<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">W</font> be   <a href="classes2.html#NM1">Universe</a>;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="zf_refle.html#NM1">Subclass</a> of <font color="Maroon">W</font>;<br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">Y</font> is <a href="zf_fund1.html#V8">closed_wrt_A1-A7</a> &amp; <font color="Maroon">Y</font> is <a href="ordinal1.html#V1">epsilon-transitive</a> )
 ;<br/>

<b>let </b><font color="Maroon">H</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_fund2.html#D2" target="_self">ZF_FUND2:def 2</a><br/><b>let </b><font color="Maroon">E</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">f</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">E</font>;<br/>





<b>assume </b><a NAME="E2:13"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">E</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:13_1_1"/>
(  not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font> or  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_1"><b>suppose </b></a><a NAME="E1:13_1_1_1"/>
not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font>
 ;<br/><div class="add"><a NAME="E2:13_1_1_1"/><b>then </b>
 <a href="zf_fund2.html#K1" target="_self">Section</a> <font color="Maroon">H</font>,<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:13_1_1_1"/>
 <a href="zf_fund2.html#K1" target="_self">Section</a> <font color="Maroon">H</font>,<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, <a class="ref" href="zf_fund1.html#T3">ZF_FUND1:3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1_2"><b>suppose </b></a><a NAME="E1:13_1_1_2"/><i><font color="Green">E49</font></i>: 
 <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font>
 ;<br/><div class="add"><b>reconsider </b><font color="Maroon">n</font> =  <a href="xboole_0.html#K1">{}</a>  as    <a href="subset_1.html#M1">Element</a> of  <a href="ordinal1.html#K5">omega</a>  <b>by </b><i><a class="ref" href="ordinal1.html#D12">ORDINAL1:def 12</a></i>;<br/><b>set </b><font color="Maroon">fs</font> = <span class="p1">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span>;<br/><b>reconsider </b><font color="Maroon">a</font> = <font color="Maroon">E</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> <b>by </b><i/>;<br/><a NAME="E4:13_1_1_2"/><i><font color="Green">E50</font></i>: 
 <a href="zf_fund1.html#K7">Diagram</a> <font color="Maroon">H</font>,<font color="Maroon">E</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, , <a class="ref" href="zf_fund1.html#T22">ZF_FUND1:22</a></i>;<br/><b>then reconsider </b><font color="Maroon">b</font> =  <a href="zf_fund1.html#K7">Diagram</a> <font color="Maroon">H</font>,<font color="Maroon">E</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> ;<br/><a NAME="E6:13_1_1_2"/><i><font color="Green">E51</font></i>: 
 <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, , <a class="ref" href="zf_fund1.html#T9">ZF_FUND1:9</a></i>;<br/><a NAME="E7:13_1_1_2"/><i><font color="Green">E52</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="zf_fund1.html#T32">ZF_FUND1:32</a></i>;<br/><b>then reconsider </b><font color="Maroon">y</font> = <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p3">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span></span>)</span> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> <b>by </b><i>, <a class="ref" href="zf_fund1.html#T1">ZF_FUND1:1</a></i>;<br/><b>set </b><font color="Maroon">A</font> = <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> : ( <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">w</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> ) </span>}</span> ;<br/><b>set </b><font color="Maroon">B</font> = <span class="p1">{<span class="default"> <font color="Olive">e</font> where <font color="Olive">e</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">e</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> </span>}</span> ;<br/><a NAME="E9:13_1_1_2"/><i><font color="Green">E53</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> : ( <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">w</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> ) </span>}</span>  <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">e</font> where <font color="Olive">e</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">e</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> </span>}</span> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:13_1_1_2_1"/>
<span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> : ( <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">w</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">e</font> where <font color="Olive">e</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">e</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:13_1_1_2_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> : ( <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">w</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> ) </span>}</span> 
 ;<br/>

<a NAME="E2:13_1_1_2_1_1"/><b>then </b>
 ex <font color="Olive">w</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> st <br/>( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Olive">w</font> &amp; <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">w</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> )
 
;<br/>
<b>hence </b><a NAME="E3:13_1_1_2_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">e</font> where <font color="Olive">e</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">e</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> </span>}</span> 
 ;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:13_1_1_2_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">e</font> where <font color="Olive">e</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">e</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">e</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font><b> such that </b><br/><a NAME="E4:13_1_1_2_1"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Maroon">e</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> )
 ;<br/>
<b>reconsider </b><font color="Maroon">e</font> = <font color="Maroon">e</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> <b>by </b><i>, <a class="ref" href="zf_fund1.html#T1">ZF_FUND1:1</a></i>;<br/>
<a NAME="E6:13_1_1_2_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> : ( <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">w</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> ) </span>}</span> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:13_1_1_2_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> : ( <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">w</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> ) </span>}</span> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div><a NAME="E10:13_1_1_2"/>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E11:13_1_1_2"/><b>then </b><i><font color="Green">E55</font></i>: 
not <font color="Maroon">n</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E12:13_1_1_2"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">Y</font>
 <b>by </b><i>, , <a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/><a NAME="E13:13_1_1_2"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p4">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<font color="Maroon">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:13_1_1_2_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E2:13_1_1_2_2"/><b>then </b><i><font color="Green">E69</font></i>: 
 ex <font color="Olive">f1</font> being  <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">E</font> st <br/>( <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">f1</font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> &amp; <font color="Olive">f1</font> <a href="hidden.html#R2">in</a>  <a href="zf_model.html#K5">St</a> <font color="Maroon">H</font>,<font color="Maroon">E</font> )
 
<b>by </b><i><a class="ref" href="zf_fund1.html#D5">ZF_FUND1:def 5</a></i>;<br/>
<a NAME="E3:13_1_1_2_2"/>
 <a href="zf_fund1.html#K4">x".</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span> <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K5">code</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="zf_fund1.html#T34">ZF_FUND1:34</a></i>;<br/>
<a NAME="E4:13_1_1_2_2"/><b>then </b>
<font color="Maroon">n</font> <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K5">code</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span>
 
<b>by </b><i><a class="ref" href="zf_fund1.html#D3">ZF_FUND1:def 3</a></i>;<br/>
<a NAME="E5:13_1_1_2_2"/><b>then </b><i><font color="Green">E71</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="zf_fund1.html#K5">code</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a></i>;<br/>
<a NAME="E6:13_1_1_2_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p2">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span>,<font color="Maroon">a</font>
 
<b>by </b><i>, <a class="ref" href="zf_fund1.html#T32">ZF_FUND1:32</a></i>;<br/>
<b>hence </b><a NAME="E7:13_1_1_2_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_fund1.html#K5">code</a> <span class="p4">(<span class="default"><a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font></span>)</span></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">n</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T45">XBOOLE_1:45</a></i>;<br/>


</div><b>end;</b></div><a NAME="E14:13_1_1_2"/><b>then </b>
<span class="p1">{<span class="default"> <font color="Olive">w</font> where <font color="Olive">w</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">W</font> : ( <font color="Olive">w</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">n</font>,<font color="Olive">w</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">b</font> ) </span>}</span>  <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, , , , , , <a class="ref" href="zf_fund1.html#T16">ZF_FUND1:16</a></i>;<br/><b>hence </b><a NAME="E15:13_1_1_2"/>
 <a href="zf_fund2.html#K1" target="_self">Section</a> <font color="Maroon">H</font>,<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:13"/>
 <a href="zf_fund2.html#K1" target="_self">Section</a> <font color="Maroon">H</font>,<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font>
 ;<br/>


</div>
