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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <a href="zf_lang.html#K1">VAR</a> ;<br/>

<a NAME="E1:17"/><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><a href="zf_fund1.html#K3" target="_self">decode</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>1</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E4"><i><font color="Green">Lemma4</font></i></a>, <a class="ref" href="funct_1.html#T84">FUNCT_1:84</a></i>;<br/>
<i><font color="Green">E22</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K3" target="_self">decode</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K3" target="_self">decode</a>  <a href="funct_1.html#K2">"</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="zf_fund1.html#E4"><i><font color="Green">Lemma4</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K3" target="_self">decode</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="relat_1.html#K7">|</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="zf_fund1.html#K3" target="_self">decode</a>  <a href="funct_1.html#K2">"</a> </span>)</span> <a href="relat_1.html#K9">.:</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="relat_1.html#T148">RELAT_1:148</a></i>
<br/>.= 
 <a href="zf_fund1.html#K5" target="_self">code</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<b>hence </b><a NAME="E4:17"/>
<font color="Maroon">c<sub>1</sub></font>, <a href="zf_fund1.html#K5" target="_self">code</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R2">are_equipotent</a> 
 <b>by </b><i><a class="txt" href="zf_fund1.html#E1:17"><i><font color="Green">E21</font></i></a>, <a class="txt" href="zf_fund1.html#E2:17"><i><font color="Green">E22</font></i></a>, <a class="ref" href="wellord2.html#D4">WELLORD2:def 4</a></i>;<br/>


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