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<b>let </b><font color="Maroon">C</font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>



<a NAME="E1:126"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> implies  not <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</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</font> )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E2:126"/><i><font color="Green">E27</font></i>: 
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</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</font> &amp; not <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> implies <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</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</font> )
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D12" target="_self">Def12</a></i>;<br/>
<a NAME="E3:126"/><i><font color="Green">E36</font></i>: 
 <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</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C</font>
 
<b>by </b><i><a class="ref" href="cohsp_1.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E4:126"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">C</font></span>)</span> implies ( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C</font> &amp; ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> or  not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C</font> ) ) )
 <b>by </b><i><a class="ref" href="cohsp_1.html#D13" target="_self">Def13</a>, <a class="ref" href="coh_sp.html#T5">COH_SP:5</a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>

<b>assume </b><a NAME="E5:126"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <font color="Maroon">C</font> &amp; ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> or  not <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <font color="Maroon">C</font> ) )
 ;<br/>

<a NAME="E6:126"/><b>then </b>
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</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</font> &amp; ( ( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a>  <a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">C</font> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> ) or  not <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> ) )
 
<b>by </b><i>, <a class="ref" href="coh_sp.html#T4">COH_SP:4</a>, <a class="ref" href="coh_sp.html#T5">COH_SP:5</a>, <a class="ref" href="enumset1.html#T69">ENUMSET1:69</a>, <a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/>
<b>hence </b><a NAME="E7:126"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K1">Web</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" target="_self">'not'</a> <font color="Maroon">C</font></span>)</span>
 <b>by </b><i><a class="ref" href="cohsp_1.html#T19" target="_self">Th19</a>, <a class="ref" href="coh_sp.html#T5">COH_SP:5</a></i>;<br/>


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