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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <a href="numbers.html#K5">NAT</a>  <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <a href="numbers.html#K5">NAT</a>  <a href="borsuk_1.html#K1">--&gt;</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<a NAME="E4:5_1_1"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T14">FUNCOP_1:14</a></i>;<br/>
<a NAME="E5:5_1_1"/><b>then </b>
not  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:5_1_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="relat_1.html#V2">non-empty</a>
 <b>by </b><i><a class="ref" href="relat_1.html#D9">RELAT_1:def 9</a></i>;<br/>


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