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<span class="kw">let </span><font color="Maroon" title="c1">IPP</font> be   <a href="incproj.html#V5" title="INCPROJ:attr.5">2-dimensional</a>   <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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">q</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="b5">A</font>, <font color="Olive" title="b6">B</font>, <font color="Olive" title="b7">C</font>, <font color="Olive" title="b8">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  not <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">A</font> &amp;  not <font color="Olive" title="b2">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b6">B</font> &amp;  not <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">C</font> &amp;  not <font color="Olive" title="b2">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">C</font> &amp; <font color="Olive" title="b3">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">A</font> &amp; <font color="Olive" title="b3">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">C</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b1">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">O</font> &amp; <font color="Olive" title="b2">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">O</font> &amp; <font color="Olive" title="b4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b8">O</font> &amp;  not <font color="Olive" title="b4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">A</font> &amp; <font color="Olive" title="b4">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp;  not <font color="Olive" title="b5">A</font>,<font color="Olive" title="b6">B</font>,<font color="Olive" title="b7">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b6">B</font>,<font color="Olive" title="b7">C</font>,<font color="Olive" title="b8">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  holds <br/> ex <font color="Olive" title="b9">Q</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b3">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b9">Q</font> &amp;  not <font color="Olive" title="b2">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b9">Q</font> &amp;  not <font color="Olive" title="b4">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b9">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b7">C</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b6">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b5">A</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b7">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b9">Q</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b6">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b5">A</font>,<font color="Olive" title="b4">q</font>,<font color="Olive" title="b9">Q</font>)</span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">q</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font>, <font color="Olive" title="b3">C</font>, <font color="Olive" title="b4">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  not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">A</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">B</font> &amp;  not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">C</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">C</font> &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">C</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">O</font> &amp; <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">O</font> &amp; <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">O</font> &amp;  not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">A</font> &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp;  not <font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b4">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  holds <br/> ex <font color="Olive" title="b5">Q</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">Q</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">Q</font> &amp;  not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b3">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b2">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b1">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b3">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b5">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b2">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b1">A</font>,<font color="Maroon" title="c5">q</font>,<font color="Olive" title="b5">Q</font>)</span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">A</font>, <font color="Maroon" title="c7">B</font>, <font color="Maroon" title="c8">C</font>, <font color="Maroon" title="c9">O</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="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">A</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font> &amp;  not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">C</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">C</font> &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">A</font> &amp; <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">C</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">O</font> &amp; <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">O</font> &amp; <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">O</font> &amp;  not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">A</font> &amp; <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp;  not <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c9">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  implies  ex <font color="Olive" title="b1">Q</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp;  not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c5">q</font>,<font color="Olive" title="b1">Q</font>)</span>)</span> ) )</span><br/>

















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:28"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
(  not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">A</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font> &amp;  not <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">C</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">C</font> )
 <span class="kw">and </span><br/><a NAME="E2:28"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">A</font>
 <span class="kw">and </span><br/><a NAME="E3:28"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">C</font>
 <span class="kw">and </span><br/><a NAME="E4:28"/><span class="lab"><font color="Green" title="E24">A4</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 <span class="kw">and </span><br/><a NAME="E5:28"/><span class="lab"><font color="Green" title="E25">A5</font></span>: 
( <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">O</font> &amp; <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">O</font> )
 <span class="kw">and </span><br/><a NAME="E6:28"/><span class="lab"><font color="Green" title="E26">A6</font></span>: 
<font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">O</font>
 <span class="kw">and </span><br/><a NAME="E7:28"/><span class="lab"><font color="Green" title="E27">A7</font></span>: 
 not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">A</font>
 <span class="kw">and </span><br/><a NAME="E8:28"/><span class="lab"><font color="Green" title="E28">A8</font></span>: 
( <font color="Maroon" title="c5">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> &amp;  not <font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  )
 <span class="kw">and </span><br/><a NAME="E9:28"/><span class="lab"><font color="Green" title="E29">A9</font></span>: 
<font color="Maroon" title="c7">B</font>,<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c9">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">Q</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp;  not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c5">q</font>,<font color="Olive" title="b1">Q</font>)</span>)</span> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c10">d</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E11:28"/><span class="lab"><font color="Green" title="E30">A10</font></span>: 
<font color="Maroon" title="c10">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font>
 <span class="kw">and </span><br/><a NAME="E12:28"/><span class="lab"><font color="Green" title="E31">A11</font></span>: 
<font color="Maroon" title="c10">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">C</font>
 <span class="kw">and </span><br/><a NAME="E13:28"/><span class="lab"><font color="Green" title="E32">A12</font></span>: 
<font color="Maroon" title="c10">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c9">O</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:28"><span class="lab"><font color="Green" title="E29">A9</font></span></a>, <a class="ref" href="projred2.html#D1" target="_self" title="PROJRED2:def.1">Def1</a></span>;<br/>
<a NAME="E14:28"/><span class="lab"><font color="Green" title="E33">A13</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">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">d</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="c9">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E13:28"><span class="lab"><font color="Green" title="E32">A12</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">o</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E16:28"/><span class="lab"><font color="Green" title="E34">A14</font></span>: 
<font color="Maroon" title="c11">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">A</font>
 <span class="kw">and </span><br/><a NAME="E17:28"/><span class="lab"><font color="Green" title="E35">A15</font></span>: 
<font color="Maroon" title="c11">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font>
 <span class="kw">by</span> <span class="lab"><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="c12">O1</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="E19:28"/><span class="lab"><font color="Green" title="E36">A16</font></span>: 
( <font color="Maroon" title="c11">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">O1</font> &amp; <font color="Maroon" title="c2">a</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">O1</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D5" title="INCPROJ:def.5">INCPROJ:def 5</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">o9</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E21:28"/><span class="lab"><font color="Green" title="E37">A17</font></span>: 
<font color="Maroon" title="c13">o9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">C</font>
 <span class="kw">and </span><br/><a NAME="E22:28"/><span class="lab"><font color="Green" title="E38">A18</font></span>: 
<font color="Maroon" title="c13">o9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">O1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E23:28"/><span class="lab"><font color="Green" title="E39">A19</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">a</font>,<font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c13">o9</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">O1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:28"><span class="lab"><font color="Green" title="E36">A16</font></span></a>, <a class="txt" href="#E22:28"><span class="lab"><font color="Green" title="E38">A18</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<a NAME="E24:28"/><span class="lab"><font color="Green" title="E40">A20</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">a</font>,<font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c13">o9</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">O1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:28"><span class="lab"><font color="Green" title="E36">A16</font></span></a>, <a class="txt" href="#E22:28"><span class="lab"><font color="Green" title="E38">A18</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<a NAME="E25:28"/><span class="lab"><font color="Green" title="E41">A21</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c10">d</font>,<font color="Maroon" title="c13">o9</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="c8">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E12:28"><span class="lab"><font color="Green" title="E31">A11</font></span></a>, <a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E37">A17</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<a NAME="E26:28"/><span class="lab"><font color="Green" title="E42">A22</font></span>: 
<span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c10">d</font>,<font color="Maroon" title="c13">o9</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="c8">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:28"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E12:28"><span class="lab"><font color="Green" title="E31">A11</font></span></a>, <a class="txt" href="#E21:28"><span class="lab"><font color="Green" title="E37">A17</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">O2</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="E28:28"/><span class="lab"><font color="Green" title="E43">A23</font></span>: 
( <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O2</font> &amp; <font color="Maroon" title="c13">o9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O2</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D5" title="INCPROJ:def.5">INCPROJ:def 5</a></span>;<br/>
<a NAME="E29:28"/><span class="lab"><font color="Green" title="E44">A24</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">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">d</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="c9">O</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E13:28"><span class="lab"><font color="Green" title="E32">A12</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<a NAME="E30:28"/><span class="lab"><font color="Green" title="E45">A25</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c11">o</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E34">A14</font></span></a>, <a class="ref" href="incsp_1.html#T1" title="INCSP_1:th.1">INCSP_1:1</a></span>;<br/>
<a NAME="E31:28"/><span class="lab"><font color="Green" title="E46">A26</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c11">o</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c6">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E16:28"><span class="lab"><font color="Green" title="E34">A14</font></span></a>, <a class="ref" href="incsp_1.html#T1" title="INCSP_1:th.1">INCSP_1:1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">O3</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="E33:28"/><span class="lab"><font color="Green" title="E47">A27</font></span>: 
( <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O3</font> &amp; <font color="Maroon" title="c11">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O3</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D5" title="INCPROJ:def.5">INCPROJ:def 5</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c16">o99</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E35:28"/><span class="lab"><font color="Green" title="E48">A28</font></span>: 
<font color="Maroon" title="c16">o99</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">B</font>
 <span class="kw">and </span><br/><a NAME="E36:28"/>
<font color="Maroon" title="c16">o99</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E37:28"/><span class="lab"><font color="Green" title="E49">A29</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">o</font>,<font color="Maroon" title="c16">o99</font>,<font color="Maroon" title="c10">d</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="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E30">A10</font></span></a>, <a class="txt" href="#E17:28"><span class="lab"><font color="Green" title="E35">A15</font></span></a>, <a class="txt" href="#E35:28"><span class="lab"><font color="Green" title="E48">A28</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c17">oo9</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E39:28"/><span class="lab"><font color="Green" title="E50">A30</font></span>: 
<font color="Maroon" title="c17">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c14">O2</font>
 <span class="kw">and </span><br/><a NAME="E40:28"/><span class="lab"><font color="Green" title="E51">A31</font></span>: 
<font color="Maroon" title="c17">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D9" title="INCPROJ:def.9">INCPROJ:def 9</a></span>;<br/>
<a NAME="E41:28"/><span class="lab"><font color="Green" title="E52">A32</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">b</font>,<font color="Maroon" title="c13">o9</font>,<font color="Maroon" title="c17">oo9</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">O2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:28"><span class="lab"><font color="Green" title="E43">A23</font></span></a>, <a class="txt" href="#E39:28"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<a NAME="E42:28"/><span class="lab"><font color="Green" title="E53">A33</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">o</font>,<font color="Maroon" title="c17">oo9</font>,<font color="Maroon" title="c5">q</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">O3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:28"><span class="lab"><font color="Green" title="E47">A27</font></span></a>, <a class="txt" href="#E40:28"><span class="lab"><font color="Green" title="E51">A31</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<a NAME="E43:28"/><span class="lab"><font color="Green" title="E54">A34</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">o</font>,<font color="Maroon" title="c17">oo9</font>,<font color="Maroon" title="c5">q</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">O3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:28"><span class="lab"><font color="Green" title="E47">A27</font></span></a>, <a class="txt" href="#E40:28"><span class="lab"><font color="Green" title="E51">A31</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<a NAME="E44:28"/><span class="lab"><font color="Green" title="E55">A35</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">b</font>,<font color="Maroon" title="c13">o9</font>,<font color="Maroon" title="c17">oo9</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">O2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:28"><span class="lab"><font color="Green" title="E43">A23</font></span></a>, <a class="txt" href="#E39:28"><span class="lab"><font color="Green" title="E50">A30</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c18">Q</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="E46:28"/><span class="lab"><font color="Green" title="E56">A36</font></span>: 
<font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">Q</font>
 <span class="kw">and </span><br/><a NAME="E47:28"/><span class="lab"><font color="Green" title="E57">A37</font></span>: 
<font color="Maroon" title="c17">oo9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="incproj.html#D5" title="INCPROJ:def.5">INCPROJ:def 5</a></span>;<br/>
<a NAME="E48:28"/><span class="lab"><font color="Green" title="E58">A38</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c17">oo9</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c18">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:28"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E47:28"><span class="lab"><font color="Green" title="E57">A37</font></span></a>, <a class="ref" href="incsp_1.html#T1" title="INCSP_1:th.1">INCSP_1:1</a></span>;<br/>
<a NAME="E49:28"/><span class="lab"><font color="Green" title="E59">A39</font></span>: 
<span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c17">oo9</font></span><a href="domain_1.html#K7" title="DOMAIN_1:func.7">}</a></span> <a href="incsp_1.html#R4" title="INCSP_1:pred.4">on</a> <font color="Maroon" title="c18">Q</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:28"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E47:28"><span class="lab"><font color="Green" title="E57">A37</font></span></a>, <a class="ref" href="incsp_1.html#T1" title="INCSP_1:th.1">INCSP_1:1</a></span>;<br/>
<a NAME="E50:28"/><span class="lab"><font color="Green" title="E60">A40</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">o</font>,<font color="Maroon" title="c16">o99</font>,<font color="Maroon" title="c10">d</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="c7">B</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:28"><span class="lab"><font color="Green" title="E30">A10</font></span></a>, <a class="txt" href="#E17:28"><span class="lab"><font color="Green" title="E35">A15</font></span></a>, <a class="txt" href="#E35:28"><span class="lab"><font color="Green" title="E48">A28</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/>
<a NAME="E51:28"/><span class="kw">then </span>
(  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">Q</font> &amp; <font color="Maroon" title="c6">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">Q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E27">A7</font></span></a>, <a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="txt" href="#E30:28"><span class="lab"><font color="Green" title="E45">A25</font></span></a>, <a class="txt" href="#E25:28"><span class="lab"><font color="Green" title="E41">A21</font></span></a>, <a class="txt" href="#E14:28"><span class="lab"><font color="Green" title="E33">A13</font></span></a>, <a class="txt" href="#E48:28"><span class="lab"><font color="Green" title="E58">A38</font></span></a>, <a class="txt" href="#E23:28"><span class="lab"><font color="Green" title="E39">A19</font></span></a>, <a class="txt" href="#E41:28"><span class="lab"><font color="Green" title="E52">A32</font></span></a>, <a class="txt" href="#E43:28"><span class="lab"><font color="Green" title="E54">A34</font></span></a>, <a class="ref" href="projred2.html#T19" target="_self" title="PROJRED2:th.19">Th20</a></span>;<br/>
<a NAME="E52:28"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A41</font></span>: 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c18">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c18">Q</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="txt" href="#E31:28"><span class="lab"><font color="Green" title="E46">A26</font></span></a>, <a class="txt" href="#E37:28"><span class="lab"><font color="Green" title="E49">A29</font></span></a>, <a class="txt" href="#E26:28"><span class="lab"><font color="Green" title="E42">A22</font></span></a>, <a class="txt" href="#E29:28"><span class="lab"><font color="Green" title="E44">A24</font></span></a>, <a class="txt" href="#E49:28"><span class="lab"><font color="Green" title="E59">A39</font></span></a>, <a class="txt" href="#E24:28"><span class="lab"><font color="Green" title="E40">A20</font></span></a>, <a class="txt" href="#E44:28"><span class="lab"><font color="Green" title="E55">A35</font></span></a>, <a class="txt" href="#E42:28"><span class="lab"><font color="Green" title="E53">A33</font></span></a>, <a class="ref" href="projred2.html#T15" target="_self" title="PROJRED2:th.15">Th16</a></span>;<br/>
<a NAME="E53:28"/>
(  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">Q</font> &amp;  not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c18">Q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E7:28"><span class="lab"><font color="Green" title="E27">A7</font></span></a>, <a class="txt" href="#E8:28"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="txt" href="#E30:28"><span class="lab"><font color="Green" title="E45">A25</font></span></a>, <a class="txt" href="#E50:28"><span class="lab"><font color="Green" title="E60">A40</font></span></a>, <a class="txt" href="#E25:28"><span class="lab"><font color="Green" title="E41">A21</font></span></a>, <a class="txt" href="#E14:28"><span class="lab"><font color="Green" title="E33">A13</font></span></a>, <a class="txt" href="#E48:28"><span class="lab"><font color="Green" title="E58">A38</font></span></a>, <a class="txt" href="#E23:28"><span class="lab"><font color="Green" title="E39">A19</font></span></a>, <a class="txt" href="#E41:28"><span class="lab"><font color="Green" title="E52">A32</font></span></a>, <a class="txt" href="#E43:28"><span class="lab"><font color="Green" title="E54">A34</font></span></a>, <a class="ref" href="projred2.html#T19" target="_self" title="PROJRED2:th.19">Th20</a></span>;<br/>
<span class="kw">hence </span><a NAME="E54:28"/>
 ex <font color="Olive" title="b1">Q</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Maroon" title="c4">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp;  not <font color="Maroon" title="c3">b</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp;  not <font color="Maroon" title="c5">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b1">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c8">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c8">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b1">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">A</font>,<font color="Maroon" title="c5">q</font>,<font color="Olive" title="b1">Q</font>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:28"><span class="lab"><font color="Green" title="E56">A36</font></span></a>, <a class="txt" href="#E52:28"><span class="lab"><font color="Green" title="E61">A41</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
