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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:63_2_1_1"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">CS</font> is <a href="collsp.html#V3">transitive</a>
 ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">r1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">r2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E2:63_2_1_1"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 <b>and </b><br/><a NAME="E3:63_2_1_1"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r2</font> <a href="collsp.html#R1">is_collinear</a>  )
 ;<br/><a NAME="E4:63_2_1_1"/>
( <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="collsp.html#U1">Collinearity</a> of <font color="Maroon">CS</font> &amp; <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r1</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="collsp.html#U1">Collinearity</a> of <font color="Maroon">CS</font> &amp; <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r2</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="collsp.html#U1">Collinearity</a> of <font color="Maroon">CS</font> )
 <b>by </b><i>, <a class="ref" href="collsp.html#D2">COLLSP:def 2</a></i>;<br/><a NAME="E5:63_2_1_1"/><b>then </b>
<span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">r1</font>,<font color="Maroon">r2</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="collsp.html#U1">Collinearity</a> of <font color="Maroon">CS</font>
 <b>by </b><i><a class="ref" href="anproj_2.html#T1" target="_self">Th1</a>, , <a class="ref" href="collsp.html#D4">COLLSP:def 4</a></i>;<br/><b>hence </b><a NAME="E6:63_2_1_1"/>
<font color="Maroon">r</font>,<font color="Maroon">r1</font>,<font color="Maroon">r2</font> <a href="collsp.html#R1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="collsp.html#D2">COLLSP:def 2</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:63_2_1"/><i><font color="Green">E69</font></i>: 
for <font color="Olive">p</font>, <font color="Olive">q</font>, <font color="Olive">r</font>, <font color="Olive">r1</font>, <font color="Olive">r2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>  st <font color="Olive">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">q</font> &amp; <font color="Olive">p</font>,<font color="Olive">q</font>,<font color="Olive">r</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">p</font>,<font color="Olive">q</font>,<font color="Olive">r1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Olive">p</font>,<font color="Olive">q</font>,<font color="Olive">r2</font> <a href="collsp.html#R1">is_collinear</a>  holds <br/><font color="Olive">r</font>,<font color="Olive">r1</font>,<font color="Olive">r2</font> <a href="collsp.html#R1">is_collinear</a> 
 ;<br/>

<b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">r1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>, <font color="Maroon">r2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">CS</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="collsp.html#D4">COLLSP:def 4</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E3:63_2_1"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 <b>and </b><br/><a NAME="E4:63_2_1"/><i><font color="Green">E71</font></i>: 
( <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="collsp.html#U1">Collinearity</a> of <font color="Maroon">CS</font> &amp; <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r1</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="collsp.html#U1">Collinearity</a> of <font color="Maroon">CS</font> &amp; <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r2</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="collsp.html#U1">Collinearity</a> of <font color="Maroon">CS</font> )
 ;<br/>

<a NAME="E5:63_2_1"/>
( <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r1</font> <a href="collsp.html#R1">is_collinear</a>  &amp; <font color="Maroon">p</font>,<font color="Maroon">q</font>,<font color="Maroon">r2</font> <a href="collsp.html#R1">is_collinear</a>  )
 
<b>by </b><i>, <a class="ref" href="collsp.html#D2">COLLSP:def 2</a></i>;<br/>
<a NAME="E6:63_2_1"/><b>then </b>
<font color="Maroon">r</font>,<font color="Maroon">r1</font>,<font color="Maroon">r2</font> <a href="collsp.html#R1">is_collinear</a> 
 
<b>by </b><i><a class="ref" href="anproj_2.html#T1" target="_self">Th1</a>, </i>;<br/>
<b>hence </b><a NAME="E7:63_2_1"/>
<span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">r1</font>,<font color="Maroon">r2</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="collsp.html#U1">Collinearity</a> of <font color="Maroon">CS</font>
 <b>by </b><i><a class="ref" href="collsp.html#D2">COLLSP:def 2</a></i>;<br/>


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