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<span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">are_collinear</a> </span><br/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">are_collinear</a>  )</span><br/>





<span class="kw">consider </span><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><span class="kw"> such that </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E23">A1</font></span>: 
 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">are_collinear</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="collsp.html#D6" target="_self" onmouseover="rs('collsp/D6')" onmouseout="rh()">Def6</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:26"/>
<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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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">are_collinear</a> </span><br/>

<a NAME="E4:26"/><span class="kw">then </span>
(  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">are_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">are_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">are_collinear</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="collsp.html#T3" target="_self" onmouseover="rs('collsp/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:26"/>
 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">are_collinear</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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