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<span class="kw">let </span><font color="Maroon" title="c6">T</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a>  iff  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V2" title="CONNSP_2:attr.2">locally_connected</a>  )</span><br/>

<a NAME="E1:15"/>
<font color="Maroon" title="c6">T</font> is    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c6">T</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tsep_1.html#T2" title="TSEP_1:th.2">TSEP_1:2</a></span>;<br/>
<a NAME="E2:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A1</font></span>: 
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">T</font>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c6">T</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font></span>)</span></span>)</span>, the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c6">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font></span>)</span></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T8" title="PRE_TOPC:th.8">PRE_TOPC:8</a>, <a class="ref" href="tsep_1.html#T5" title="TSEP_1:th.5">TSEP_1:5</a></span>;<br/>
<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V2" title="CONNSP_2:attr.2">locally_connected</a>  implies <font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:15_1"/>
<font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V2" title="CONNSP_2:attr.2">locally_connected</a> </span><br/><a NAME="E2:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font></span>)</span> is  <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="topalg_5.html#T12" target="_self" title="TOPALG_5:th.12">Th12</a></span>;<br/><span class="kw">hence </span><a NAME="E3:15_1"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V2" title="CONNSP_2:attr.2">locally_connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="connsp_2.html#D6" title="CONNSP_2:def.6">CONNSP_2:def 6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E4:15"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V2" title="CONNSP_2:attr.2">locally_connected</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a> </span><br/>

<a NAME="E5:15"/><span class="kw">then </span>
<font color="Maroon" title="c6">T</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c6">T</font></span>)</span> is  <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="connsp_2.html#D6" title="CONNSP_2:def.6">CONNSP_2:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:15"/>
<font color="Maroon" title="c6">T</font> is  <a href="connsp_2.html#V1" title="CONNSP_2:attr.1">locally_connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="topalg_5.html#T12" target="_self" title="TOPALG_5:th.12">Th12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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