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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">o</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="b2">A</font>, <font color="Olive" title="b3">B</font>, <font color="Olive" title="b4">C</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">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b2">A</font> &amp;  not <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">B</font> &amp;  not <font color="Olive" title="b1">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b4">C</font> holds <br/><span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b4">C</font>,<font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">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="b2">A</font>,<font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b2">A</font>,<font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">B</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c2">o</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> 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">o</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="c2">o</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">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Olive" title="b3">C</font> holds <br/><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="c2">o</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">o</font>,<font color="Olive" title="b3">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Olive" title="b1">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Olive" title="b2">B</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font>, <font color="Maroon" title="c5">C</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">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font> &amp;  not <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">B</font> &amp;  not <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">C</font> implies <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">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="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>) )</span><br/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 not <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E2:14"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 not <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">B</font>
 <span class="kw">and </span><br/><a NAME="E3:14"/><span class="lab"><font color="Green" title="E12">A3</font></span>: 
 not <font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">C</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">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="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">f</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">g</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c8">h</font> =  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>);<br/>
<a NAME="E4:14"/><span class="lab"><font color="Green" title="E13">A4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="projred2.html#T4" target="_self" title="PROJRED2:th.4">Th5</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">X</font> =  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font>;<br/>
<a NAME="E5:14"/><span class="lab"><font color="Green" title="E14">A5</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="ref" href="projred2.html#T4" target="_self" title="PROJRED2:th.4">Th5</a></span>;<br/>
<a NAME="E6:14"/><span class="lab"><font color="Green" title="E15">A6</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="incsp_1.html#NM1" title="INCSP_1:NM.1">POINT</a> of <font color="Maroon" title="c1">IPP</font>  st <font color="Olive" title="b1">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font> holds <br/><span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">x</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"> ( <font color="Maroon" title="c10">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font> implies <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:14_1"/><span class="lab"><font color="Green" title="E16">A7</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c11">Q1</font> being   <a href="incsp_1.html#NM2" title="INCSP_1:NM.2">LINE</a> of <font color="Maroon" title="c1">IPP</font><span class="kw"> such that </span><br/><a NAME="E3:14_1"/><span class="lab"><font color="Green" title="E17">A8</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">Q1</font>
 <span class="kw">and </span><br/><a NAME="E4:14_1"/><span class="lab"><font color="Green" title="E18">A9</font></span>: 
<font color="Maroon" title="c10">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">Q1</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">x9</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="E6:14_1"/><span class="lab"><font color="Green" title="E19">A10</font></span>: 
( <font color="Maroon" title="c12">x9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">Q1</font> &amp; <font color="Maroon" title="c12">x9</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c5">C</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="E7:14_1"/><span class="lab"><font color="Green" title="E20">A11</font></span>: 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E6:14_1"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">y</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="E9:14_1"/><span class="lab"><font color="Green" title="E21">A12</font></span>: 
( <font color="Maroon" title="c13">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c11">Q1</font> &amp; <font color="Maroon" title="c13">y</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c4">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/>
<a NAME="E10:14_1"/><span class="lab"><font color="Green" title="E22">A13</font></span>: 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>;<br/>
<a NAME="E11:14_1"/>
<font color="Maroon" title="c10">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E16">A7</font></span></a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> = 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E6:14_1"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="txt" href="#E9:14_1"><span class="lab"><font color="Green" title="E21">A12</font></span></a>, <a class="txt" href="#E10:14_1"><span class="lab"><font color="Green" title="E22">A13</font></span></a>, <a class="txt" href="#E7:14_1"><span class="lab"><font color="Green" title="E20">A11</font></span></a>, <a class="ref" href="projred1.html#D1" title="PROJRED1:def.1">PROJRED1:def 1</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E13:14_1"/>
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">x</font>
 ; <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>
<div><span class="lab"><font color="Green" title="E16">A14</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">y</font> <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="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">y</font> )</span><br/><span class="kw">assume </span><a NAME="E1:14_2"/>
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">y</font> <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="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">y</font></span><br/><a NAME="E2:14_2"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</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="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b1">x</font> <a href="incsp_1.html#R1" title="INCSP_1:pred.1">on</a> <font color="Maroon" title="c3">A</font> )
 ;<br/><span class="kw">hence </span><a NAME="E3:14_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">y</font> <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="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E15">A6</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>
<a NAME="E8:14"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)</span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p2">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred2.html#K1" title="PROJRED2:func.1">CHAIN</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E12">A3</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E14">A5</font></span></a>, <a class="ref" href="projred1.html#T22" title="PROJRED1:th.22">PROJRED1:22</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:14"/>
<span class="p1">(<span class="default"><a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c5">C</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">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="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">C</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="projred1.html#K1" title="PROJRED1:func.1">IncProj</a> (<font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">B</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E13">A4</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E16">A14</font></span></a>, <a class="ref" href="funct_1.html#T2" title="FUNCT_1:th.2">FUNCT_1:2</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>
