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<b>let </b><font color="Maroon">C1</font> be   <a href="coh_sp.html#NM1">Coherence_Space</a>, <font color="Maroon">C2</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> ;<br/>



<b>assume </b><a NAME="E1:146"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> <a href="cohsp_1.html#K16" target="_self">"\/"</a> <font color="Maroon">C2</font>
 ;<br/>

<a NAME="E2:146"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">a</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> : verum </span>}</span>  <a href="xboole_0.html#K2">\/</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</font></span>)</span> where <font color="Olive">b</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C2</font> : verum </span>}</span> 
 
;<br/>
<a NAME="E3:146"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">a</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <a href="xboole_0.html#K1">{}</a> </span>)</span> where <font color="Olive">a</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> : verum </span>}</span>  or <font color="Maroon">x</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</font></span>)</span> where <font color="Olive">b</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C2</font> : verum </span>}</span>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E4:146"/><b>then </b>
( (  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">C2</font> &amp;  ex <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> st <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <a href="xboole_0.html#K1">{}</a>  ) or (  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">C1</font> &amp;  ex <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C2</font> st <font color="Maroon">x</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="Olive">b</font> ) )
 
<b>by </b><i><a class="ref" href="coh_sp.html#T1">COH_SP:1</a></i>;<br/>
<b>hence </b><a NAME="E5:146"/>
 ex <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C1</font> ex <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C2</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> <a href="cohsp_1.html#K14" target="_self">U+</a> <font color="Olive">b</font> &amp; ( <font color="Olive">a</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Olive">b</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 ;<br/>


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