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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="tdlat_3.html#V2">anti-discrete</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:92_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V4" target="_self">maximal_discrete</a>
 ;<br/><a NAME="E2:92_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V3" target="_self">discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D7" target="_self">Def7</a></i>;<br/><b>hence </b><a NAME="E3:92_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i><a class="ref" href="tex_2.html#T44" target="_self">Th44</a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:92_2"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="realset1.html#V1">trivial</a>
 ;<br/><a NAME="E2:92_2"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V3" target="_self">discrete</a>
 <b>by </b><i><a class="ref" href="tex_2.html#T44" target="_self">Th44</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="92_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:92_2_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="tex_2.html#V3" target="_self">discrete</a>
 ;<br/><b>assume </b><a NAME="E2:92_2_1"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/><a NAME="E4:92_2_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:92_2_1"><i><font color="Green">E40</font></i></a>, <a class="ref" href="tex_2.html#T44" target="_self">Th44</a></i>;<br/><b>hence </b><a NAME="E5:92_2_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="tex_2.html#E2:92_2_1"><i><font color="Green">E41</font></i></a>, <a class="ref" href="tex_2.html#T1" target="_self">Th1</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:92_2"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V4" target="_self">maximal_discrete</a>
 <b>by </b><i><a class="txt" href="tex_2.html#E2:92_2"><i><font color="Green">E39</font></i></a>, <a class="ref" href="tex_2.html#D7" target="_self">Def7</a></i>;<br/></div>
<b>end;</b></div>


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