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<span class="kw">let </span><font color="Maroon" title="c1">H</font> be   <a href="zf_lang.html#NM2" title="ZF_LANG:NM.2">ZF-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">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> holds <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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> implies ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:142"/>
<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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 )</span><br/>

<a NAME="E2:142"/><span class="kw">then </span>
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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/>
<a NAME="E3:142"/><span class="kw">then </span>
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#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default">2,3,4</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T48" title="ENUMSET1:th.48">ENUMSET1:48</a></span>;<br/>
<a NAME="E4:142"/><span class="kw">then </span>
( 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#K2" title="TARSKI:func.2">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></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#K1" title="ENUMSET1:func.1">{</a><span class="default">2,3,4</span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:142"/>
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 1 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 2 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 3 &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> 4 )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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