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<b>let </b><font color="Maroon" title="c5">CLSP</font> be   <a href="collsp.html#NM2" title="COLLSP:NM.2">CollSp</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">r</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">CLSP</font>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">q</font> &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b1">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b2">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b5">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  holds <br/><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font>,<font color="Olive" title="b5">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><b>let </b><font color="Maroon" title="c6">p</font>, <font color="Maroon" title="c7">q</font>, <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c10">r</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">CLSP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">p</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="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c7">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  implies <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/>











<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c6">p</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="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c6">p</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c7">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:17_1"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c8">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><a NAME="E2:17_1"/><b>then </b><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="collsp.html#T11" target="_self" title="COLLSP:th.11">Th11</a></i>;<br/><a NAME="E3:17_1"/>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c9">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="collsp.html#T7" target="_self" title="COLLSP:th.7">Th7</a></i>;<br/><a NAME="E4:17_1"/><b>then </b>
( <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c8">a</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font>,<font color="Maroon" title="c9">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E1:17_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E2:17_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="collsp.html#T8" target="_self" title="COLLSP:th.8">Th8</a>, <a class="ref" href="collsp.html#T13" target="_self" title="COLLSP:th.13">Th13</a></i>;<br/><b>hence </b><a NAME="E5:17_1"/>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="txt" href="#E1:17"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="collsp.html#T8" target="_self" title="COLLSP:th.8">Th8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:17"/>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="collsp.html#T7" target="_self" title="COLLSP:th.7">Th7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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