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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="zf_lang.html#K1">VAR</a> ;<br/>





<a NAME="E1:13"/><i><font color="Green">E17</font></i>: 
 <a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K5">omega</a> 
 
;<br/>
<b>thus </b><i><font color="Green">E18</font></i>: <a href="zf_fund1.html#K3" target="_self">decode</a>  <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
 <a href="zf_lang.html#K2">x.</a> <span class="p1">(<span class="default"><a href="card_1.html#K4">card</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="zf_fund1.html#D2" target="_self">Def2</a></i>
<br/>.= 
 <a href="zf_lang.html#K2">x.</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T78">FINSEQ_1:78</a></i>
<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="zf_fund1.html#D3" target="_self">Def3</a></i>
;<br/>

<b>hence </b><a NAME="E3:13"/>
<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="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">c<sub>3</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="funct_1.html#T56">FUNCT_1:56</a></i>;<br/>

<a NAME="E4:13"/>
 <a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3" target="_self">decode</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:13"><i><font color="Green">E17</font></i></a>, <a class="txt" href="zf_fund1.html#E16"><i><font color="Green">Lemma15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:13"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3" target="_self">decode</a> </span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K4" target="_self">x".</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="zf_fund1.html#E2:13"><i><font color="Green">E18</font></i></a>, <a class="ref" href="funct_1.html#T22">FUNCT_1:22</a></i>;<br/>


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