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<span class="kw">set </span><font color="Maroon" title="c5">s</font> =  the   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">x</font> =  the    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Maroon" title="c2">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a>  the   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E1:112_1_1"/>
(  <a href="msafree5.html#NK12" title="MSAFREE5:NK.12">deg</a> <span class="p1">(<span class="default"> the    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Maroon" title="c2">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a>  the   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font> <a href="msafree5.html#K6" title="MSAFREE5:func.6">-term</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font> &amp;  the    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Maroon" title="c2">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a>  the   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font> <a href="msafree5.html#K6" title="MSAFREE5:func.6">-term</a>  <a href="msafree5.html#R1" title="MSAFREE5:pred.1">in</a> <font color="Maroon" title="c3">T</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msafree5.html#T42" target="_self" onmouseover="rs('msafree5/T42')" onmouseout="rh()">Th24</a>, <a class="ref" href="msafree5.html#T49" target="_self" onmouseover="rs('msafree5/T49')" onmouseout="rh()">Th21</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">r</font> =  the    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Maroon" title="c2">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a>  the   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font> <a href="msafree5.html#K6" title="MSAFREE5:func.6">-term</a>  as   <a href="msafree3.html#NM1" title="MSAFREE3:NM.1">Element</a> of <font color="Maroon" title="c3">T</font> ;<br/>
<a NAME="E3:112_1_1"/>
(  <a href="msafree5.html#NK12" title="MSAFREE5:NK.12">deg</a> <font color="Maroon" title="c7">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msafree5.html#NK12" title="MSAFREE5:NK.12">deg</a> <span class="p1">(<span class="default"><a href="msafree5.html#K1" title="MSAFREE5:func.1">@</a> <font color="Maroon" title="c7">r</font></span>)</span> &amp;  <a href="msafree5.html#NK12" title="MSAFREE5:NK.12">deg</a> <span class="p1">(<span class="default"><a href="msafree5.html#K1" title="MSAFREE5:func.1">@</a> <font color="Maroon" title="c7">r</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  &amp;  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msafree5.html#T49" target="_self" onmouseover="rs('msafree5/T49')" onmouseout="rh()">Th21</a></span>;<br/>
<a NAME="E4:112_1_1"/><span class="kw">then </span>
 the    <a href="msafree4.html#M1" title="MSAFREE4:mode.1">Element</a> of <font color="Maroon" title="c2">X</font> <a href="msafree4.html#K1" title="MSAFREE4:func.1">.</a>  the   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font> <a href="msafree5.html#K6" title="MSAFREE5:func.6">-term</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">r1</font> where <font color="Olive" title="b1">r1</font> is   <a href="msafree3.html#NM1" title="MSAFREE3:NM.1">Element</a> of <font color="Maroon" title="c3">T</font> :  <a href="msafree5.html#NK12" title="MSAFREE5:NK.12">deg</a> <font color="Olive" title="b1">r1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">i</font> </span> } </span> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:112_1_1"/>
 not <font color="Maroon" title="c3">T</font> <a href="msafree5.html#K13" title="MSAFREE5:func.13">deg&lt;=</a> <font color="Maroon" title="c4">i</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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