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<b>set </b><font color="Maroon">Sm</font> = the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t</font>;<br/>
<b>set </b><font color="Maroon">X</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">s</font>,<font color="Maroon">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">s</font>,<font color="Maroon">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">s</font>,<font color="Maroon">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t</font></span>)</span>,<span class="p2"><a href="domain_1.html#K8">{</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8">}</a></span></span><a href="zfmisc_1.html#K3">:]</a></span> =  <a href="turing_1.html#K30" target="_self">Uniontran</a> <font color="Maroon">s</font>,<font color="Maroon">t</font>,<font color="Maroon">a<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">s</font>,<font color="Maroon">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">s</font>,<font color="Maroon">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t</font></span>)</span>,<span class="p2"><a href="domain_1.html#K8">{</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span>,0,1</span><a href="domain_1.html#K8">}</a></span></span><a href="zfmisc_1.html#K3">:]</a></span><b> such that </b><br/><a NAME="E2:93_1_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">s</font>,<font color="Maroon">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">x</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S4">FUNCT_2:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E3:93_1_1"/>
for <font color="Olive">x</font> being   <a href="subset_1.html#M1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" target="_self">UnionSt</a> <font color="Maroon">s</font>,<font color="Maroon">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">s</font> <a href="xboole_0.html#K2">\/</a> the <a href="turing_1.html#U1" target="_self">Symbols</a> of <font color="Maroon">t</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> holds  <font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a>  <a href="turing_1.html#K30" target="_self">Uniontran</a> <font color="Maroon">s</font>,<font color="Maroon">t</font>,<font color="Olive">x</font>
 <b>by </b><i><a class="ref" href="turing_1.html#D8" target="_self">Def8</a></i>;<br/>


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