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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">b</font>, <font color="Olive" title="b2">q</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">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">b</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">p</font>,<font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">q</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b4">a</font>,<font color="Olive" title="b5">p</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b6">r</font> holds <br/> <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">q</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b6">r</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">c</font>, <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">p</font>, <font color="Maroon" title="c7">r</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"> (  not <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a>  &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">r</font> implies  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">r</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:55"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
 not <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_2.html#R1" title="PARSP_2:pred.1">is_collinear</a> 
 <span class="kw">and </span><br/><a NAME="E2:55"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font>
 <span class="kw">and </span><br/><a NAME="E3:55"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">r</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">r</font></span><br/>

<a NAME="E4:55"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E48">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="E5:55"/>
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">p</font> &amp; <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">p</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E47">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="E6:55"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A5</font></span>: 
<font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:55"><span class="lab"><font color="Green" title="E49">A4</font></span></a>, <a class="ref" href="parsp_1.html#D12" title="PARSP_1:def.12">PARSP_1:def 12</a></span>;<br/>
<a NAME="E7:55"/>
<font color="Maroon" title="c2">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">q</font>,<font color="Maroon" title="c7">r</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:55"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="txt" href="#E3:55"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="ref" href="parsp_2.html#T39" target="_self" title="PARSP_2:th.39">Th47</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:55"/>
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">b</font>,<font color="Maroon" title="c3">q</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c7">r</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:55"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="txt" href="#E6:55"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="ref" href="parsp_2.html#D3" target="_self" title="PARSP_2:def.3">Def3</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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