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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>;<br/><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/>



<div><i><font color="Green">E86</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="145_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:145_1"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="cohsp_1.html#K14" target="_self">U+</a> <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:145_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:145_1"><i><font color="Green">E87</font></i></a>, <a class="ref" href="cohsp_1.html#T81" target="_self">Th81</a></i>;<br/><b>hence </b><a NAME="E3:145_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/></div><b>end;</b></div>
<div><i><font color="Green">E87</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="145_2"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>5</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><a NAME="E1:145_2"/><i><font color="Green">E88</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <a href="xboole_0.html#K1">{}</a>  <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/><a NAME="E2:145_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:145_2"><i><font color="Green">E88</font></i></a>, <a class="ref" href="cohsp_1.html#T81" target="_self">Th81</a></i>;<br/><b>hence </b><a NAME="E3:145_2"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/></div><b>end;</b></div>
<a NAME="E3:145"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="cohsp_1.html#K16" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font> iff ( <font color="Maroon">c<sub>3</sub></font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="cohsp_1.html#K14" target="_self">U+</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> : verum </span>}</span>  or <font color="Maroon">c<sub>3</sub></font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="xboole_0.html#K1">{}</a>  <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Olive">b<sub>1</sub></font></span>)</span> where B is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font> : verum </span>}</span>  ) )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:145"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="cohsp_1.html#K16" target="_self">"\/"</a> <font color="Maroon">c<sub>2</sub></font> iff ( ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) or ( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> ) ) )
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:145"><i><font color="Green">E86</font></i></a>, <a class="txt" href="cohsp_1.html#E2:145"><i><font color="Green">E87</font></i></a></i>;<br/>


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