<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>;<br/>



<a NAME="E1:21"/><i><font color="Green" title="E17">A1</font></i>: 
( <font color="Maroon" title="c1">X</font> <a href="connsp_2.html#R1" title="CONNSP_2:pred.1">is_locally_connected_in</a> <font color="Maroon" title="c2">x</font> implies for <font color="Olive" title="b1">U1</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">U1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">U1</font> holds <br/> ex <font color="Olive" title="b2">x1</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b1">U1</font></span>)</span> st <br/>( <font color="Olive" title="b2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Olive" title="b2">x1</font></span>)</span> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_1"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="connsp_2.html#R1" title="CONNSP_2:pred.1">is_locally_connected_in</a> <font color="Maroon" title="c2">x</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c3">U1</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:21_1"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c3">U1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E3:21_1"/><i><font color="Green" title="E20">A4</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">U1</font>
 ;<br/>

<a NAME="E4:21_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">U1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="connsp_2.html#E3:21_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">x1</font> = <font color="Maroon" title="c2">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">U1</font></span>)</span> ;<br/>
<b>take </b>
<font color="Maroon" title="c4">x1</font>
;<br/>

<b>reconsider </b><font color="Maroon" title="c5">S1</font> =  <a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c4">x1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">U1</font></span>)</span> ;<br/>
<a NAME="E7:21_1"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c5">S1</font> <a href="connsp_1.html#R3" title="CONNSP_1:pred.3">is_a_component_of</a> <font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">U1</font>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T43" title="CONNSP_1:th.43">CONNSP_1:43</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">S</font> = <font color="Maroon" title="c5">S1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="pre_topc.html#T39" title="PRE_TOPC:th.39">PRE_TOPC:39</a></i>;<br/>
<a NAME="E9:21_1"/><i><font color="Green" title="E22">A6</font></i>: 
<font color="Maroon" title="c6">S</font> <a href="connsp_1.html#R4" title="CONNSP_1:pred.4">is_a_component_of</a> <font color="Maroon" title="c3">U1</font>
 
<b>by </b><i><a class="txt" href="connsp_2.html#E7:21_1"><i><font color="Green" title="E21">A5</font></i></a>, <a class="ref" href="connsp_1.html#D6" title="CONNSP_1:def.6">CONNSP_1:def 6</a></i>;<br/>
<a NAME="E10:21_1"/><i><font color="Green" title="E23">A7</font></i>: 
<font color="Maroon" title="c3">U1</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="txt" href="connsp_2.html#E2:21_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="connsp_2.html#E3:21_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="connsp_2.html#T5" target="_self" title="CONNSP_2:th.5">Th5</a></i>;<br/>
<a NAME="E11:21_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">S</font>
 
<b>by </b><i><a class="ref" href="connsp_1.html#T40" title="CONNSP_1:th.40">CONNSP_1:40</a></i>;<br/>
<a NAME="E12:21_1"/><b>then </b>
<font color="Maroon" title="c6">S</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">x</font>
 
<b>by </b><i><a class="txt" href="connsp_2.html#E1:21_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="connsp_2.html#E9:21_1"><i><font color="Green" title="E22">A6</font></i></a>, <a class="txt" href="connsp_2.html#E10:21_1"><i><font color="Green" title="E23">A7</font></i></a>, <a class="ref" href="connsp_2.html#T19" target="_self" title="CONNSP_2:th.19">Th19</a></i>;<br/>
<a NAME="E13:21_1"/><b>then </b>
<font color="Maroon" title="c5">S1</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c4">x1</font>
 
<b>by </b><i><a class="ref" href="connsp_2.html#T12" target="_self" title="CONNSP_2:th.12">Th12</a></i>;<br/>
<b>hence </b><a NAME="E14:21_1"/>
( <font color="Maroon" title="c4">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c4">x1</font></span>)</span> )
 <b>by </b><i><a class="ref" href="connsp_2.html#D1" target="_self" title="CONNSP_2:def.1">Def1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:21"/>
( ( for <font color="Olive" title="b1">U1</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">U1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">U1</font> holds <br/> ex <font color="Olive" title="b2">x1</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b1">U1</font></span>)</span> st <br/>( <font color="Olive" title="b2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Olive" title="b2">x1</font></span>)</span> ) ) implies <font color="Maroon" title="c1">X</font> <a href="connsp_2.html#R1" title="CONNSP_2:pred.1">is_locally_connected_in</a> <font color="Maroon" title="c2">x</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:21_2"/><i><font color="Green" title="E18">A8</font></i>: 
for <font color="Olive" title="b1">U1</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">U1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">U1</font> holds <br/> ex <font color="Olive" title="b2">x1</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b1">U1</font></span>)</span> st <br/>( <font color="Olive" title="b2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Olive" title="b2">x1</font></span>)</span> )
 ;<br/>

<a NAME="E2:21_2"/>
for <font color="Olive" title="b1">U1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">U1</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">x</font> holds <br/> ex <font color="Olive" title="b2">V1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b2">V1</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">x</font> &amp; <font color="Olive" title="b2">V1</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> &amp; <font color="Olive" title="b2">V1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">U1</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">U1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>;<br/>

<b>assume </b><a NAME="E1:21_2_1"/>
<font color="Maroon" title="c3">U1</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">x</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c4">V</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:21_2_1"/><i><font color="Green" title="E19">A9</font></i>: 
<font color="Maroon" title="c4">V</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">x</font>
 <b>and </b><br/><a NAME="E4:21_2_1"/><i><font color="Green" title="E20">A10</font></i>: 
<font color="Maroon" title="c4">V</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E5:21_2_1"/><i><font color="Green" title="E21">A11</font></i>: 
<font color="Maroon" title="c4">V</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">U1</font>
 <b>by </b><i><a class="ref" href="connsp_2.html#T7" target="_self" title="CONNSP_2:th.7">Th7</a></i>;<br/>
<a NAME="E6:21_2_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="txt" href="connsp_2.html#E3:21_2_1"><i><font color="Green" title="E19">A9</font></i></a>, <a class="ref" href="connsp_2.html#T6" target="_self" title="CONNSP_2:th.6">Th6</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c5">x1</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">V</font></span>)</span><b> such that </b><br/><a NAME="E8:21_2_1"/><i><font color="Green" title="E22">A12</font></i>: 
<font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font>
 <b>and </b><br/><a NAME="E9:21_2_1"/><i><font color="Green" title="E23">A13</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c5">x1</font></span>)</span>
 <b>by </b><i><a class="txt" href="connsp_2.html#E1:21_2"><i><font color="Green" title="E18">A8</font></i></a>, <a class="txt" href="connsp_2.html#E4:21_2_1"><i><font color="Green" title="E20">A10</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">S1</font> =  <a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c5">x1</font>;<br/>
<a NAME="E10:21_2_1"/><i><font color="Green" title="E24">A14</font></i>: 
 <a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c5">x1</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c5">x1</font>
 
<b>by </b><i><a class="txt" href="connsp_2.html#E8:21_2_1"><i><font color="Green" title="E22">A12</font></i></a>, <a class="txt" href="connsp_2.html#E9:21_2_1"><i><font color="Green" title="E23">A13</font></i></a>, <a class="ref" href="connsp_2.html#D1" target="_self" title="CONNSP_2:def.1">Def1</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">S</font> =  <a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c5">x1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="pre_topc.html#T39" title="PRE_TOPC:th.39">PRE_TOPC:39</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c7">S</font>
;<br/>

<a NAME="E12:21_2_1"/><i><font color="Green" title="E25">A15</font></i>: 
( <font color="Maroon" title="c7">S</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c5">x1</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )
 
<b>by </b><i><a class="ref" href="connsp_1.html#T40" title="CONNSP_1:th.40">CONNSP_1:40</a>, <a class="ref" href="connsp_1.html#T41" title="CONNSP_1:th.41">CONNSP_1:41</a></i>;<br/>
<a NAME="E13:21_2_1"/>
 <a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Maroon" title="c5">x1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">V</font></span>)</span>
 
;<br/>
<a NAME="E14:21_2_1"/><b>then </b>
<font color="Maroon" title="c7">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">V</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/>
<b>hence </b><a NAME="E15:21_2_1"/>
( <font color="Maroon" title="c7">S</font> is    <a href="connsp_2.html#M1" title="CONNSP_2:mode.1">a_neighborhood</a> of <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c7">S</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> &amp; <font color="Maroon" title="c7">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">U1</font> )
 <b>by </b><i><a class="txt" href="connsp_2.html#E4:21_2_1"><i><font color="Green" title="E20">A10</font></i></a>, <a class="txt" href="connsp_2.html#E5:21_2_1"><i><font color="Green" title="E21">A11</font></i></a>, <a class="txt" href="connsp_2.html#E8:21_2_1"><i><font color="Green" title="E22">A12</font></i></a>, <a class="txt" href="connsp_2.html#E10:21_2_1"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="connsp_2.html#E12:21_2_1"><i><font color="Green" title="E25">A15</font></i></a>, <a class="ref" href="connsp_2.html#T11" target="_self" title="CONNSP_2:th.11">Th11</a>, <a class="ref" href="connsp_1.html#T24" title="CONNSP_1:th.24">CONNSP_1:24</a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:21_2"/>
<font color="Maroon" title="c1">X</font> <a href="connsp_2.html#R1" title="CONNSP_2:pred.1">is_locally_connected_in</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="ref" href="connsp_2.html#D3" target="_self" title="CONNSP_2:def.3">Def3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:21"/>
( <font color="Maroon" title="c1">X</font> <a href="connsp_2.html#R1" title="CONNSP_2:pred.1">is_locally_connected_in</a> <font color="Maroon" title="c2">x</font> iff for <font color="Olive" title="b1">U1</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">U1</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">U1</font> holds <br/> ex <font color="Olive" title="b2">x1</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Olive" title="b1">U1</font></span>)</span> st <br/>( <font color="Olive" title="b2">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="connsp_1.html#K1" title="CONNSP_1:func.1">Component_of</a> <font color="Olive" title="b2">x1</font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="connsp_2.html#E1:21"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>


</div>
