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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="77_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:77_1_1_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="77_1_1_1_1"><b>suppose </b></a><a NAME="E1:77_1_1_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/><b>assume </b><a NAME="E3:77_1_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="topgen_4.html#V7" target="_self">T_1/2</a>
 ;<br/><a NAME="E4:77_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is <a href="topgen_4.html#V7" target="_self">T_1/2</a>
 ;<br/><b>hence </b><a NAME="E5:77_1_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="t_0topsp.html#V2">T_0</a>
 <b>by </b><i><a class="ref" href="topgen_4.html#T49" target="_self">Th49</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="77_1_1_1_2"><b>suppose </b></a><a NAME="E1:77_1_1_1_2"/>
<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  <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a> ;<br/><a NAME="E3:77_1_1_1_2"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="t_0topsp.html#V2">T_0</a>
 <b>by </b><i><a class="ref" href="tsp_1.html#D4">TSP_1:def 4</a></i>;<br/><b>hence </b><a NAME="E4:77_1_1_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> is <a href="topgen_4.html#V7" target="_self">T_1/2</a> implies <font color="Maroon">c<sub>1</sub></font> is <a href="t_0topsp.html#V2">T_0</a> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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