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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>set </b><font color="Maroon">c<sub>2</sub></font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">.}</a></span>;<br/>
<a NAME="E1:24"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="pcomps_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D1">ZFMISC_1:def 1</a></i>;<br/>
<a NAME="E2:24"/><b>then </b>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">.}</a></span> <a href="tarski.html#R1">c=</a>  <a href="pcomps_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">.}</a></span> as   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> , <a href="pcomps_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="pcomps_1.html#K1">bool</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="funcop_1.html#T57">FUNCOP_1:57</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><a NAME="E1:24_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="nagata_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K1">.}</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> is   <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="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="zfmisc_1.html#D1">ZFMISC_1:def 1</a></i>;<br/><b>hence </b><a NAME="E2:24_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="nagata_1.html#K1" target="_self">.</a> <font color="Maroon">c<sub>4</sub></font> is <a href="nagata_1.html#V1" target="_self">discrete</a>
 <b>by </b><i><a class="ref" href="nagata_1.html#T1" target="_self">Th1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:24"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="nagata_1.html#V2" target="_self">sigma_discrete</a>
 <b>by </b><i><a class="ref" href="nagata_1.html#D2" target="_self">Def2</a></i>;<br/>


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