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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:20"/><i><font color="Green">E18</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">c<sub>2</sub></font>
 ;<br/>

<b>thus </b><a NAME="E2:20"/>
( <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></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> implies for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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="Olive">b<sub>1</sub></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="Olive">b<sub>3</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></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>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<a NAME="E2:20_1"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>2</sub></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="txt" href="zfmodel2.html#E1:20_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="zf_lang1.html#T80">ZF_LANG1:80</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E4:20_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>2</sub></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>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>thus </b><a NAME="E5:20_1"/>
( <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:20_1_1"/>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:20_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>5</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="zfmodel2.html#E1:20"><i><font color="Green">E18</font></i></a>, <a class="ref" href="zfmodel2.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E3:20_1_1"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></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> &amp; <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="zfmodel2.html#E4:20_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="zfmodel2.html#E12"><i><font color="Green">Lemma11</font></i></a>, <a class="ref" href="zf_lang1.html#T79">ZF_LANG1:79</a>, <a class="ref" href="zf_lang1.html#T80">ZF_LANG1:80</a></i>;<br/>
<a NAME="E4:20_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></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">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></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">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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; <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></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="txt" href="zfmodel2.html#E12"><i><font color="Green">Lemma11</font></i></a>, <a class="ref" href="zf_lang1.html#D1">ZF_LANG1:def 1</a>, <a class="ref" href="zf_model.html#T19">ZF_MODEL:19</a></i>;<br/>
<b>hence </b><a NAME="E5:20_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="zf_model.html#T12">ZF_MODEL:12</a></i>;<br/>


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

<a NAME="E6:20_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>6</sub></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">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>6</sub></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">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>6</sub></font> )
 
<b>by </b><i><a class="txt" href="zfmodel2.html#E12"><i><font color="Green">Lemma11</font></i></a>, <a class="ref" href="zf_lang1.html#D1">ZF_LANG1:def 1</a></i>;<br/>
<a NAME="E7:20_1"/><b>then </b><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>6</sub></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/>
<b>assume </b><a NAME="E8:20_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<a NAME="E9:20_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></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="txt" href="zfmodel2.html#E4:20_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="zf_lang1.html#T80">ZF_LANG1:80</a></i>;<br/>
<a NAME="E10:20_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="zfmodel2.html#E7:20_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="zf_model.html#T19">ZF_MODEL:19</a></i>;<br/>
<a NAME="E11:20_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="zfmodel2.html#E12"><i><font color="Green">Lemma11</font></i></a>, <a class="ref" href="zf_lang1.html#T79">ZF_LANG1:79</a></i>;<br/>
<b>hence </b><a NAME="E12:20_1"/>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E1:20"><i><font color="Green">E18</font></i></a>, <a class="ref" href="zfmodel2.html#T10" target="_self">Th10</a></i>;<br/>


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

<b>assume </b><a NAME="E3:20"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>for <font color="Olive">b<sub>3</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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="Olive">b<sub>1</sub></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="Olive">b<sub>3</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:20_2"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds <br/>( <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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="Olive">b<sub>1</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="zfmodel2.html#E3:20"><i><font color="Green">E19</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><a NAME="E1:20_2_1"/><i><font color="Green">E21</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></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">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></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">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="zfmodel2.html#E12"><i><font color="Green">Lemma11</font></i></a>, <a class="ref" href="zf_lang1.html#D1">ZF_LANG1:def 1</a></i>;<br/><div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_1_1"/>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:20_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>5</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E12"><i><font color="Green">Lemma11</font></i></a>, <a class="ref" href="zf_lang1.html#T79">ZF_LANG1:79</a></i>;<br/><a NAME="E3:20_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E1:20"><i><font color="Green">E18</font></i></a>, <a class="ref" href="zfmodel2.html#T10" target="_self">Th10</a></i>;<br/><a NAME="E4:20_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:20_2"><i><font color="Green">E20</font></i></a></i>;<br/><b>hence </b><a NAME="E5:20_2_1_1"/>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></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="txt" href="zfmodel2.html#E1:20_2_1"><i><font color="Green">E21</font></i></a>, <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="20_2_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_1_2"/>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></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="E2:20_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E1:20_2_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="zf_model.html#T12">ZF_MODEL:12</a></i>;<br/><a NAME="E3:20_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:20_2"><i><font color="Green">E20</font></i></a></i>;<br/><a NAME="E4:20_2_1_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>6</sub></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">c<sub>5</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E1:20"><i><font color="Green">E18</font></i></a>, <a class="ref" href="zfmodel2.html#T10" target="_self">Th10</a></i>;<br/><b>hence </b><a NAME="E5:20_2_1_2"/>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E12"><i><font color="Green">Lemma11</font></i></a>, <a class="ref" href="zf_lang1.html#T79">ZF_LANG1:79</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:20_2_1"/>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>6</sub></font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">c<sub>2</sub></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="txt" href="zfmodel2.html#E2:20_2_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="zf_model.html#T19">ZF_MODEL:19</a></i>;<br/></div><b>end;</b></div><a NAME="E4:20_2"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>5</sub></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">c<sub>2</sub></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#T80">ZF_LANG1:80</a></i>;<br/><b>hence </b><a NAME="E5:20_2"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></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">c<sub>2</sub></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#T82">ZF_LANG1:82</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:20"/>
<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></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>by </b><i><a class="ref" href="zf_lang1.html#T80">ZF_LANG1:80</a></i>;<br/>


</div>
