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

<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/><b>let </b><font color="Maroon" title="c3">M</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c4">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/><b>let </b><font color="Maroon" title="c5">v</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="zf_lang.html#K1" title="ZF_LANG:func.1">VAR</a> ,<font color="Maroon" title="c3">M</font>;<br/>









<b>set </b><font color="Maroon" title="c6">F</font> = <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>;<br/>
<b>set </b><font color="Maroon" title="c7">f</font> = <font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:15"/><i><font color="Green" title="E16">A1</font></i>: 
( not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> &amp; <font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>and </b><br/><a NAME="E2:15"/><i><font color="Green" title="E17">A2</font></i>: 
( not <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c4">H</font> &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 &amp; not <font color="Maroon" title="c2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp; <font color="Maroon" title="c1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 )
 ;<br/>

<a NAME="E3:15"/>
( (  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> &amp; not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> ) or ( not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )
 
<b>by </b><i><a class="txt" href="zfmodel2.html#E1:15"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E4:15"/><b>then </b>
(  not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> or (  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) )
 
<b>by </b><i><a class="ref" href="zfmodel2.html#T1" target="_self" title="ZFMODEL2:th.1">Th1</a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:15"/><i><font color="Green" title="E18">A3</font></i>: 
not  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span>
 ;<br/>

<a NAME="E6:15"/><i><font color="Green" title="E19">A4</font></i>: 
(  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 &amp;  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 &amp;  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3 <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4 )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T86" title="ZF_LANG1:th.86">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" title="c8">m3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</font>;<br/><a NAME="E1:15_1"/>
<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E1:15"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="zf_lang1.html#T80" title="ZF_LANG1:th.80">ZF_LANG1:80</a></i>;<br/><b>then consider </b><font color="Maroon" title="c9">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</font><b> such that </b><br/><a NAME="E3:15_1"/><i><font color="Green" title="E20">A5</font></i>: 
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T82" title="ZF_LANG1:th.82">ZF_LANG1:82</a></i>;<br/><b>set </b><font color="Maroon" title="c10">f1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">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" title="c11">m4</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</font>;<br/><a NAME="E1:15_1_1"/><i><font color="Green" title="E21">A6</font></i>: 
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E3:15_1"><i><font color="Green" title="E20">A5</font></i></a>, <a class="ref" href="zf_lang1.html#T80" title="ZF_LANG1:th.80">ZF_LANG1:80</a></i>;<br/><a NAME="E2:15_1_1"/><i><font color="Green" title="E22">A7</font></i>: 
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">m4</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">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" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">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" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">m</font> )
 <b>by </b><i><a class="txt" href="zfmodel2.html#E6:15"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="zf_lang1.html#D1" title="ZF_LANG1:def.1">ZF_LANG1:def 1</a></i>;<br/><div><i><font color="Green" title="E23">A8</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" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>
 ;<br/><a NAME="E2:15_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">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" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c2">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" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T13" target="_self" title="ZFMODEL2:th.13">Th13</a></i>;<br/><a NAME="E3:15_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T10" target="_self" title="ZFMODEL2:th.10">Th10</a></i>;<br/><a NAME="E4:15_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="zfmodel2.html#E6:15"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="zfmodel2.html#T8" target="_self" title="ZFMODEL2:th.8">Th8</a></i>;<br/><a NAME="E5:15_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T6" target="_self" title="ZFMODEL2:th.6">Th6</a></i>;<br/><a NAME="E6:15_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E1:15_1_1"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="zf_model.html#T19" title="ZF_MODEL:th.19">ZF_MODEL:19</a></i>;<br/><a NAME="E7:15_1_1_1"/><b>then </b>
<font color="Maroon" title="c9">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">m4</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15_1_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></i>;<br/><b>hence </b><a NAME="E8:15_1_1_1"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15_1_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">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" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 ;<br/><a NAME="E2:15_1_1_2"/><b>then </b>
<font color="Maroon" title="c9">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">m4</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15_1_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></i>;<br/><a NAME="E3:15_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15_1_1"><i><font color="Green" title="E22">A7</font></i></a>, <a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></i>;<br/><a NAME="E4:15_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E1:15_1_1"><i><font color="Green" title="E21">A6</font></i></a>, <a class="ref" href="zf_model.html#T19" title="ZF_MODEL:th.19">ZF_MODEL:19</a></i>;<br/><a NAME="E5:15_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T6" target="_self" title="ZFMODEL2:th.6">Th6</a></i>;<br/><a NAME="E6:15_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="zfmodel2.html#E6:15"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="zfmodel2.html#T8" target="_self" title="ZFMODEL2:th.8">Th8</a></i>;<br/><a NAME="E7:15_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">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" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c2">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" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p0">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T10" target="_self" title="ZFMODEL2:th.10">Th10</a></i>;<br/><b>hence </b><a NAME="E8:15_1_1_2"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T13" target="_self" title="ZFMODEL2:th.13">Th13</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:15_1_1"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<font color="Maroon" title="c11">m4</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E3:15_1_1"><i><font color="Green" title="E23">A8</font></i></a>, <a class="ref" href="zf_model.html#T19" title="ZF_MODEL:th.19">ZF_MODEL:19</a></i>;<br/></div><b>end;</b></div><a NAME="E5:15_1"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<font color="Maroon" title="c9">m</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T80" title="ZF_LANG1:th.80">ZF_LANG1:80</a></i>;<br/><b>hence </b><a NAME="E6:15_1"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c8">m3</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T82" title="ZF_LANG1:th.82">ZF_LANG1:82</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:15"/><i><font color="Green" title="E20">A9</font></i>: 
<font color="Maroon" title="c3">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<span class="p1">(<span class="default"><a href="zf_lang.html#K13" title="ZF_LANG:func.13">Ex</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>,<span class="p2">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> <a href="zf_lang.html#K12" title="ZF_LANG:func.12">&lt;=&gt;</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <span class="p5">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T80" title="ZF_LANG1:th.80">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" title="c8">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:15_2"/>
<font color="Maroon" title="c8">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c9">m</font> = <font color="Maroon" title="c8">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">M</font> ;<br/><b>set </b><font color="Maroon" title="c10">m'</font> = <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">m</font>;<br/><a NAME="E3:15_2"/>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E1:15"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="zfmodel2.html#T11" target="_self" title="ZFMODEL2:th.11">Th11</a></i>;<br/><a NAME="E4:15_2"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">m</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T6" target="_self" title="ZFMODEL2:th.6">Th6</a></i>;<br/><a NAME="E5:15_2"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="txt" href="zfmodel2.html#E6:15"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="zfmodel2.html#T7" target="_self" title="ZFMODEL2:th.7">Th7</a></i>;<br/><a NAME="E6:15_2"/><b>then </b><i><font color="Green" title="E21">A10</font></i>: 
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p4">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">m</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">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" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p5">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p4">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p3">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">m</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T14" target="_self" title="ZFMODEL2:th.14">Th14</a></i>;<br/><a NAME="E7:15_2"/>
(  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> &amp;  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c4">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K4" title="ZF_LANG1:func.4">variables_in</a> <font color="Maroon" title="c4">H</font> )
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="zfmodel2.html#T2" target="_self" title="ZFMODEL2:th.2">Th2</a>, <a class="ref" href="zf_lang1.html#T164" title="ZF_LANG1:th.164">ZF_LANG1:164</a></i>;<br/><a NAME="E8:15_2"/><b>then </b>
not <font color="Maroon" title="c1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E2:15"><i><font color="Green" title="E17">A2</font></i></a></i>;<br/><a NAME="E9:15_2"/><b>then </b>
<font color="Maroon" title="c3">M</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 3</span>)</span>,<font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K2" title="ZF_LANG:func.2">x.</a> 4</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">m</font></span>)</span> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E6:15_2"><i><font color="Green" title="E21">A10</font></i></a>, <a class="ref" href="zfmodel2.html#T10" target="_self" title="ZFMODEL2:th.10">Th10</a></i>;<br/><b>hence </b><a NAME="E10:15_2"/>
<span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p3">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font>
 <b>by </b><i><a class="txt" href="zfmodel2.html#E5:15"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="zfmodel2.html#E8:15"><i><font color="Green" title="E20">A9</font></i></a>, <a class="ref" href="zfmodel2.html#T11" target="_self" title="ZFMODEL2:th.11">Th11</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:15"/>
 <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <font color="Maroon" title="c4">H</font>,<font color="Maroon" title="c5">v</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="zfmodel1.html#K1" title="ZFMODEL1:func.1">def_func'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="zf_lang1.html#K6" title="ZF_LANG1:func.6">/</a> <font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c1">x</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c1">x</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T18" title="FUNCT_2:th.18">FUNCT_2:18</a></i>;<br/>


</div>
