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<span class="kw">let </span><font color="Maroon" title="c1">C</font> be   <a href="coh_sp.html#NM1" title="COH_SP:NM.1">Coherence_Space</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">C</font></span><br/>

<span class="kw">thus </span><a NAME="E1:129"/>
 <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="cohsp_1.html#E99"><span class="lab"><font color="Green" title="E70">Lm7</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</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="c1">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span></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> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font> or <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E2:129"/><span class="lab"><font color="Green" title="E72">A1</font></span>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</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#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span></span><br/>

<a NAME="E3:129"/><span class="lab"><font color="Green" title="E73">A2</font></span>: 
(  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span> &amp;  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p2">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cohsp_1.html#T67" target="_self" title="COHSP_1:th.67">Th67</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="129_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</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="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font> implies <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:129_1"/><span class="lab"><font color="Green" title="E74">A3</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">and </span><br/><a NAME="E2:129_1"/><span class="lab"><font color="Green" title="E75">A4</font></span>: 
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span></span><br/><a NAME="E3:129_1"/><span class="lab"><font color="Green" title="E76">A5</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:129"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="txt" href="#E1:129_1"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/><a NAME="E4:129_1"/>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:129_1"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="txt" href="#E2:129_1"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="ref" href="zfmisc_1.html#T38" title="ZFMISC_1:th.38">ZFMISC_1:38</a></span>;<br/><a NAME="E5:129_1"/><span class="kw">then </span>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:129"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="classes1.html#D1" title="CLASSES1:def.1">CLASSES1:def 1</a></span>;<br/><a NAME="E6:129_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A6</font></span>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">y</font> implies  not <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cohsp_1.html#T68" target="_self" title="COHSP_1:th.68">Th68</a></span>;<br/><a NAME="E7:129_1"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:129"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="txt" href="#E2:129_1"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="ref" href="tarski.html#D4" title="TARSKI:def.4">TARSKI:def 4</a></span>;<br/><a NAME="E8:129_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A7</font></span>: 
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c1">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:129_1"><span class="lab"><font color="Green" title="E76">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#T38" title="ZFMISC_1:th.38">ZFMISC_1:38</a></span>;<br/><a NAME="E9:129_1"/>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c3">x</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#T69" title="ENUMSET1:th.69">ENUMSET1:69</a></span>;<br/><span class="kw">hence </span><a NAME="E10:129_1"/>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:129"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="txt" href="#E3:129_1"><span class="lab"><font color="Green" title="E76">A5</font></span></a>, <a class="txt" href="#E8:129_1"><span class="lab"><font color="Green" title="E78">A7</font></span></a>, <a class="txt" href="#E6:129_1"><span class="lab"><font color="Green" title="E77">A6</font></span></a>, <a class="ref" href="cohsp_1.html#T69" target="_self" title="COHSP_1:th.69">Th69</a>, <a class="ref" href="coh_sp.html#T4" title="COH_SP:th.4">COH_SP:4</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/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:129"/>
<font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <span class="p1">(<span class="default"><a href="cohsp_1.html#K13" title="COHSP_1:func.13">'not'</a> <font color="Maroon" title="c1">C</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="coh_sp.html#T6" title="COH_SP:th.6">COH_SP:6</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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