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

<b>let </b><font color="Maroon">x</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">y</font> be   <a href="zf_lang.html#NM1">Variable</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">H</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<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>set </b><font color="Maroon">F</font> = <font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font>;<br/>
<b>set </b><font color="Maroon">f</font> = <font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:15"/><i><font color="Green">E46</font></i>: 
( not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a>  <a href="zf_model.html#K2">Free</a> <font color="Maroon">H</font> &amp; <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang.html#K12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green">E47</font></i>: 
( not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zf_lang1.html#K4">variables_in</a> <font color="Maroon">H</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> 3 &amp; <font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> 4 &amp; not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="zf_model.html#K2">Free</a> <font color="Maroon">H</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> 0 &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> 3 &amp; <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> 4 )
 ;<br/>

<a NAME="E3:15"/>
( (  <a href="zf_model.html#K2">Free</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="zf_lang1.html#K4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> &amp; not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a>  <a href="zf_lang1.html#K4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> ) or ( not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp; not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2">Free</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> ) )
 
<b>by </b><i>, , <a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E4:15"/><b>then </b>
(  not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a>  <a href="zf_model.html#K2">Free</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> or (  <a href="zf_model.html#K2">Free</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2">Free</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp; not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2">Free</a> <font color="Maroon">H</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> ) )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/><i><font color="Green">E48</font></i>: 
not  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#R2">in</a>  <a href="zf_model.html#K2">Free</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span>
 ;<br/>

<a NAME="E6:15"/><i><font color="Green">E49</font></i>: 
(  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> 3 &amp;  <a href="zf_lang.html#K2">x.</a> 0 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> 4 &amp;  <a href="zf_lang.html#K2">x.</a> 3 <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="zf_lang.html#K2">x.</a> 4 )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T86">ZF_LANG1:86</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m3</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font>;<br/><a NAME="E1:15_1"/>
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m3</font> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang.html#K12">&lt;=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="zf_lang1.html#T80">ZF_LANG1:80</a></i>;<br/><b>then consider </b><font color="Maroon">m</font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font><b> such that </b><br/><a NAME="E3:15_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">M</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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang.html#K12">&lt;=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T82">ZF_LANG1:82</a></i>;<br/><b>set </b><font color="Maroon">f1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m4</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font>;<br/><a NAME="E1:15_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font> <a href="zf_lang.html#K12">&lt;=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="zf_lang1.html#T80">ZF_LANG1:80</a></i>;<br/><a NAME="E2:15_1_1"/><i><font color="Green">E52</font></i>: 
( <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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m4</font> &amp; <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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span> &amp; <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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p5">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m4</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p5">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span> <a href="hidden.html#R1">=</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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span> &amp; <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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> )
 <b>by </b><i>, <a class="ref" href="zf_lang1.html#D1">ZF_LANG1:def 1</a></i>;<br/><div><i><font color="Green">E53</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_1_1"/>
<font color="Maroon">M</font>,<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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font>
 ;<br/><a NAME="E2:15_1_1_1"/><b>then </b>
<font color="Maroon">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p5">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">y</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> <font color="Maroon">x</font>,<span class="p0">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/><a NAME="E3:15_1_1_1"/><b>then </b>
<font color="Maroon">M</font>,<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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/><a NAME="E4:15_1_1_1"/><b>then </b>
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E5:15_1_1_1"/><b>then </b>
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/><a NAME="E6:15_1_1_1"/><b>then </b>
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>
 <b>by </b><i>, <a class="ref" href="zf_model.html#T19">ZF_MODEL:19</a></i>;<br/><a NAME="E7:15_1_1_1"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m4</font>
 <b>by </b><i>, <a class="ref" href="zf_model.html#T12">ZF_MODEL:12</a></i>;<br/><b>hence </b><a NAME="E8:15_1_1_1"/>
<font color="Maroon">M</font>,<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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>
 <b>by </b><i>, <a class="ref" href="zf_model.html#T12">ZF_MODEL:12</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_1_2"/>
<font color="Maroon">M</font>,<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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>
 ;<br/><a NAME="E2:15_1_1_2"/><b>then </b>
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m4</font>
 <b>by </b><i>, <a class="ref" href="zf_model.html#T12">ZF_MODEL:12</a></i>;<br/><a NAME="E3:15_1_1_2"/><b>then </b>
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>
 <b>by </b><i>, <a class="ref" href="zf_model.html#T12">ZF_MODEL:12</a></i>;<br/><a NAME="E4:15_1_1_2"/><b>then </b>
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, <a class="ref" href="zf_model.html#T19">ZF_MODEL:19</a></i>;<br/><a NAME="E5:15_1_1_2"/><b>then </b>
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/><a NAME="E6:15_1_1_2"/><b>then </b>
<font color="Maroon">M</font>,<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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E7:15_1_1_2"/><b>then </b>
<font color="Maroon">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p5">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">y</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><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> <font color="Maroon">x</font>,<span class="p0">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E8:15_1_1_2"/>
<font color="Maroon">M</font>,<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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:15_1_1"/>
<font color="Maroon">M</font>,<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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<font color="Maroon">m4</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> <a href="zf_lang.html#K12">&lt;=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="zf_model.html#T19">ZF_MODEL:19</a></i>;<br/></div><b>end;</b></div><a NAME="E5:15_1"/><b>then </b>
<font color="Maroon">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<font color="Maroon">m</font> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> <a href="zf_lang.html#K12">&lt;=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T80">ZF_LANG1:80</a></i>;<br/><b>hence </b><a NAME="E6:15_1"/>
<font color="Maroon">M</font>,<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m3</font> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> <a href="zf_lang.html#K12">&lt;=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T82">ZF_LANG1:82</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:15"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> <a href="zf_lang.html#K12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2">x.</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T80">ZF_LANG1:80</a></i>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:15_2"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">M</font>
 ;<br/><b>then reconsider </b><font color="Maroon">m</font> = <font color="Maroon">a</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font> ;<br/><b>set </b><font color="Maroon">m'</font> = <span class="p1">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font>;<br/><a NAME="E3:15_2"/>
<font color="Maroon">M</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> 3</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/><a NAME="E4:15_2"/><b>then </b>
<font color="Maroon">M</font>,<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> 3</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, </i>;<br/><a NAME="E5:15_2"/><b>then </b>
<font color="Maroon">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font>
 <b>by </b><i>, , </i>;<br/><a NAME="E6:15_2"/><b>then </b><i><font color="Green">E55</font></i>: 
<font color="Maroon">M</font>,<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> <font color="Maroon">x</font>,<span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p5">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/><a NAME="E7:15_2"/>
(  <a href="zf_model.html#K2">Free</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="zf_model.html#K2">Free</a> <font color="Maroon">H</font> &amp;  <a href="zf_model.html#K2">Free</a> <font color="Maroon">H</font> <a href="tarski.html#R1">c=</a>  <a href="zf_lang1.html#K4">variables_in</a> <font color="Maroon">H</font> )
 <b>by </b><i>, , <a class="ref" href="zf_lang1.html#T164">ZF_LANG1:164</a></i>;<br/><a NAME="E8:15_2"/><b>then </b>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zf_model.html#K2">Free</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span>
 <b>by </b><i/>;<br/><a NAME="E9:15_2"/><b>then </b>
<font color="Maroon">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2">x.</a> 3</span>)</span>,<font color="Maroon">m</font></span>)</span> <a href="zf_lang1.html#K1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">m</font></span>)</span> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E10:15_2"/>
<span class="p1">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1">def_func'</a> <span class="p2">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p3">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:15"/>
 <a href="zfmodel1.html#K1">def_func'</a> <font color="Maroon">H</font>,<font color="Maroon">v</font> <a href="funct_2.html#R2">=</a>  <a href="zfmodel1.html#K1">def_func'</a> <span class="p1">(<span class="default"><font color="Maroon">H</font> <a href="zf_lang1.html#K6">/</a> <font color="Maroon">y</font>,<font color="Maroon">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="zf_lang1.html#K1">/</a> <font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">y</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


</div>
