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<b>let </b><font color="Maroon" title="c1">Y0</font>, <font color="Maroon" title="c2">Y1</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><font color="Maroon" title="c3">D0</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y0</font>;<br/><b>let </b><font color="Maroon" title="c4">D1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y1</font>;<br/>





<b>assume </b><a NAME="E1:63"/><i><font color="Green" title="E20">A1</font></i>: 
 <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="c1">Y0</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">Y0</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 <font color="Maroon" title="c2">Y1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y1</font> #)
 ;<br/>

<b>assume </b><a NAME="E2:63"/><i><font color="Green" title="E21">A2</font></i>: 
<font color="Maroon" title="c3">D0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">D1</font>
 ;<br/>

<b>assume </b><a NAME="E3:63"/><i><font color="Green" title="E22">A3</font></i>: 
<font color="Maroon" title="c3">D0</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">discrete</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">D</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y1</font>;<br/><b>reconsider </b><font color="Maroon" title="c6">E</font> = <font color="Maroon" title="c5">D</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y0</font> <b>by </b><i><a class="txt" href="tex_2.html#E1:63"><i><font color="Green" title="E20">A1</font></i></a></i>;<br/><b>assume </b><a NAME="E2:63_1"/>
<font color="Maroon" title="c5">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D1</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c7">G0</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y0</font><b> such that </b><br/><a NAME="E4:63_1"/><i><font color="Green" title="E23">A4</font></i>: 
<font color="Maroon" title="c7">G0</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>and </b><br/><a NAME="E5:63_1"/><i><font color="Green" title="E24">A5</font></i>: 
<font color="Maroon" title="c3">D0</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c7">G0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">E</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E2:63"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="tex_2.html#E3:63"><i><font color="Green" title="E22">A3</font></i></a>, <a class="ref" href="tex_2.html#D5" target="_self" title="TEX_2:def.5">Def5</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">G</font> = <font color="Maroon" title="c7">G0</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y1</font> <b>by </b><i><a class="txt" href="tex_2.html#E1:63"><i><font color="Green" title="E20">A1</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon" title="c9">G</font> = <font color="Maroon" title="c8">G</font>;<br/><a NAME="E1:63_1_1"/>
<font color="Maroon" title="c9">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">Y1</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:63"><i><font color="Green" title="E20">A1</font></i></a>, <a class="txt" href="tex_2.html#E4:63_1"><i><font color="Green" title="E23">A4</font></i></a>, <a class="ref" href="pre_topc.html#D5" title="PRE_TOPC:def.5">PRE_TOPC:def 5</a></i>;<br/><b>hence </b><a NAME="E2:63_1_1"/>
<font color="Maroon" title="c9">G</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 <b>by </b><i><a class="ref" href="pre_topc.html#D5" title="PRE_TOPC:def.5">PRE_TOPC:def 5</a></i>;<br/><b>thus </b><a NAME="E3:63_1_1"/>
<font color="Maroon" title="c4">D1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c9">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="tex_2.html#E2:63"><i><font color="Green" title="E21">A2</font></i></a>, <a class="txt" href="tex_2.html#E5:63_1"><i><font color="Green" title="E24">A5</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E8:63_1"/>
 ex <font color="Olive" title="b1">G</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">Y1</font> st <br/>( <font color="Olive" title="b1">G</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> &amp; <font color="Maroon" title="c4">D1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:63"/>
<font color="Maroon" title="c4">D1</font> is <a href="tex_2.html#V3" title="TEX_2:attr.3">discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D5" target="_self" title="TEX_2:def.5">Def5</a></i>;<br/>


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