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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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>, <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font>, <font color="Olive" title="b7">r</font>, <font color="Olive" title="b8">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PS</font>  st not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font> &amp; <font color="Olive" title="b5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">q</font> &amp; <font color="Olive" title="b7">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b8">s</font> holds <br/> not <font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b7">r</font>,<font color="Olive" title="b8">s</font></span><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">d</font>, <font color="Maroon" title="c6">p</font>, <font color="Maroon" title="c7">q</font>, <font color="Maroon" title="c8">r</font>, <font color="Maroon" title="c9">s</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 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="c4">c</font>,<font color="Maroon" title="c5">d</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="c6">p</font>,<font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font> &amp; <font color="Maroon" title="c6">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c8">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">s</font> implies  not <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font> )</span><br/>

















<b>assume </b><a NAME="E1:53"/><i><font color="Green" title="E41">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="c4">c</font>,<font color="Maroon" title="c5">d</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="c6">p</font>,<font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font> &amp; <font color="Maroon" title="c6">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">q</font> &amp; <font color="Maroon" title="c8">r</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">s</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font></span><br/>

<b>assume </b><a NAME="E2:53"/>
<font color="Maroon" title="c6">p</font>,<font color="Maroon" title="c7">q</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:53"/><b>then </b>
<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="c8">r</font>,<font color="Maroon" title="c9">s</font>
 
<b>by </b><i><a class="txt" href="#E1:53"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="parsp_1.html#T43" target="_self" title="PARSP_1:th.43">Th43</a></i>;<br/>
<a NAME="E4:53"/><b>then </b>
( <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c8">r</font>,<font color="Maroon" title="c9">s</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Maroon" title="c4">c</font>,<font color="Maroon" title="c5">d</font> )
 
<b>by </b><i><a class="txt" href="#E1:53"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="parsp_1.html#T40" target="_self" title="PARSP_1:th.40">Th40</a></i>;<br/>
<b>hence </b><a NAME="E5:53"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:53"><i><font color="Green" title="E41">A1</font></i></a>, <a class="ref" href="parsp_1.html#D12" target="_self" title="PARSP_1:def.12">Def12</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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