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<b>let </b><font color="Maroon" title="c10">CLSP</font> be  <a href="collsp.html#V4" title="COLLSP:attr.4">proper</a> <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> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c10">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> holds <br/> ex <font color="Olive" title="b3">r</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c10">CLSP</font> st not <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/><b>let </b><font color="Maroon" title="c11">p</font>, <font color="Maroon" title="c12">q</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c10">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="c11">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">q</font> implies  ex <font color="Olive" title="b1">r</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c10">CLSP</font> st not <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>,<font color="Olive" title="b1">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )</span><br/>





<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E24">A1</font></i>: 
<font color="Maroon" title="c11">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not for <font color="Olive" title="b1">r</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c10">CLSP</font> holds  <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>,<font color="Olive" title="b1">r</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> </span><br/>

<b>consider </b><font color="Maroon" title="c13">a</font>, <font color="Maroon" title="c14">b</font>, <font color="Maroon" title="c15">c</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c10">CLSP</font><b> such that </b><br/><a NAME="E3:28"/><i><font color="Green" title="E25">A2</font></i>: 
not <font color="Maroon" title="c13">a</font>,<font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c15">c</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a> 
 <b>by </b><i><a class="ref" href="collsp.html#D6" target="_self" title="COLLSP:def.6">Def6</a></i>;<br/>
<a NAME="E4:28"/>
(  not <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>,<font color="Maroon" title="c13">a</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>,<font color="Maroon" title="c14">b</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>,<font color="Maroon" title="c15">c</font> <a href="collsp.html#R1" title="COLLSP:pred.1">is_collinear</a>  )
 
<b>by </b><i><a class="txt" href="collsp.html#E1:28"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="collsp.html#E3:28"><i><font color="Green" title="E25">A2</font></i></a>, <a class="ref" href="collsp.html#T8" target="_self" title="COLLSP:th.8">Th8</a></i>;<br/>
<b>hence </b><a NAME="E5:28"/>
not for <font color="Olive" title="b1">r</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c10">CLSP</font> holds  <font color="Maroon" title="c11">p</font>,<font color="Maroon" title="c12">q</font>,<font color="Olive" title="b1">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"> verum</span><br/>


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