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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">a</font>, <font color="Olive" title="b2">b</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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> holds <br/> ex <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 <br/>( <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>  &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</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">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> implies  ex <font color="Olive" title="b1">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 <br/>( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b1">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:53"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">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 <br/>( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b1">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font><span class="kw"> such that </span><br/><a NAME="E3:53"/><span class="lab"><font color="Green" title="E44">A1</font></span>: 
 not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">p</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="ref" href="parsp_2.html#T14" target="_self" title="PARSP_2:th.14">Th20</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font><span class="kw"> such that </span><br/><a NAME="E5:53"/><span class="lab"><font color="Green" title="E45">A2</font></span>: 
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:53"><span class="lab"><font color="Green" title="E44">A1</font></span></a>, <a class="ref" href="parsp_2.html#T34" target="_self" title="PARSP_2:th.34">Th42</a></span>;<br/>
<a NAME="E6:53"/>
 not <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</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="#E5:53"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="parsp_2.html#T28" target="_self" title="PARSP_2:th.28">Th36</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font><span class="kw"> such that </span><br/><a NAME="E8:53"/><span class="lab"><font color="Green" title="E46">A3</font></span>: 
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_2.html#T34" target="_self" title="PARSP_2:th.34">Th42</a></span>;<br/>
<a NAME="E9:53"/><span class="lab"><font color="Green" title="E47">A4</font></span>: 
<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:53"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="parsp_2.html#D3" target="_self" title="PARSP_2:def.3">Def3</a></span>;<br/>
<a NAME="E10:53"/>
( <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font> &amp; <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="c4">p</font>,<font color="Maroon" title="c5">q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:53"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="parsp_2.html#D3" target="_self" title="PARSP_2:def.3">Def3</a>, <a class="ref" href="parsp_2.html#T26" target="_self" title="PARSP_2:th.26">Th34</a></span>;<br/>
<a NAME="E11:53"/><span class="kw">then </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="c3">b</font>,<font color="Maroon" title="c6">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:53"><span class="lab"><font color="Green" title="E47">A4</font></span></a>, <a class="ref" href="parsp_1.html#T26" title="PARSP_1:th.26">PARSP_1:26</a></span>;<br/>
<a NAME="E12:53"/><span class="kw">then </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="c6">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_1.html#T23" title="PARSP_1:th.23">PARSP_1:23</a></span>;<br/>
<a NAME="E13:53"/><span class="kw">then </span>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">c</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="ref" href="parsp_2.html#D2" target="_self" title="PARSP_2:def.2">Def2</a></span>;<br/>
<a NAME="E14:53"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A5</font></span>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">c</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="ref" href="parsp_2.html#T10" target="_self" title="PARSP_2:th.10">Th15</a></span>;<br/>
<a NAME="E15:53"/><span class="lab"><font color="Green" title="E49">A6</font></span>: 
 not <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">q</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">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:53"><span class="lab"><font color="Green" title="E45">A2</font></span></a>, <a class="ref" href="parsp_2.html#T36" target="_self" title="PARSP_2:th.36">Th44</a></span>;<br/>
<a NAME="E16:53"/>
<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:53"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="parsp_2.html#D3" target="_self" title="PARSP_2:def.3">Def3</a></span>;<br/>
<a NAME="E17:53"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A7</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:53"><span class="lab"><font color="Green" title="E49">A6</font></span></a>, <a class="ref" href="parsp_1.html#T23" title="PARSP_1:th.23">PARSP_1:23</a></span>;<br/>
<a NAME="E18:53"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:53"><span class="lab"><font color="Green" title="E46">A3</font></span></a>, <a class="ref" href="parsp_2.html#T26" target="_self" title="PARSP_2:th.26">Th34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:53"/>
 ex <font color="Olive" title="b1">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 <br/>( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Olive" title="b1">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp; <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Olive" title="b1">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:53"><span class="lab"><font color="Green" title="E50">A7</font></span></a>, <a class="txt" href="#E14:53"><span class="lab"><font color="Green" title="E48">A5</font></span></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/>


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