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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">A</font> be    <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:22"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font>
 ;<br/>

<a NAME="E2:22"/>
<font color="Maroon">s</font> <a href="hidden.html#R2">in</a>  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">s</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:22"/><b>then </b>
<font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s1</font></span>)</span> where <font color="Olive">s1</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> : <font color="Olive">s1</font> <a href="hidden.html#R2">in</a>  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">s</font> </span>}</span> 
 
;<br/>
<a NAME="E4:22"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">s1</font></span>)</span> where <font color="Olive">s1</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font> : <font color="Olive">s1</font> <a href="hidden.html#R2">in</a>  <a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">s</font> </span>}</span> 
 
<b>by </b><i>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:22"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="osalg_4.html#K4" target="_self">-carrier_of</a> <span class="p1">(<span class="default"><a href="osalg_4.html#K3" target="_self">CComp</a> <font color="Maroon">s</font></span>)</span>
 ;<br/>


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