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<b>set </b><font color="Maroon" title="c3">Sm</font> = the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font>;<br/>
<b>set </b><font color="Maroon" title="c4">X</font> = <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" title="TURING_1:func.21">UnionSt</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<b>let </b><font color="Maroon" title="c5">f</font>, <font color="Maroon" title="c6">g</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" title="TURING_1:func.21">UnionSt</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" title="TURING_1:func.21">UnionSt</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><span class="p3">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:91_1_2"/><i><font color="Green" title="E65">A2</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" title="TURING_1:func.21">UnionSt</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds  <font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="turing_1.html#K30" title="TURING_1:func.30">Uniontran</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<font color="Olive" title="b1">x</font>
 <b>and </b><br/><a NAME="E2:91_1_2"/><i><font color="Green" title="E66">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" title="TURING_1:func.21">UnionSt</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> holds  <font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="turing_1.html#K30" title="TURING_1:func.30">Uniontran</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<font color="Olive" title="b1">x</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="turing_1.html#K21" title="TURING_1:func.21">UnionSt</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font></span>)</span>,<span class="p2">(<span class="default">the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c1">s</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="turing_1.html#U1" title="TURING_1:sel.1">Symbols</a> of <font color="Maroon" title="c2">t</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/><b>thus </b><font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x</font> = 
 <a href="turing_1.html#K30" title="TURING_1:func.30">Uniontran</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="turing_1.html#E1:91_1_2"><i><font color="Green" title="E65">A2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c6">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x</font>
<b>by </b><i><a class="txt" href="turing_1.html#E2:91_1_2"><i><font color="Green" title="E66">A3</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:91_1_2"/>
<font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">g</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


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