<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">PS</font> be   <a href="parsp_1.html#NM2">ParSp</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PS</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PS</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PS</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PS</font>;<br/><b>let </b><font color="Maroon">q</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PS</font>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PS</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">PS</font>;<br/>















<b>assume </b><a NAME="E1:57"/><i><font color="Green">E24</font></i>: 
( not <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">q</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">r</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">s</font> &amp; <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">q</font>,<font color="Maroon">r</font> &amp; <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">q</font>,<font color="Maroon">s</font> )
 ;<br/>

<a NAME="E2:57"/><b>then </b><i><font color="Green">E33</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> implies ( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r</font> &amp; <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> ) )
 
<b>by </b><i><a class="ref" href="parsp_1.html#D3" target="_self">Def3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:57_1"/>
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font>
 ;<br/><a NAME="E2:57_1"/><b>then </b>
( not <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">r</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> )
 <b>by </b><i>, <a class="txt" href="parsp_1.html#E14"><i><font color="Green">Lemma34</font></i></a>, <a class="txt" href="parsp_1.html#E15"><i><font color="Green">Lemma35</font></i></a>, </i>;<br/><a NAME="E3:57_1"/><b>then </b>
( not <font color="Maroon">p</font>,<font color="Maroon">q</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">r</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">r</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">s</font> &amp; <font color="Maroon">q</font>,<font color="Maroon">r</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">q</font>,<font color="Maroon">s</font> )
 <b>by </b><i>, <a class="txt" href="parsp_1.html#E14"><i><font color="Green">Lemma34</font></i></a></i>;<br/><b>hence </b><a NAME="E4:57_1"/>
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="parsp_1.html#T7" target="_self">Th7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:57"/>
<font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 <b>by </b><i><a class="ref" href="parsp_1.html#D5" target="_self">Def5</a></i>;<br/>


</div>
