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<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>assume </b><a NAME="E1:61"/><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">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">q</font> )
 ;<br/>

<b>assume </b><a NAME="E2:61"/><i><font color="Green">E33</font></i>: 
( <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">a</font> &amp; <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">b</font> &amp; <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">c</font> )
 ;<br/>

<a NAME="E3:61"/><b>then </b><i><font color="Green">E41</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="parsp_1.html#D5" target="_self">Def5</a>, <a class="txt" href="parsp_1.html#E14"><i><font color="Green">Lemma34</font></i></a></i>;<br/>
<a NAME="E4:61"/>
( <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">p</font>,<font color="Maroon">a</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">p</font>,<font color="Maroon">c</font> )
 
<b>by </b><i><a class="ref" href="parsp_1.html#D5" target="_self">Def5</a>, , <a class="txt" href="parsp_1.html#E14"><i><font color="Green">Lemma34</font></i></a></i>;<br/>
<a NAME="E5:61"/><b>then </b>
( <font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <font color="Maroon">a</font>,<font color="Maroon">p</font> <a href="parsp_1.html#R1" target="_self">'||'</a> <font color="Maroon">a</font>,<font color="Maroon">c</font> )
 
<b>by </b><i><a class="txt" href="parsp_1.html#E3:61"><i><font color="Green">E41</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:61"/>
contradiction
 <b>by </b><i><a class="ref" href="parsp_1.html#D5" target="_self">Def5</a>, , <a class="txt" href="parsp_1.html#E14"><i><font color="Green">Lemma34</font></i></a></i>;<br/>


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