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<span class="kw">let </span><font color="Maroon" title="c2">C</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K3" title="COH_SP:func.3">CSp</a> <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">C</font> is  <a href="classes1.html#V1" title="CLASSES1:attr.1">subset-closed</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="coh_sp.html#V1" title="COH_SP:attr.1">binary_complete</a>  &amp;  not <font color="Maroon" title="c2">C</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</span><br/>

<a NAME="E1:22_1_1"/>
<font color="Maroon" title="c2">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">x</font> where <font color="Olive" title="b1">x</font> is   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">X</font> : <font color="Olive" title="b1">x</font> is   <a href="coh_sp.html#NM1" title="COH_SP:NM.1">Coherence_Space</a> </span> } </span> 
 
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<a NAME="E2:22_1_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">x</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> &amp; <font color="Olive" title="b1">x</font> is   <a href="coh_sp.html#NM1" title="COH_SP:NM.1">Coherence_Space</a> )
 
;<br/>
<span class="kw">hence </span><a NAME="E3:22_1_1"/>
( <font color="Maroon" title="c2">C</font> is  <a href="classes1.html#V1" title="CLASSES1:attr.1">subset-closed</a>  &amp; <font color="Maroon" title="c2">C</font> is  <a href="coh_sp.html#V1" title="COH_SP:attr.1">binary_complete</a>  &amp;  not <font color="Maroon" title="c2">C</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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