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<b>let </b><font color="Maroon" title="c1">FT1</font>, <font color="Maroon" title="c2">FT2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">FT1</font>,<font color="Maroon" title="c2">FT2</font>;<br/><b>let </b><font color="Maroon" title="c4">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><b>let </b><font color="Maroon" title="c5">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FT1</font>;<br/><b>let </b><font color="Maroon" title="c6">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">FT2</font>;<br/>









<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c3">h</font> <a href="fintopo5.html#R1" title="FINTOPO5:pred.1">is_homeomorphism</a>  &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">x</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c7">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">FT2</font>,<font color="Maroon" title="c1">FT1</font><b> such that </b><br/><a NAME="E3:6"/><i><font color="Green" title="E6">A2</font></i>: 
( <font color="Maroon" title="c7">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  &amp; <font color="Maroon" title="c7">g</font> <a href="fintopo5.html#R1" title="FINTOPO5:pred.1">is_homeomorphism</a>  )
 <b>by </b><i><a class="ref" href="fintopo5.html#T3" target="_self" title="FINTOPO5:th.3">Th3</a></i>;<br/>
<a NAME="E4:6"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">FT1</font>
 
;<br/>
<a NAME="E5:6"/><b>then </b><i><font color="Green" title="E7">A3</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E6:6"/>
( <font color="Maroon" title="c3">h</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c3">h</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a> &amp; ( for <font color="Olive" title="b1">x2</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FT1</font> holds  <font color="Maroon" title="c3">h</font> <a href="relset_1.html#K10" title="RELSET_1:func.10">.:</a> <span class="p1">(<span class="default"><a href="fin_topo.html#K1" title="FIN_TOPO:func.1">U_FT</a> <font color="Olive" title="b1">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K11" title="RELAT_1:func.11">Im</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">FT2</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x2</font></span>)</span> ) )
 
<b>by </b><i><a class="ref" href="fintopo5.html#D1" target="_self" title="FINTOPO5:def.1">Def1</a>, <a class="txt" href="fintopo5.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a></i>;<br/>
<a NAME="E7:6"/><b>then </b>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">y</font>
 
<b>by </b><i><a class="txt" href="fintopo5.html#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="fintopo5.html#E3:6"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="fintopo5.html#E5:6"><i><font color="Green" title="E7">A3</font></i></a>, <a class="ref" href="funct_1.html#T56" title="FUNCT_1:th.56">FUNCT_1:56</a></i>;<br/>
<b>hence </b><a NAME="E8:6"/>
for <font color="Olive" title="b1">v</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">FT2</font> holds <br/> ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fintopo3.html#K10" title="FINTOPO3:func.10">U_FT</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c4">n</font> iff <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fintopo3.html#K10" title="FINTOPO3:func.10">U_FT</a> <font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c4">n</font> )
 <b>by </b><i><a class="ref" href="fintopo5.html#T4" target="_self" title="FINTOPO5:th.4">Th4</a>, <a class="txt" href="fintopo5.html#E3:6"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/>


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