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<b>let </b><font color="Maroon">S</font> be   <a href="osalg_1.html#NM3">OrderSortedSign</a>;<br/><b>let </b><font color="Maroon">X</font> be  <a href="relat_1.html#V2">V5</a> <a href="struct_0.html#NM8">ManySortedSet</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:36"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">s2</font> = <font color="Maroon">s</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> ;<br/>
<b>let </b><font color="Maroon">t</font> be    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="osafree.html#K2" target="_self">DTConOSA</a> <font color="Maroon">X</font></span>)</span>;<br/>

<b>assume </b><a NAME="E3:36"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R1">=</a>  <a href="trees_4.html#K1">root-tree</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span>
 ;<br/>

<a NAME="E4:36"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osafree.html#K8" target="_self">ParsedTermsOSA</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">s2</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:36"/>
for <font color="Olive">s1</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>  st <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><a href="osafree.html#K8" target="_self">ParsedTermsOSA</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">s1</font> holds <br/><font color="Maroon">s2</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">s1</font>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E6:36"/>
 <a href="osafree.html#K10" target="_self">LeastSort</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 <b>by </b><i>, </i>;<br/>


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