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<b>let </b><font color="Maroon" title="c1">X1</font>, <font color="Maroon" title="c2">X2</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">D1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X1</font>;<br/><b>let </b><font color="Maroon" title="c4">D2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X2</font>;<br/>







<b>assume </b><a NAME="E1:86"/><i><font color="Green" title="E53">A1</font></i>: 
<font color="Maroon" title="c3">D1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">D2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">C2</font> = <font color="Maroon" title="c3">D1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X2</font> <b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>assume </b><a NAME="E3:86"/><i><font color="Green" title="E54">A2</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">X1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X1</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">X2</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">X2</font> #)
 ;<br/>

<b>assume </b><a NAME="E4:86"/>
<font color="Maroon" title="c3">D1</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a>
 ;<br/>

<a NAME="E5:86"/><b>then </b>
(  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c3">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X1</font> &amp;  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c3">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c5">C2</font> )
 
<b>by </b><i><a class="txt" href="tops_3.html#E3:86"><i><font color="Green" title="E54">A2</font></i></a>, <a class="ref" href="tops_3.html#D2" target="_self" title="TOPS_3:def.2">Def2</a>, <a class="ref" href="tops_3.html#T80" target="_self" title="TOPS_3:th.80">Th80</a></i>;<br/>
<a NAME="E6:86"/><b>then </b>
<font color="Maroon" title="c5">C2</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a>
 
<b>by </b><i><a class="txt" href="tops_3.html#E3:86"><i><font color="Green" title="E54">A2</font></i></a>, <a class="ref" href="tops_3.html#D2" target="_self" title="TOPS_3:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E7:86"/>
<font color="Maroon" title="c4">D2</font> is <a href="tops_1.html#V1" title="TOPS_1:attr.1">dense</a>
 <b>by </b><i><a class="txt" href="tops_3.html#E1:86"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="tops_1.html#T79" title="TOPS_1:th.79">TOPS_1:79</a></i>;<br/>


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