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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>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FdSp</font>  st  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> holds <br/>(  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b3">c</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b2">b</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> )</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>, <font color="Maroon" title="c5">d</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"> (  <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">c</font>,<font color="Maroon" title="c5">d</font> implies (  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> ) )</span><br/>









<span class="kw">assume </span><a NAME="E1:48"/><span class="lab"><font color="Green" title="E39">A1</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">c</font>,<font color="Maroon" title="c5">d</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">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> )</span><br/>

<a NAME="E2:48"/><span class="kw">then </span>
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_2.html#T31" target="_self" title="PARSP_2:th.31">Th39</a></span>;<br/>
<a NAME="E3:48"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A2</font></span>: 
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="parsp_2.html#T30" target="_self" title="PARSP_2:th.30">Th38</a></span>;<br/>
<a NAME="E4:48"/>
 <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="ref" href="parsp_2.html#T32" target="_self" title="PARSP_2:th.32">Th40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:48"/>
(  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> &amp;  <a href="parsp_2.html#R2" title="PARSP_2:pred.2">parallelogram</a> <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:48"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="txt" href="#E3:48"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="parsp_2.html#T30" target="_self" title="PARSP_2:th.30">Th38</a>, <a class="ref" href="parsp_2.html#T31" target="_self" title="PARSP_2:th.31">Th39</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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