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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T</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">A</font> be  <a href="yellow_8.html#V2">irreducible</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:38"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E2:38"/><i><font color="Green">E39</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</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">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> #)
 ;<br/>

<a NAME="E3:38"/>
( not <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">A</font> is <a href="pre_topc.html#V4">closed</a> )
 
<b>by </b><i><a class="ref" href="yellow_8.html#D4">YELLOW_8:def 4</a></i>;<br/>
<b>hence </b><a NAME="E4:38"/>
( not <font color="Maroon">B</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Maroon">B</font> is <a href="pre_topc.html#V4">closed</a> )
 <b>by </b><i>, , <a class="ref" href="tops_3.html#T79">TOPS_3:79</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_8.html#D4">YELLOW_8:def 4</a><br/>

<b>let </b><font color="Maroon">B1</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>, <font color="Maroon">B2</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>

<b>assume </b><a NAME="E5:38"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">B1</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">B2</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B2</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">A1</font> = <font color="Maroon">B1</font>, <font color="Maroon">A2</font> = <font color="Maroon">B2</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<a NAME="E7:38"/>
( <font color="Maroon">A1</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">A2</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">A2</font> )
 
<b>by </b><i>, , , <a class="ref" href="tops_3.html#T79">TOPS_3:79</a></i>;<br/>
<b>hence </b><a NAME="E8:38"/>
( <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> or <font color="Maroon">B2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> )
 <b>by </b><i>, <a class="ref" href="yellow_8.html#D4">YELLOW_8:def 4</a></i>;<br/>


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