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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>









<span class="kw">assume </span><a NAME="E1:32"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
 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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:32_1"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
<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> 
 <span class="kw">and </span><br/><a NAME="E2:32_1"/><span class="lab"><font color="Green" title="E32">A3</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E3:32_1"/>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="parsp_2.html#T10" target="_self" title="PARSP_2:th.10">Th15</a></span>;<br/><a NAME="E4:32_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A4</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></span>;<br/><a NAME="E5:32_1"/>
<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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32_1"><span class="lab"><font color="Green" title="E32">A3</font></span></a>, <a class="ref" href="parsp_2.html#T10" target="_self" title="PARSP_2:th.10">Th15</a></span>;<br/><a NAME="E6:32_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A5</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></span>;<br/><a NAME="E7:32_1"/>
 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> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="parsp_2.html#T10" target="_self" title="PARSP_2:th.10">Th15</a></span>;<br/><a NAME="E8:32_1"/><span class="kw">then </span>
 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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></span>;<br/><span class="kw">hence </span><a NAME="E9:32_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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:32_1"><span class="lab"><font color="Green" title="E33">A4</font></span></a>, <a class="txt" href="#E6:32_1"><span class="lab"><font color="Green" title="E34">A5</font></span></a>, <a class="ref" href="parsp_1.html#T33" title="PARSP_1:th.33">PARSP_1:33</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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