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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:16_1_1"/><i><font color="Green">E9</font></i>: 
not <font color="Maroon">c<sub>1</sub></font> is <a href="tdlat_3.html#V1">discrete</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:16_1_1_1"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/><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="realset2.html#V3">trivial</a> <a href="pre_topc.html#NM1">TopSpace</a> ;<br/><a NAME="E3:16_1_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tdlat_3.html#V1">discrete</a>
 ;<br/><b>hence </b><a NAME="E4:16_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="tex_1.html#E1:16_1_1"><i><font color="Green">E9</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:16_1_1"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a>
 ;<br/>


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