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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K3">Union</a> <font color="Maroon">A</font>, <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="card_3.html#K3">Union</a> <font color="Maroon">A</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:44_1_2"/><i><font color="Green">E46</font></i>: 
for <font color="Olive">f</font> being  <a href="funct_1.html#NM1">Function</a>  st <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> holds <br/><font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">t</font></span>)</span>
 <b>and </b><br/><a NAME="E2:44_1_2"/><i><font color="Green">E48</font></i>: 
for <font color="Olive">f</font> being  <a href="funct_1.html#NM1">Function</a>  st <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="mcart_1.html#K2">`2</a> </span>)</span> holds <br/><font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">t</font></span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon">s</font> being   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>, <font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:44_1_2"/><i><font color="Green">E49</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> &amp; <font color="Maroon">t</font> <a href="hidden.html#R1">=</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> )
 <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">F</font> <a href="msualg_3.html#K1">.</a> <font color="Maroon">s</font> as   <a href="funct_1.html#NM1">Function</a> ;<br/>
<a NAME="E6:44_1_2"/>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">t</font> <a href="mcart_1.html#K2">`2</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<a NAME="E7:44_1_2"/><b>then </b>
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">t</font></span>)</span> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="trees_4.html#K2">root-tree</a> <font color="Maroon">t</font></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:44_1_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>


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