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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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</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">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  holds <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  implies ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:29"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  )</span><br/>

<a NAME="E2:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A1</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</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="E3:29"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A2</font></span>: 
( <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_1.html#T41" title="PARSP_1:th.41">PARSP_1:41</a></span>;<br/>
<a NAME="E4:29"/><span class="lab"><font color="Green" title="E25">A3</font></span>: 
<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="parsp_1.html#T41" title="PARSP_1:th.41">PARSP_1:41</a></span>;<br/>
<a NAME="E5:29"/>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:29"><span class="lab"><font color="Green" title="E23">A1</font></span></a>, <a class="ref" href="parsp_1.html#T41" title="PARSP_1:th.41">PARSP_1:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:29"/>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</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="#E3:29"><span class="lab"><font color="Green" title="E24">A2</font></span></a>, <a class="txt" href="#E4:29"><span class="lab"><font color="Green" title="E25">A3</font></span></a>, <a class="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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