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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:61_1"/>
(  not <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_1"><b>suppose </b></a><a NAME="E1:61_1_1"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a> ;<br/><a NAME="E3:61_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><b>then </b> <a href="xboole_0.html#K1">{}</a>  = 
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" target="_self">Der</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topgen_1.html#T31" target="_self">Th31</a></i>
<br/>.= 
 <a href="topgen_1.html#K2" target="_self">Der</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>

;<br/><b>hence </b><a NAME="E5:61_1_1"/>
 <a href="topgen_1.html#K2" target="_self">Der</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="61_1_2"><b>suppose </b></a><a NAME="E1:61_1_2"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:61_1_2"/>
 <a href="topgen_1.html#K2" target="_self">Der</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K1">{}</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="topgen_1.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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