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<b>let </b><font color="Maroon" title="c1">PS</font> be   <a href="parsp_1.html#NM2" title="PARSP_1:NM.2">ParSp</a>;<br/><b>let </b><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">p</font>, <font color="Maroon" title="c6">q</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">PS</font>;<br/>













<b>assume </b><a NAME="E1:54"/><i><font color="Green" title="E42">A1</font></i>: 
( not <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="c2">a</font>,<font color="Maroon" title="c4">c</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="c5">p</font>,<font color="Maroon" title="c6">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c7">r</font> &amp; <font color="Maroon" title="c3">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="c6">q</font>,<font color="Maroon" title="c7">r</font> &amp; <font color="Maroon" title="c5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q</font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:54_1"/>
<font color="Maroon" title="c5">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">r</font>
 ;<br/><a NAME="E2:54_1"/><b>then </b>
( <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">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="c2">a</font> &amp; <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">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">c</font> )
 <b>by </b><i><a class="txt" href="parsp_1.html#E1:54"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="parsp_1.html#T40" target="_self" title="PARSP_1:th.40">Th40</a></i>;<br/><a NAME="E3:54_1"/><b>then </b>
<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="c4">c</font>
 <b>by </b><i><a class="txt" href="parsp_1.html#E1:54"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="parsp_1.html#D12" target="_self" title="PARSP_1:def.12">Def12</a></i>;<br/><b>hence </b><a NAME="E4:54_1"/>
contradiction
 <b>by </b><i><a class="txt" href="parsp_1.html#E1:54"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="parsp_1.html#T41" target="_self" title="PARSP_1:th.41">Th41</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:54"/>
not <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="parsp_1.html#E1:54"><i><font color="Green" title="E42">A1</font></i></a>, <a class="ref" href="parsp_1.html#T48" target="_self" title="PARSP_1:th.48">Th48</a></i>;<br/>


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