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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> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">PS</font>  st <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> holds <br/>( <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</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="b4">d</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b4">d</font>,<font color="Olive" title="b3">c</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="b1">a</font>,<font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b4">d</font>,<font color="Olive" title="b3">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</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="b2">b</font>,<font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b4">d</font>,<font color="Olive" title="b3">c</font> <a href="parsp_1.html#R1" title="PARSP_1:pred.1">'||'</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</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> 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"> ( <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> implies ( <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="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="c5">d</font>,<font color="Maroon" title="c4">c</font> &amp; <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="c5">d</font>,<font color="Maroon" title="c4">c</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="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</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="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="c3">b</font>,<font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</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> ) )</span><br/>









<b>assume </b><a NAME="E1:49"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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="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="c5">d</font>,<font color="Maroon" title="c4">c</font> &amp; <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="c5">d</font>,<font color="Maroon" title="c4">c</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="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</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="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="c3">b</font>,<font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</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> )</span><br/>

<a NAME="E2:49"/><b>then </b>
<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="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="parsp_1.html#T36" target="_self" title="PARSP_1:th.36">Th36</a></i>;<br/>
<a NAME="E3:49"/><b>then </b><i><font color="Green" title="E37">A1</font></i>: 
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</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>
 
<b>by </b><i><a class="ref" href="parsp_1.html#T38" target="_self" title="PARSP_1:th.38">Th38</a></i>;<br/>
<a NAME="E4:49"/><b>then </b><i><font color="Green" title="E38">A2</font></i>: 
<font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</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>
 
<b>by </b><i><a class="ref" href="parsp_1.html#T39" target="_self" title="PARSP_1:th.39">Th39</a></i>;<br/>
<a NAME="E5:49"/><b>then </b>
<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="c3">b</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="parsp_1.html#T38" target="_self" title="PARSP_1:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E6:49"/>
( <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="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="c5">d</font>,<font color="Maroon" title="c4">c</font> &amp; <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="c5">d</font>,<font color="Maroon" title="c4">c</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="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</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="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="c3">b</font>,<font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c5">d</font>,<font color="Maroon" title="c4">c</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> )
 <b>by </b><i><a class="txt" href="#E3:49"><i><font color="Green" title="E37">A1</font></i></a>, <a class="txt" href="#E4:49"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="parsp_1.html#T36" target="_self" title="PARSP_1:th.36">Th36</a>, <a class="ref" href="parsp_1.html#T38" target="_self" title="PARSP_1:th.38">Th38</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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