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

<b>let </b><font color="Maroon">H</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">M</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">m</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">M</font>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>









<b>set </b><font color="Maroon">e</font> = <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> ;<br/>
<b>set </b><font color="Maroon">f</font> = <font color="Maroon">v</font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> ;<br/>
<b>set </b><font color="Maroon">b</font> = <span class="p1">(<span class="default"><font color="Maroon">v</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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:11"/>
 <a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font>
 ;<br/>

<a NAME="E2:11"/><b>then </b>
 <a href="zf_fund1.html#K4">x".</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></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="E3:11"/><b>then </b>
<font color="Maroon">i</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="E4:11"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</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="E5:11"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</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/>
<i><font color="Green">E49</font></i>:  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<a href="ordinal1.html#K5">omega</a>  <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="zf_fund1.html#T32">ZF_FUND1:32</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T52">ZFMISC_1:52</a></i>
;<br/>
<b>then </b><i><font color="Green">E50</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <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"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span> = 
<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">i</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="partfun1.html#K2">|</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="grfunc_1.html#T18">GRFUNC_1:18</a></i>
<br/>.= 
<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">i</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p0">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<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">i</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p0">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="funct_1.html#K1">.</a> <span class="p4">(<span class="default"><a href="zf_fund1.html#K4">x".</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="zf_fund1.html#D3">ZF_FUND1:def 3</a></i>
<br/>.= 
<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">i</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span></span>)</span></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="zf_fund1.html#T33">ZF_FUND1:33</a></i>
<br/>.= 
<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">i</font>,<font color="Maroon">m</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="zf_lang1.html#D1">ZF_LANG1:def 1</a></i>
;<br/>
<a NAME="E8:11"/><i><font color="Green">E51</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">v</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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3"><b>proof </b></a><div class="add">

<i><font color="Green">E52</font></i>:  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</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="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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
<a href="ordinal1.html#K5">omega</a>  <a href="subset_1.html#K9">/\</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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="zf_fund1.html#T32">ZF_FUND1:32</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="zf_fund1.html#T32">ZF_FUND1:32</a></i>
<br/>.= 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="partfun1.html#K2">|</a> <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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:11_3_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</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="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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
 ;<br/><a NAME="E2:11_3_2"/><b>then </b>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span></span>)</span> <a href="subset_1.html#K9">/\</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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/><a NAME="E3:11_3_2"/><b>then </b>
<font color="Maroon">u</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">i</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:11_3_2"/><b>then </b><i><font color="Green">E54</font></i>: 
( <font color="Maroon">u</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> &amp; not <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</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/><b>then consider </b><font color="Maroon">x</font> being   <a href="zf_lang.html#NM1">Variable</a><b> such that </b><br/><a NAME="E6:11_3_2"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zf_fund1.html#K6">Free</a> <font color="Maroon">H</font> &amp; <font color="Maroon">u</font> <a href="hidden.html#R1">=</a>  <a href="zf_fund1.html#K4">x".</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="zf_fund1.html#T34">ZF_FUND1:34</a></i>;<br/><a NAME="E7:11_3_2"/>
<font color="Maroon">i</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_fund1.html#K4">x".</a> <font color="Maroon">x</font>
 <b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E8:11_3_2"/><b>then </b><i><font color="Green">E56</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font>
 <b>by </b><i><a class="ref" href="zf_fund1.html#D3">ZF_FUND1:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</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="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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font> = 
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="zf_fund1.html#T33">ZF_FUND1:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="zf_lang1.html#D1">ZF_LANG1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font>
<b>by </b><i>, <a class="ref" href="zf_fund1.html#T33">ZF_FUND1:33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="partfun1.html#K1">*</a> <a href="zf_fund1.html#K3">decode</a> </span>)</span> <a href="partfun1.html#K2">|</a> <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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:11_3"/>
<span class="p1">(<span class="default"><font color="Maroon">v</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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div><b>end;</b></div>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <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> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <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"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T45">XBOOLE_1:45</a></i>
<br/>.= 
<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">i</font>,<font color="Maroon">m</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</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="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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i>, , <a class="ref" href="relat_1.html#T107">RELAT_1:107</a></i>
;<br/>
<b>hence </b><a NAME="E10:11"/>
<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">i</font>,<font color="Maroon">m</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</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="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">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> <font color="Maroon">i</font></span>)</span>,<font color="Maroon">m</font></span>)</span> <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>
 ;<br/>


</div>
