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<b>let </b><font color="Maroon">X</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">X0</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">X</font>;<br/>



<b>set </b><font color="Maroon">Y</font> = <font color="Maroon">X</font> <a href="tmap_1.html#K8" target="_self">modified_with_respect_to</a> <font color="Maroon">X0</font>;<br/>
<b>reconsider </b><font color="Maroon">A</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1">TSEP_1:1</a></i>;<br/>
<a NAME="E2:120"/>
<font color="Maroon">X</font> <a href="tmap_1.html#K8" target="_self">modified_with_respect_to</a> <font color="Maroon">X0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="tmap_1.html#K6" target="_self">modified_with_respect_to</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:120"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">X</font> <a href="tmap_1.html#K8" target="_self">modified_with_respect_to</a> <font color="Maroon">X0</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">X</font>,<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="tmap_1.html#K5" target="_self">-extension_of_the_topology_of</a> <font color="Maroon">X</font></span>)</span> #)
 
;<br/>
<b>hence </b><a NAME="E4:120"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="tmap_1.html#K8" target="_self">modified_with_respect_to</a> <font color="Maroon">X0</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 ;<br/>

<b>thus </b><a NAME="E5:120"/>
for <font color="Olive">A</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">X</font>  st <font color="Olive">A</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X0</font> holds <br/>the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="tmap_1.html#K8" target="_self">modified_with_respect_to</a> <font color="Maroon">X0</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">A</font> <a href="tmap_1.html#K5" target="_self">-extension_of_the_topology_of</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


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