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

<b>let </b><font color="Maroon" title="c1">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="c2">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>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>] <b>means </b>for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">v'</font> being  <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="c2">M</font>  st ( for <font color="Olive" title="b3">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b3">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> $1 holds <br/><font color="Olive" title="b2">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">x</font> ) &amp; <font color="Maroon" title="c2">M</font>,<font color="Olive" title="b1">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> $1 holds <br/><font color="Maroon" title="c2">M</font>,<font color="Olive" title="b2">v'</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> $1;<br/>
<a NAME="E1:68"/><i><font color="Green" title="E27">A1</font></i>: 
for <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a> holds <br/> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Olive" title="b2">x2</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">x1</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Olive" title="b2">x2</font>] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x1</font>, <font color="Maroon" title="c4">x2</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/>



<a NAME="E1:68_1"/><i><font color="Green" title="E28">A2</font></i>: 
(  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Maroon" title="c4">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> &amp;  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x1</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c4">x2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x1</font>,<font color="Maroon" title="c4">x2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T63" target="_self" title="ZF_LANG1:th.63">Th63</a>, <a class="ref" href="zf_lang1.html#T64" target="_self" title="ZF_LANG1:th.64">Th64</a></i>;<br/>
<b>thus </b><a NAME="E2:68_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">x1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Maroon" title="c4">x2</font>]
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">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="c2">M</font>;<br/>



<b>assume </b><a NAME="E1:68_1_1"/><i><font color="Green" title="E29">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">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="c3">x1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Maroon" title="c4">x2</font></span>)</span> holds <br/><font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 ;<br/>

<b>assume </b><a NAME="E2:68_1_1"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">x1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Maroon" title="c4">x2</font>
 ;<br/>

<a NAME="E3:68_1_1"/><b>then </b><i><font color="Green" title="E30">A4</font></i>: 
<font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x2</font>
 
<b>by </b><i><a class="ref" href="zf_model.html#T12" title="ZF_MODEL:th.12">ZF_MODEL:12</a></i>;<br/>
<a NAME="E4:68_1_1"/>
( <font color="Maroon" title="c3">x1</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="c3">x1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Maroon" title="c4">x2</font></span>)</span> &amp; <font color="Maroon" title="c4">x2</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="c3">x1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Maroon" title="c4">x2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:68_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E5:68_1_1"/><b>then </b>
( <font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x2</font> )
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:68_1_1"><i><font color="Green" title="E29">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:68_1_1"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c6">v'</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">x1</font> <a href="zf_lang.html#K4" title="ZF_LANG:func.4">'='</a> <font color="Maroon" title="c4">x2</font>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E3:68_1_1"><i><font color="Green" title="E30">A4</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>

<b>let </b><font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">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="c2">M</font>;<br/>



<b>assume </b><a NAME="E3:68_1"/><i><font color="Green" title="E29">A5</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">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="c3">x1</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c4">x2</font></span>)</span> holds <br/><font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 ;<br/>

<b>assume </b><a NAME="E4:68_1"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">x1</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c4">x2</font>
 ;<br/>

<a NAME="E5:68_1"/><b>then </b><i><font color="Green" title="E30">A6</font></i>: 
<font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x2</font>
 
<b>by </b><i><a class="ref" href="zf_model.html#T13" title="ZF_MODEL:th.13">ZF_MODEL:13</a></i>;<br/>
<a NAME="E6:68_1"/>
( <font color="Maroon" title="c3">x1</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="c3">x1</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c4">x2</font></span>)</span> &amp; <font color="Maroon" title="c4">x2</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="c3">x1</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c4">x2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:68_1"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<a NAME="E7:68_1"/><b>then </b>
( <font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x1</font> &amp; <font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">x2</font> )
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E3:68_1"><i><font color="Green" title="E29">A5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:68_1"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c6">v'</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">x1</font> <a href="zf_lang.html#K5" title="ZF_LANG:func.5">'in'</a> <font color="Maroon" title="c4">x2</font>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E5:68_1"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="zf_model.html#T13" title="ZF_MODEL:th.13">ZF_MODEL:13</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:68"/><i><font color="Green" title="E28">A7</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Olive" title="b1">H</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/>

<b>assume </b><a NAME="E1:68_2"/><i><font color="Green" title="E29">A8</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">H</font>]
 ;<br/>

<b>let </b><font color="Maroon" title="c4">v</font>, <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="c2">M</font>;<br/>



<b>assume </b><a NAME="E2:68_2"/><i><font color="Green" title="E30">A9</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">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"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c3">H</font></span>)</span> holds <br/><font color="Maroon" title="c5">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 ;<br/>

<b>assume </b><a NAME="E3:68_2"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a>  <a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c3">H</font>
 ;<br/>

<a NAME="E4:68_2"/><b>then </b><i><font color="Green" title="E31">A10</font></i>: 
not <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c4">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="ref" href="zf_model.html#T14" title="ZF_MODEL:th.14">ZF_MODEL:14</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c6">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/><b>assume </b><a NAME="E1:68_2_1"/>
<font color="Maroon" title="c6">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> <font color="Maroon" title="c3">H</font>
 ;<br/><a NAME="E2:68_2_1"/><b>then </b>
<font color="Maroon" title="c6">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"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c3">H</font></span>)</span>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T65" target="_self" title="ZF_LANG1:th.65">Th65</a></i>;<br/><b>hence </b><a NAME="E3:68_2_1"/>
<font color="Maroon" title="c4">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E2:68_2"><i><font color="Green" title="E30">A9</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:68_2"/><b>then </b>
not <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c5">v'</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font>
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:68_2"><i><font color="Green" title="E29">A8</font></i></a>, <a class="txt" href="zf_lang1.html#E4:68_2"><i><font color="Green" title="E31">A10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:68_2"/>
<font color="Maroon" title="c2">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#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="ref" href="zf_model.html#T14" title="ZF_MODEL:th.14">ZF_MODEL:14</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:68"/><i><font color="Green" title="E29">A11</font></i>: 
for <font color="Olive" title="b1">H1</font>, <font color="Olive" title="b2">H2</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H1</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b2">H2</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Olive" title="b2">H2</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">H1</font>, <font color="Maroon" title="c4">H2</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>;<br/>



<b>assume </b><a NAME="E1:68_3"/><i><font color="Green" title="E30">A12</font></i>: 
( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">H1</font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c4">H2</font>] )
 ;<br/>

<a NAME="E2:68_3"/><i><font color="Green" title="E31">A13</font></i>: 
 <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">H2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c3">H1</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</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">H2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="zf_lang1.html#T66" target="_self" title="ZF_LANG1:th.66">Th66</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">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="c2">M</font>;<br/>



<b>assume </b><a NAME="E3:68_3"/><i><font color="Green" title="E32">A14</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">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="c3">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">H2</font></span>)</span> holds <br/><font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 ;<br/>

<b>assume </b><a NAME="E4:68_3"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">H2</font>
 ;<br/>

<a NAME="E5:68_3"/><b>then </b><i><font color="Green" title="E33">A15</font></i>: 
( <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H1</font> &amp; <font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c5">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H2</font> )
 
<b>by </b><i><a class="ref" href="zf_model.html#T15" title="ZF_MODEL:th.15">ZF_MODEL:15</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_3_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/><b>assume </b><a NAME="E1:68_3_1"/>
<font color="Maroon" title="c7">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> <font color="Maroon" title="c3">H1</font>
 ;<br/><a NAME="E2:68_3_1"/><b>then </b>
<font color="Maroon" title="c7">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="c3">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">H2</font></span>)</span>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E2:68_3"><i><font color="Green" title="E31">A13</font></i></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="E3:68_3_1"/>
<font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E3:68_3"><i><font color="Green" title="E32">A14</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E7:68_3"/><b>then </b><i><font color="Green" title="E34">A16</font></i>: 
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c6">v'</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H1</font>
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:68_3"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="zf_lang1.html#E5:68_3"><i><font color="Green" title="E33">A15</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_3_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/><b>assume </b><a NAME="E1:68_3_2"/>
<font color="Maroon" title="c7">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> <font color="Maroon" title="c4">H2</font>
 ;<br/><a NAME="E2:68_3_2"/><b>then </b>
<font color="Maroon" title="c7">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="c3">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">H2</font></span>)</span>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E2:68_3"><i><font color="Green" title="E31">A13</font></i></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="E3:68_3_2"/>
<font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E3:68_3"><i><font color="Green" title="E32">A14</font></i></a></i>;<br/></div><b>end;</b></div>
<a NAME="E9:68_3"/><b>then </b>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c6">v'</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c4">H2</font>
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:68_3"><i><font color="Green" title="E30">A12</font></i></a>, <a class="txt" href="zf_lang1.html#E5:68_3"><i><font color="Green" title="E33">A15</font></i></a></i>;<br/>
<b>hence </b><a NAME="E10:68_3"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c6">v'</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H1</font> <a href="zf_lang.html#K7" title="ZF_LANG:func.7">'&amp;'</a> <font color="Maroon" title="c4">H2</font>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E7:68_3"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="zf_model.html#T15" title="ZF_MODEL:th.15">ZF_MODEL:15</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:68"/><i><font color="Green" title="E30">A17</font></i>: 
for <font color="Olive" title="b1">H</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a><br/> for <font color="Olive" title="b2">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">H</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">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="c4">x1</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/>



<b>assume </b><a NAME="E1:68_4"/><i><font color="Green" title="E31">A18</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c3">H</font>]
 ;<br/>

<b>let </b><font color="Maroon" title="c5">v</font>, <font color="Maroon" title="c6">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="c2">M</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E2:68_4"/><i><font color="Green" title="E32">A19</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b1">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"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c3">H</font></span>)</span> holds <br/><font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 <b>and </b><br/><a NAME="E3:68_4"/><i><font color="Green" title="E33">A20</font></i>: 
<font color="Maroon" title="c2">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> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c3">H</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_4_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c7">m</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">M</font>;<br/><a NAME="E1:68_4_1"/><i><font color="Green" title="E34">A21</font></i>: 
( <font color="Maroon" title="c2">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="c4">x1</font>,<font color="Maroon" title="c7">m</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font> &amp;  <a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c3">H</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zf_model.html#K2" title="ZF_MODEL:func.2">Free</a> <font color="Maroon" title="c3">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="c4">x1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="txt" href="zf_lang1.html#E3:68_4"><i><font color="Green" title="E33">A20</font></i></a>, <a class="ref" href="zf_lang1.html#T67" target="_self" title="ZF_LANG1:th.67">Th67</a>, <a class="ref" href="zf_lang1.html#T80" target="_self" title="ZF_LANG1:th.80">Th80</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_4_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c8">x</font> be   <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>;<br/><b>assume </b><a NAME="E1:68_4_1_1"/>
<font color="Maroon" title="c8">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> <font color="Maroon" title="c3">H</font>
 ;<br/><a NAME="E2:68_4_1_1"/><b>then </b>
( ( <font color="Maroon" title="c8">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"><a href="zf_lang.html#K8" title="ZF_LANG:func.8">All</a> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c3">H</font></span>)</span> &amp; not <font color="Maroon" title="c8">x</font> <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="c4">x1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) or <font color="Maroon" title="c8">x</font> <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="c4">x1</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="txt" href="zf_lang1.html#E1:68_4_1"><i><font color="Green" title="E34">A21</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/><a NAME="E3:68_4_1_1"/><b>then </b>
( ( <font color="Maroon" title="c6">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> &amp; <font color="Maroon" title="c8">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x1</font> ) or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">x1</font> )
 <b>by </b><i><a class="txt" href="zf_lang1.html#E2:68_4"><i><font color="Green" title="E32">A19</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E4:68_4_1_1"/><b>then </b>
( ( <span class="p1">(<span class="default"><font color="Maroon" title="c6">v'</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c7">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> &amp; <font color="Maroon" title="c5">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c4">x1</font>,<font color="Maroon" title="c7">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> ) or ( <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="c4">x1</font>,<font color="Maroon" title="c7">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c6">v'</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c7">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">m</font> ) )
 <b>by </b><i><a class="ref" href="zf_lang1.html#D1" target="_self" title="ZF_LANG1:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E5:68_4_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c6">v'</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c7">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c4">x1</font>,<font color="Maroon" title="c7">m</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">x</font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:68_4_1"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c6">v'</font> <a href="zf_lang1.html#K1" title="ZF_LANG1:func.1">/</a> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c7">m</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E1:68_4"><i><font color="Green" title="E31">A18</font></i></a>, <a class="txt" href="zf_lang1.html#E1:68_4_1"><i><font color="Green" title="E34">A21</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:68_4"/>
<font color="Maroon" title="c2">M</font>,<font color="Maroon" title="c6">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> <font color="Maroon" title="c4">x1</font>,<font color="Maroon" title="c3">H</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T80" target="_self" title="ZF_LANG1:th.80">Th80</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:68"/>
for <font color="Olive" title="b1">H</font> being  <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">H</font>]
 
<b>from </b><i><a class="ref" href="zf_lang1.html#S1" target="_self" title="ZF_LANG1:sch.1">ZF_LANG1:sch 1</a>(<a class="txt" href="zf_lang1.html#E1:68"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="zf_lang1.html#E2:68"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="zf_lang1.html#E3:68"><i><font color="Green" title="E29">A11</font></i></a>, <a class="txt" href="zf_lang1.html#E4:68"><i><font color="Green" title="E30">A17</font></i></a>);<br/></i>
<b>hence </b><a NAME="E6:68"/>
for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">v'</font> being  <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="c2">M</font>  st ( for <font color="Olive" title="b3">x</font> being  <a href="zf_lang.html#NM1" title="ZF_LANG:NM.1">Variable</a>  st <font color="Olive" title="b3">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> <font color="Maroon" title="c1">H</font> holds <br/><font color="Olive" title="b2">v'</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">x</font> ) &amp; <font color="Maroon" title="c2">M</font>,<font color="Olive" title="b1">v</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c1">H</font> holds <br/><font color="Maroon" title="c2">M</font>,<font color="Olive" title="b2">v'</font> <a href="zf_model.html#R1" title="ZF_MODEL:pred.1">|=</a> <font color="Maroon" title="c1">H</font>
 ;<br/>


</div>
