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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> 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="b3">A</font>, <font color="Olive" title="b4">B</font>, <font color="Olive" title="b5">C</font>, <font color="Olive" title="b6">Q</font>, <font color="Olive" title="b7">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="b3">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="b4">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="b5">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="b5">C</font> &amp;  not <font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">B</font>,<font color="Olive" title="b5">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Olive" title="b3">A</font>,<font color="Olive" title="b5">C</font>,<font color="Olive" title="b6">Q</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &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">Q</font> &amp; <font color="Olive" title="b3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">Q</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="b7">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="b7">O</font> &amp;  not <font color="Olive" title="b4">B</font>,<font color="Olive" title="b5">C</font>,<font color="Olive" title="b7">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  holds <br/> ex <font color="Olive" title="b8">q</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b8">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b7">O</font> &amp;  not <font color="Olive" title="b8">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">A</font> &amp;  not <font color="Olive" title="b8">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b6">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b5">C</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">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="b3">A</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">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="b6">Q</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">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="b3">A</font>,<font color="Olive" title="b8">q</font>,<font color="Olive" title="b6">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> 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">Q</font>, <font color="Olive" title="b5">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;  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="b1">A</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b4">Q</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &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="b4">Q</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="b4">Q</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="b5">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="b5">O</font> &amp;  not <font color="Olive" title="b2">B</font>,<font color="Olive" title="b3">C</font>,<font color="Olive" title="b5">O</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  holds <br/> ex <font color="Olive" title="b6">q</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b6">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b5">O</font> &amp;  not <font color="Olive" title="b6">q</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="Olive" title="b6">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">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="b4">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="Olive" title="b6">q</font>,<font color="Olive" title="b4">Q</font>)</span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font>, <font color="Maroon" title="c6">C</font>, <font color="Maroon" title="c7">Q</font>, <font color="Maroon" title="c8">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="c4">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="c5">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="c6">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="c6">C</font> &amp;  not <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &amp; <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c7">Q</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  &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">Q</font> &amp; <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">Q</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="c8">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="c8">O</font> &amp;  not <font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c8">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#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">O</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">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="c7">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">Q</font>)</span>)</span> ) )</span><br/>















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:22"/><span class="lab"><font color="Green" title="E17">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="c4">A</font>
 <span class="kw">and </span><br/><a NAME="E2:22"/><span class="lab"><font color="Green" title="E18">A2</font></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="c5">B</font>
 <span class="kw">and </span><br/><a NAME="E3:22"/><span class="lab"><font color="Green" title="E19">A3</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">C</font>
 <span class="kw">and </span><br/><a NAME="E4:22"/><span class="lab"><font color="Green" title="E20">A4</font></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="c6">C</font> &amp;  not <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">C</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a>  )
 <span class="kw">and </span><br/><a NAME="E5:22"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c7">Q</font> <a href="projred2.html#R1" title="PROJRED2:pred.1">are_concurrent</a> 
 <span class="kw">and </span><br/><a NAME="E6:22"/><span class="lab"><font color="Green" title="E22">A6</font></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="c7">Q</font> &amp; <font color="Maroon" title="c4">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">Q</font> )
 <span class="kw">and </span><br/><a NAME="E7:22"/><span class="lab"><font color="Green" title="E23">A7</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="E8:22"/><span class="lab"><font color="Green" title="E24">A8</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="c8">O</font>
 <span class="kw">and </span><br/><a NAME="E9:22"/><span class="lab"><font color="Green" title="E25">A9</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="c8">O</font>
 <span class="kw">and </span><br/><a NAME="E10:22"/><span class="lab"><font color="Green" title="E26">A10</font></span>: 
 not <font color="Maroon" title="c5">B</font>,<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c8">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#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">O</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">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="c7">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">Q</font>)</span>)</span> )</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c9">c</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="E12:22"/><span class="lab"><font color="Green" title="E27">A11</font></span>: 
( <font color="Maroon" title="c9">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c9">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c6">C</font> )
 <span class="kw">and </span><br/><a NAME="E13:22"/><span class="lab"><font color="Green" title="E28">A12</font></span>: 
<font color="Maroon" title="c9">c</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="projred2.html#D1" target="_self" title="PROJRED2:def.1">Def1</a></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="E15:22"/><span class="lab"><font color="Green" title="E29">A13</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="c6">C</font>
 <span class="kw">and </span><br/><a NAME="E16:22"/><span class="lab"><font color="Green" title="E30">A14</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="c5">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="c11">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="E18:22"/><span class="lab"><font color="Green" title="E31">A15</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="c11">O1</font> &amp; <font color="Maroon" title="c10">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">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="c12">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="E20:22"/><span class="lab"><font color="Green" title="E32">A16</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="c12">O3</font> &amp; <font color="Maroon" title="c10">d</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">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="c13">pp9</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="E22:22"/><span class="lab"><font color="Green" title="E33">A17</font></span>: 
<font color="Maroon" title="c13">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c12">O3</font>
 <span class="kw">and </span><br/><a NAME="E23:22"/><span class="lab"><font color="Green" title="E34">A18</font></span>: 
<font color="Maroon" title="c13">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</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="c14">p</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="E25:22"/><span class="lab"><font color="Green" title="E35">A19</font></span>: 
<font color="Maroon" title="c14">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font>
 <span class="kw">and </span><br/><a NAME="E26:22"/><span class="lab"><font color="Green" title="E36">A20</font></span>: 
<font color="Maroon" title="c14">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">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/>
<span class="kw">consider </span><font color="Maroon" title="c15">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="E28:22"/><span class="lab"><font color="Green" title="E37">A21</font></span>: 
( <font color="Maroon" title="c14">p</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">O2</font> &amp; <font color="Maroon" title="c13">pp9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">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/>
<span class="kw">consider </span><font color="Maroon" title="c16">q</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="E30:22"/><span class="lab"><font color="Green" title="E38">A22</font></span>: 
<font color="Maroon" title="c16">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">O</font>
 <span class="kw">and </span><br/><a NAME="E31:22"/><span class="lab"><font color="Green" title="E39">A23</font></span>: 
<font color="Maroon" title="c16">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c15">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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:22_1"/><span class="lab"><font color="Green" title="E40">A24</font></span>: 
<font color="Maroon" title="c7">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">C</font>
 ; <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>, <font color="Olive" title="b2">q</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b2">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">O</font> &amp;  not <font color="Olive" title="b2">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp;  not <font color="Olive" title="b2">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">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="c7">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Olive" title="b2">q</font>,<font color="Maroon" title="c7">Q</font>)</span>)</span> )</span><br/><span class="kw">take </span><font color="Maroon" title="c17">q</font> = <font color="Maroon" title="c16">q</font>; <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#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">O</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">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="c7">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">Q</font>)</span>)</span> )</span><br/><a NAME="E2:22_1"/><span class="lab"><font color="Green" title="E41">A25</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="c10">d</font>,<font color="Maroon" title="c13">pp9</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">O3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:22"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E22:22"><span class="lab"><font color="Green" title="E33">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="E3:22_1"/><span class="lab"><font color="Green" title="E42">A26</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="c10">d</font>,<font color="Maroon" title="c14">p</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="c11">O1</font> &amp; <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c17">q</font>,<font color="Maroon" title="c14">p</font>,<font color="Maroon" title="c13">pp9</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">O2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:22"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E31:22"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/><a NAME="E4:22_1"/><span class="lab"><font color="Green" title="E43">A27</font></span>: 
( <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c14">p</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="c4">A</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c10">d</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">C</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:22"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="txt" href="#E15:22"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E25:22"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="ref" href="incsp_1.html#T1" title="INCSP_1:th.1">INCSP_1:1</a></span>;<br/><a NAME="E5:22_1"/><span class="lab"><font color="Green" title="E44">A28</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="c17">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="c8">O</font> &amp; <span class="p1"><a href="domain_1.html#K7" title="DOMAIN_1:func.7">{</a><span class="default"><font color="Maroon" title="c9">c</font>,<font color="Maroon" title="c13">pp9</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="c7">Q</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E9:22"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E13:22"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E23:22"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E30:22"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="ref" href="incsp_1.html#T1" title="INCSP_1:th.1">INCSP_1:1</a>, <a class="ref" href="incsp_1.html#T2" title="INCSP_1:th.2">INCSP_1:2</a></span>;<br/><a NAME="E6:22_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A29</font></span>: 
(  not <font color="Maroon" title="c17">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp;  not <font color="Maroon" title="c17">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:22"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E10:22"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="txt" href="#E16:22"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E43">A27</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E42">A26</font></span></a>, <a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E41">A25</font></span></a>, <a class="ref" href="projred2.html#T16" target="_self" title="PROJRED2:th.16">Th17</a></span>;<br/><a NAME="E7:22_1"/>
<font color="Maroon" title="c17">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E7:22"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="txt" href="#E10:22"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="txt" href="#E16:22"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E1:22_1"><span class="lab"><font color="Green" title="E40">A24</font></span></a>, <a class="txt" href="#E4:22_1"><span class="lab"><font color="Green" title="E43">A27</font></span></a>, <a class="txt" href="#E5:22_1"><span class="lab"><font color="Green" title="E44">A28</font></span></a>, <a class="txt" href="#E3:22_1"><span class="lab"><font color="Green" title="E42">A26</font></span></a>, <a class="txt" href="#E2:22_1"><span class="lab"><font color="Green" title="E41">A25</font></span></a>, <a class="ref" href="projred2.html#T16" target="_self" title="PROJRED2:th.16">Th17</a></span>;<br/><a NAME="E8:22_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">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="c7">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Maroon" title="c17">q</font>,<font color="Maroon" title="c7">Q</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E2:22"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E4:22"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E6:22"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="txt" href="#E9:22"><span class="lab"><font color="Green" title="E25">A9</font></span></a>, <a class="txt" href="#E10:22"><span class="lab"><font color="Green" title="E26">A10</font></span></a>, <a class="txt" href="#E12:22"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="txt" href="#E13:22"><span class="lab"><font color="Green" title="E28">A12</font></span></a>, <a class="txt" href="#E15:22"><span class="lab"><font color="Green" title="E29">A13</font></span></a>, <a class="txt" href="#E16:22"><span class="lab"><font color="Green" title="E30">A14</font></span></a>, <a class="txt" href="#E18:22"><span class="lab"><font color="Green" title="E31">A15</font></span></a>, <a class="txt" href="#E20:22"><span class="lab"><font color="Green" title="E32">A16</font></span></a>, <a class="txt" href="#E25:22"><span class="lab"><font color="Green" title="E35">A19</font></span></a>, <a class="txt" href="#E26:22"><span class="lab"><font color="Green" title="E36">A20</font></span></a>, <a class="txt" href="#E22:22"><span class="lab"><font color="Green" title="E33">A17</font></span></a>, <a class="txt" href="#E23:22"><span class="lab"><font color="Green" title="E34">A18</font></span></a>, <a class="txt" href="#E28:22"><span class="lab"><font color="Green" title="E37">A21</font></span></a>, <a class="txt" href="#E30:22"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E31:22"><span class="lab"><font color="Green" title="E39">A23</font></span></a>, <a class="txt" href="#E6:22_1"><span class="lab"><font color="Green" title="E45">A29</font></span></a>, <a class="ref" href="projred2.html#T14" target="_self" title="PROJRED2:th.14">Th15</a></span>;<br/><span class="kw">hence </span><a NAME="E9:22_1"/>
 ex <font color="Olive" title="b1">q</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">O</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">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="c7">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">Q</font>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:22"><span class="lab"><font color="Green" title="E38">A22</font></span></a>, <a class="txt" href="#E6:22_1"><span class="lab"><font color="Green" title="E45">A29</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E33:22"/>
 ex <font color="Olive" title="b1">q</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c8">O</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">A</font> &amp;  not <font color="Olive" title="b1">q</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c7">Q</font> &amp; <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c6">C</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">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="c7">Q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">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="c4">A</font>,<font color="Olive" title="b1">q</font>,<font color="Maroon" title="c7">Q</font>)</span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:22"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E8:22"><span class="lab"><font color="Green" title="E24">A8</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>
