<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">FT1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">FT2</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">FT1</font>,<font color="Maroon">FT2</font>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT1</font>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT2</font>;<br/>









<b>assume </b><a NAME="E1:6"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">h</font> <a href="fintopo5.html#R1" target="_self">is_homeomorphism</a>  &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> )
 ;<br/>

<b>then consider </b><font color="Maroon">g</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">FT2</font>,<font color="Maroon">FT1</font><b> such that </b><br/><a NAME="E3:6"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">h</font> <a href="funct_1.html#K2">"</a>  &amp; <font color="Maroon">g</font> <a href="fintopo5.html#R1" target="_self">is_homeomorphism</a>  )
 <b>by </b><i/>;<br/>
<a NAME="E4:6"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">FT1</font>
 
;<br/>
<a NAME="E5:6"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">h</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E6:6"/>
( <font color="Maroon">h</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">h</font> is <a href="funct_2.html#V2">onto</a> &amp; ( for <font color="Olive">x2</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT1</font> holds  <font color="Maroon">h</font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">FT1</font> <a href="relset_1.html#K10">.:</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">x2</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">FT2</font> <a href="relset_1.html#K10">.:</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">h</font> <a href="funct_2.html#K3">.</a> <font color="Olive">x2</font></span>)</span></span><a href="tarski.html#K1">}</a></span> ) )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:6"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font>
 
<b>by </b><i>, , , <a class="ref" href="funct_1.html#T56">FUNCT_1:56</a></i>;<br/>
<b>hence </b><a NAME="E8:6"/>
for <font color="Olive">v</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FT2</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="funct_1.html#K2">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="fintopo3.html#K10">U_FT</a> <font color="Maroon">x</font>,<font color="Maroon">n</font> iff <font color="Olive">v</font> <a href="hidden.html#R2">in</a>  <a href="fintopo3.html#K10">U_FT</a> <font color="Maroon">y</font>,<font color="Maroon">n</font> )
 <b>by </b><i>, </i>;<br/>


</div>
