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<b>let </b><font color="Maroon">T1</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">B1</font> be    <a href="topgen_2.html#M1">Neighborhood_System</a> of <font color="Maroon">T1</font>;<br/><b>let </b><font color="Maroon">B2</font> be    <a href="topgen_2.html#M1">Neighborhood_System</a> of <font color="Maroon">T2</font>;<br/>





<b>assume </b><a NAME="E1:34"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B2</font>
 ;<br/>

<a NAME="E2:34"/><i><font color="Green">E43</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">B2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:34"/>
(  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="topgen_2.html#K3">Union</a> <font color="Maroon">B1</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> &amp;  <a href="cantor_1.html#K1">UniCl</a> <span class="p1">(<span class="default"><a href="topgen_2.html#K3">Union</a> <font color="Maroon">B2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font> )
 
<b>by </b><i><a class="ref" href="yellow_9.html#T22">YELLOW_9:22</a></i>;<br/>
<b>hence </b><a NAME="E4:34"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T1</font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T2</font> #)
 <b>by </b><i>, </i>;<br/>


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