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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>;<br/>

<b>thus </b><a NAME="E1:128"/>
 <a href="cohsp_1.html#K13" target="_self">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E99"><i><font color="Green">Lemma70</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:128"/><i><font color="Green">E72</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E3:128"/><i><font color="Green">E73</font></i>: 
(  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp;  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <span class="p2">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#T67" target="_self">Th67</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:128_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/><a NAME="E2:128_1"/><b>then </b><i><font color="Green">E74</font></i>: 
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="cohsp_1.html#E2:128"><i><font color="Green">E72</font></i></a>, <a class="ref" href="tarski.html#D4">TARSKI:def 4</a>, <a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/><a NAME="E3:128_1"/><b>then </b><i><font color="Green">E75</font></i>: 
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="cohsp_1.html#E2:128"><i><font color="Green">E72</font></i></a>, <a class="ref" href="classes1.html#D1">CLASSES1:def 1</a>, <a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/><a NAME="E4:128_1"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> implies  not <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="cohsp_1.html#T68" target="_self">Th68</a></i>;<br/><a NAME="E5:128_1"/><b>then </b>
( ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> implies <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K13" target="_self">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> ) &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> ) )
 <b>by </b><i><a class="txt" href="cohsp_1.html#E3:128"><i><font color="Green">E73</font></i></a>, <a class="txt" href="cohsp_1.html#E3:128_1"><i><font color="Green">E75</font></i></a>, <a class="ref" href="cohsp_1.html#T69" target="_self">Th69</a>, <a class="ref" href="enumset1.html#T69">ENUMSET1:69</a></i>;<br/><b>hence </b><a NAME="E6:128_1"/>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K13" target="_self">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="cohsp_1.html#E3:128"><i><font color="Green">E73</font></i></a>, <a class="txt" href="cohsp_1.html#E2:128_1"><i><font color="Green">E74</font></i></a>, <a class="ref" href="coh_sp.html#T4">COH_SP:4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:128"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K13" target="_self">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="coh_sp.html#T6">COH_SP:6</a></i>;<br/>


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