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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">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font>  holds <br/>( <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or  not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or  not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or <font color="Olive" title="b1">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">x</font> )</span><br/><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">x</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">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> )</span><br/>









<b>assume </b><a NAME="E1:32"/><i><font color="Green" title="E30">A1</font></i>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</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"> (  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:32_1"/>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">x</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"> (  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> )</span><br/><a NAME="E2:32_1"/><b>then </b>
( not <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  )
 <b>by </b><i><a class="txt" href="parsp_2.html#E1:32"><i><font color="Green" title="E30">A1</font></i></a>, <a class="ref" href="parsp_2.html#T15" target="_self" title="PARSP_2:th.15">Th15</a></i>;<br/><a NAME="E3:32_1"/><b>then </b>
( not <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c2">o</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">x</font> &amp; <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c2">o</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">x</font> )
 <b>by </b><i><a class="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E4:32_1"/>
(  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> )
 <b>by </b><i><a class="ref" href="parsp_1.html#T51" title="PARSP_1:th.51">PARSP_1:51</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="E3:32"/>
(  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or  not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">x</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x</font> )
 ; <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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