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<b>let </b><font color="Maroon">f1</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1">oContMaps</a> <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X</font></span>)</span>, <font color="Maroon">f2</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1">oContMaps</a> <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K2">InclPoset</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">X</font></span>)</span>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:31_1_2"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">g</font> being <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a>  holds  <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Olive">g</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 <b>and </b><br/><a NAME="E2:31_1_2"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">g</font> being <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a>  holds  <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Olive">g</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel26.html#K1">oContMaps</a> <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a> </span>)</span>;<br/><b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">x</font> as  <a href="pre_topc.html#V5">continuous</a> <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">X</font>,<a href="waybel18.html#K9">Sierpinski_Space</a>  <b>by </b><i><a class="ref" href="waybel26.html#T2">WAYBEL26:2</a></i>;<br/><b>thus </b><font color="Maroon">f1</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">x</font> = 
<font color="Maroon">g</font> <a href="relset_1.html#K11">"</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">f2</font> <a href="yellow_6.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:31_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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