59">A125</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E2:14_4_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A130</font></span>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E44:14"><span class="lab"><font color="Green" title="E52">A101</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">assume </span><a NAME="E3:14_4_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E4:14_4_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A131</font></span>: 
<font color="Maroon" title="c13">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">A3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E45:14"><span class="lab"><font color="Green" title="E53">A102</font></span></a>, <a class="txt" href="#E34:14"><span class="lab"><font color="Green" title="E42">A57</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E1:14_4_1"><span class="lab"><font color="Green" title="E59">A125</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c21">C2</font> = <font color="Maroon" title="c13">C2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E5:14_4_1_2"/>
<font color="Maroon" title="c21">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">B1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E1:14_4"><span class="lab"><font color="Green" title="E57">A123</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E6:14_4_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E4:14_4_1_2"><span class="lab"><font color="Green" title="E62">A131</font></span></a>, <a class="txt" href="#E2:14_4_1_2"><span class="lab"><font color="Green" title="E61">A130</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_4_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_4_1"><span class="lab"><font color="Green" title="E60">A126</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_4_2"/><span class="lab"><font color="Green" title="E59">A132</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E60">A133</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_4_2_1"/><span class="lab"><font color="Green" title="E61">A134</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:14_4_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A135</font></span>: 
<font color="Maroon" title="c15">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">C3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E40:14"><span class="lab"><font color="Green" title="E48">A63</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c21">B2</font> = <font color="Maroon" title="c19">B2</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E3:14_4_2_1"/>
<font color="Maroon" title="c12">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">A3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E29">A21</font></span></a>, <a class="txt" href="#E34:14"><span class="lab"><font color="Green" title="E42">A57</font></span></a>, <a class="txt" href="#E24:14"><span class="lab"><font color="Green" title="E32">A24</font></span></a>, <a class="txt" href="#E1:14_4_2"><span class="lab"><font color="Green" title="E59">A132</font></span></a>, <a class="txt" href="#E1:14_4_2_1"><span class="lab"><font color="Green" title="E61">A134</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E4:14_4_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A136</font></span>: 
<font color="Maroon" title="c3">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E23:14"><span class="lab"><font color="Green" title="E31">A23</font></span></a>, <a class="txt" href="#E29:14"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E24">A16</font></span></a>, <a class="txt" href="#E47:14"><span class="lab"><font color="Green" title="E55">A121</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E5:14_4_2_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E1:14_4"><span class="lab"><font color="Green" title="E57">A123</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E6:14_4_2_1"/><span class="kw">then </span>
<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="c21">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E36:14"><span class="lab"><font color="Green" title="E44">A59</font></span></a>, <a class="txt" href="#E4:14_4_2_1"><span class="lab"><font color="Green" title="E63">A136</font></span></a>, <a class="txt" href="#E2:14_4_2_1"><span class="lab"><font color="Green" title="E62">A135</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E7:14_4_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="c21">B2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_4_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_4_2_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c21">A3</font> = <font color="Maroon" title="c17">A3</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E2:14_4_2_2"/>
( <font color="Maroon" title="c19">B2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">C1</font> &amp; <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E39:14"><span class="lab"><font color="Green" title="E47">A62</font></span></a>, <a class="txt" href="#E27:14"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E38:14"><span class="lab"><font color="Green" title="E46">A61</font></span></a>, <a class="txt" href="#E44:14"><span class="lab"><font color="Green" title="E52">A101</font></span></a>, <a class="txt" href="#E1:14_4"><span class="lab"><font color="Green" title="E57">A123</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E3:14_4_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A137</font></span>: 
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E29">A21</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E4:14_4_2_2"/>
( <font color="Maroon" title="c18">B1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">C2</font> &amp; <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E30">A22</font></span></a>, <a class="txt" href="#E35:14"><span class="lab"><font color="Green" title="E43">A58</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E37:14"><span class="lab"><font color="Green" title="E45">A60</font></span></a>, <a class="txt" href="#E17:14"><span class="lab"><font color="Green" title="E25">A17</font></span></a>, <a class="txt" href="#E19:14"><span class="lab"><font color="Green" title="E27">A19</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E26">A18</font></span></a>, <a class="txt" href="#E36:14"><span class="lab"><font color="Green" title="E44">A59</font></span></a>, <a class="txt" href="#E1:14_4"><span class="lab"><font color="Green" title="E57">A123</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E5:14_4_2_2"/><span class="kw">then </span>
<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="c21">A3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E45:14"><span class="lab"><font color="Green" title="E53">A102</font></span></a>, <a class="txt" href="#E40:14"><span class="lab"><font color="Green" title="E48">A63</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E28:14"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="txt" href="#E3:14_4_2_2"><span class="lab"><font color="Green" title="E61">A137</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E6:14_4_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">A3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="projred1.html#T13" target="_self" title="PROJRED1:th.13">Th13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_4_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_4_2"><span class="lab"><font color="Green" title="E60">A133</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_4"><span class="lab"><font color="Green" title="E58">A124</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_5"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_5"/><span class="lab"><font color="Green" title="E57">A138</font></span>: 
( <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="c6">a2</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c13">C2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E2:14_5"/><span class="lab"><font color="Green" title="E58">A139</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E3:14_5"/><span class="lab"><font color="Green" title="E59">A140</font></span>: 
( <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="c3">b1</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c19">B2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E4:14_5"/><span class="lab"><font color="Green" title="E60">A141</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E5:14_5"/><span class="lab"><font color="Green" title="E61">A142</font></span>: 
( <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="c11">t</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E6:14_5"/><span class="lab"><font color="Green" title="E62">A143</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E8:14_5"/><span class="lab"><font color="Green" title="E63">A144</font></span>: 
( <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D10" title="INCPROJ:def.10">INCPROJ:def 10</a></span>;<br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E9:14_5"/><span class="lab"><font color="Green" title="E64">A145</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E10:14_5"/>
<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>
 <span class="kw">and </span><br/><a NAME="E11:14_5"/>
<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>
 <span class="kw">and </span><br/><a NAME="E12:14_5"/><span class="lab"><font color="Green" title="E65">A146</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E13:14_5"/><span class="lab"><font color="Green" title="E66">A147</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">take </span><font color="Maroon" title="c22">O</font> = <font color="Maroon" title="c21">O</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><a NAME="E14:14_5"/><span class="lab"><font color="Green" title="E67">A148</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="ref" href="zfmisc_1.html#D5" title="ZFMISC_1:def.5">ZFMISC_1:def 5</a></span>;<br/><a NAME="E15:14_5"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E13:14_5"><span class="lab"><font color="Green" title="E66">A147</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E16:14_5"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:14"><span class="lab"><font color="Green" title="E39">A54</font></span></a>, <a class="txt" href="#E33:14"><span class="lab"><font color="Green" title="E41">A56</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E29">A21</font></span></a>, <a class="txt" href="#E41:14"><span class="lab"><font color="Green" title="E49">A64</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E28">A20</font></span></a>, <a class="txt" href="#E9:14_5"><span class="lab"><font color="Green" title="E64">A145</font></span></a>, <a class="txt" href="#E12:14_5"><span class="lab"><font color="Green" title="E65">A146</font></span></a>, <a class="txt" href="#E3:14_5"><span class="lab"><font color="Green" title="E59">A140</font></span></a>, <a class="txt" href="#E14:14_5"><span class="lab"><font color="Green" title="E67">A148</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E17:14_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A149</font></span>: 
<font color="Maroon" title="c7">b3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:14"><span class="lab"><font color="Green" title="E47">A62</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E23">A15</font></span></a>, <a class="txt" href="#E38:14"><span class="lab"><font color="Green" title="E46">A61</font></span></a>, <a class="txt" href="#E13:14_5"><span class="lab"><font color="Green" title="E66">A147</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><a NAME="E18:14_5"/><span class="lab"><font color="Green" title="E69">A150</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E13:14_5"><span class="lab"><font color="Green" title="E66">A147</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>;<br/><a NAME="E19:14_5"/>
( <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="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">A1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></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></span>;<br/><a NAME="E20:14_5"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E9:14_5"><span class="lab"><font color="Green" title="E64">A145</font></span></a>, <a class="txt" href="#E18:14_5"><span class="lab"><font color="Green" title="E69">A150</font></span></a>, <a class="txt" href="#E1:14_5"><span class="lab"><font color="Green" title="E57">A138</font></span></a>, <a class="txt" href="#E4:14_5"><span class="lab"><font color="Green" title="E60">A141</font></span></a>, <a class="txt" href="#E2:14_5"><span class="lab"><font color="Green" title="E58">A139</font></span></a>, <a class="ref" href="projred1.html#T12" target="_self" title="PROJRED1:th.12">Th12</a></span>;<br/><a NAME="E21:14_5"/><span class="kw">then </span>
<font color="Maroon" title="c9">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_5"><span class="lab"><font color="Green" title="E69">A150</font></span></a>, <a class="txt" href="#E5:14_5"><span class="lab"><font color="Green" title="E61">A142</font></span></a>, <a class="txt" href="#E6:14_5"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E17:14_5"><span class="lab"><font color="Green" title="E68">A149</font></span></a>, <a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/><span class="kw">hence </span><a NAME="E22:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_5"><span class="lab"><font color="Green" title="E63">A144</font></span></a>, <a class="ref" href="incsp_1.html#T12" title="INCSP_1:th.12">INCSP_1:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E50:14"/>
 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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E11">A3</font></span></a>, <a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E13">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E15">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E16">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E17">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E18">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E19">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E20">A12</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E21">A13</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E22">A14</font></span></a>, <a class="txt" href="#E48:14"><span class="lab"><font color="Green" title="E56">A122</font></span></a>, <a class="txt" href="#E46:14"><span class="lab"><font color="Green" title="E54">A103</font></span></a>, <a class="txt" href="#E43:14"><span class="lab"><font color="Green" title="E51">A66</font></span></a>, <a class="txt" href="#E30:14"><span class="lab"><font color="Green" title="E38">A30</font></span></a>, <a class="ref" href="incproj.html#D19" title="INCPROJ:def.19">INCPROJ:def 19</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
