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<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D16" target="_self">PENCIL_1:def 16</a><br/>

<b>assume </b><a NAME="E1:35_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="pzfmisc1.html#K1">}</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:35_1_1"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="pzfmisc1.html#K1">}</a></span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E4:35_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1"><a href="pzfmisc1.html#K1">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="pzfmisc1.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E5:35_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="txt" href="pencil_1.html#E3:35_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="pzfmisc1.html#D1">PZFMISC1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:35_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="realset1.html#V1">trivial</a>
 ;<br/>


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