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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<a NAME="E1:16"/><i><font color="Green">E72</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E2:16"/>
<font color="Maroon">T</font> is    <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="tsep_1.html#T2">TSEP_1:2</a></i>;<br/>
<a NAME="E3:16"/><b>then </b><i><font color="Green">E73</font></i>: 
 <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> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="pre_topc.html#K3">|</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span></span>)</span> #)
 
<b>by </b><i>, <a class="ref" href="tsep_1.html#T5">TSEP_1:5</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:16_1"/>
<font color="Maroon">T</font> is <a href="connsp_2.html#V1">locally_connected</a>
 ;<br/><a NAME="E2:16_1"/><b>then </b>
<font color="Maroon">T</font> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span> is <a href="connsp_2.html#V1">locally_connected</a>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:16_1"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font> is <a href="connsp_2.html#V2">locally_connected</a>
 <b>by </b><i><a class="ref" href="connsp_2.html#D6">CONNSP_2:def 6</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E5:16"/>
 <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font> is <a href="connsp_2.html#V2">locally_connected</a>
 ;<br/>

<a NAME="E6:16"/><b>then </b>
<font color="Maroon">T</font> <a href="pre_topc.html#K3">|</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span> is <a href="connsp_2.html#V1">locally_connected</a>
 
<b>by </b><i><a class="ref" href="connsp_2.html#D6">CONNSP_2:def 6</a></i>;<br/>
<b>hence </b><a NAME="E7:16"/>
<font color="Maroon">T</font> is <a href="connsp_2.html#V1">locally_connected</a>
 <b>by </b><i>, </i>;<br/>


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