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<b>let </b><font color="Maroon" title="c1">FdSp</font> be   <a href="parsp_2.html#NM1" title="PARSP_2:NM.1">FanodesSp</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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</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="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a> </span><br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">q</font> implies  ex <font color="Olive" title="b1">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font> st not <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">r</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  )</span><br/>





<b>assume </b><a NAME="E1:28"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">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="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font> holds  <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">r</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a> </span><br/>

<b>then consider </b><font color="Maroon" title="c4">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font><b> such that </b><br/><a NAME="E3:28"/><i><font color="Green" title="E27">A1</font></i>: 
not <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">r</font>
 <b>by </b><i><a class="ref" href="parsp_2.html#T13" target="_self" title="PARSP_2:th.13">Th13</a></i>;<br/>
<a NAME="E4:28"/>
not <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">r</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a> 
 
<b>by </b><i><a class="txt" href="#E3:28"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E5:28"/>
not for <font color="Olive" title="b1">r</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font> holds  <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>,<font color="Olive" title="b1">r</font> <a href="parsp_2.html#R1" title="PARSP_2: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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