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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="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">C</font> is  <a href="cohsp_1.html#V3" title="COHSP_1:attr.3">d.union-closed</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">C</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="cohsp_1.html#D6" target="_self" title="COHSP_1:def.6">COHSP_1:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">A</font> is  <a href="cohsp_1.html#V1" title="COHSP_1:attr.1">c=directed</a>  implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <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> )</span><br/>



<span class="kw">thus </span><a NAME="E1:34_1_1"/>
( <font color="Maroon" title="c2">A</font> is  <a href="cohsp_1.html#V1" title="COHSP_1:attr.1">c=directed</a>  implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cohsp_1.html#T14" target="_self" title="COHSP_1:th.14">Th15</a></span>; <a class="txt" 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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