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<b>let </b><font color="Maroon">H1</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">H2</font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="zf_lang.html#NM1">Variable</a>;<br/><b>let </b><font color="Maroon">M</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:122"/><i><font color="Green">E46</font></i>: 
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zf_model.html#K2">Free</a> <font color="Maroon">H1</font>
 ;<br/>

<b>let </b><font color="Maroon">v</font> be   <a href="funct_2.html#NM1">Function</a> of  <a href="zf_lang.html#K1">VAR</a> ,<font color="Maroon">M</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="zf_model.html#D5">ZF_MODEL:def 5</a><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:122_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">H2</font></span>)</span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:122_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H1</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="122_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">M</font>;<br/><a NAME="E1:122_1_1_1"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<font color="Maroon">H1</font>
 <b>by </b><i><a class="ref" href="zf_lang1.html#T2" target="_self">Th2</a>, <a class="ref" href="zf_lang1.html#T4" target="_self">Th4</a>, <a class="ref" href="zfmodel1.html#T10">ZFMODEL1:10</a></i>;<br/><a NAME="E2:122_1_1_1"/><b>then </b>
( <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H1</font> &amp; <font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H1</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">H2</font> )
 <b>by </b><i><a class="ref" href="zf_lang1.html#T3" target="_self">Th3</a>, </i>;<br/><b>hence </b><a NAME="E3:122_1_1_1"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_lang1.html#K1" target="_self">/</a> <font color="Maroon">x</font>,<font color="Maroon">m</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H2</font>
 <b>by </b><i><a class="ref" href="zf_model.html#T18">ZF_MODEL:18</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:122_1_1"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a>  <a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<font color="Maroon">H2</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E3:122_1"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <font color="Maroon">H1</font> <a href="zf_lang.html#K11">=&gt;</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<font color="Maroon">H2</font></span>)</span>
 <b>by </b><i><a class="ref" href="zf_model.html#T18">ZF_MODEL:18</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:122"/>
<font color="Maroon">M</font>,<font color="Maroon">v</font> <a href="zf_model.html#R1">|=</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<span class="p2">(<span class="default"><font color="Maroon">H1</font> <a href="zf_lang.html#K11">=&gt;</a> <font color="Maroon">H2</font></span>)</span></span>)</span> <a href="zf_lang.html#K11">=&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">H1</font> <a href="zf_lang.html#K11">=&gt;</a> <span class="p2">(<span class="default"><a href="zf_lang.html#K8">All</a> <font color="Maroon">x</font>,<font color="Maroon">H2</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="zf_model.html#T18">ZF_MODEL:18</a></i>;<br/>


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