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<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/>

<i><font color="Green" title="E46">A1</font></i>:  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">H</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p2"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">2</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">H</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">2</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">H</font></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T56" title="FINSEQ_1:th.56">FINSEQ_1:56</a></i>
;<br/>
<b>thus </b><a NAME="E2:134"/>
 <a href="zf_lang1.html#K3" title="ZF_LANG1:func.3">variables_in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K3" title="ZF_LANG1:func.3">variables_in</a> <font color="Maroon" title="c1">H</font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="134_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:134_2"/><i><font color="Green" title="E47">A2</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang1.html#K3" title="ZF_LANG1:func.3">variables_in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">H</font></span>)</span>
 ;<br/>

<a NAME="E2:134_2"/><b>then </b><i><font color="Green" title="E48">A3</font></i>: 
( <font color="Maroon" title="c2">a</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">2</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">H</font></span>)</span> &amp; not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="enumset1.html#K3" title="ENUMSET1:func.3">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1,2,3,4</span><a href="enumset1.html#K3" title="ENUMSET1:func.3">}</a></span> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 )
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:134"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="zf_lang1.html#T150" target="_self" title="ZF_LANG1:th.150">Th150</a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E3:134_2"/><b>then </b>
not <font color="Maroon" title="c2">a</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">2</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<a NAME="E4:134_2"/><b>then </b>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">H</font>
 
<b>by </b><i><a class="txt" href="zf_lang1.html#E1:134"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="zf_lang1.html#E1:134_2"><i><font color="Green" title="E47">A2</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="E5:134_2"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="zf_lang1.html#K3" title="ZF_LANG1:func.3">variables_in</a> <font color="Maroon" title="c1">H</font>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E2:134_2"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>


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

<b>thus </b><a NAME="E3:134"/>
 <a href="zf_lang1.html#K3" title="ZF_LANG1:func.3">variables_in</a> <font color="Maroon" title="c1">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="zf_lang1.html#K3" title="ZF_LANG1:func.3">variables_in</a> <span class="p1">(<span class="default"><a href="zf_lang.html#K6" title="ZF_LANG:func.6">'not'</a> <font color="Maroon" title="c1">H</font></span>)</span>
 <b>by </b><i><a class="txt" href="zf_lang1.html#E1:134"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T33" title="XBOOLE_1:th.33">XBOOLE_1:33</a></i>;<br/>


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