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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E43">Th38</font></span>: <a NAME="T38"><span class="comment"><font color="firebrick">:: COHSP_1:38</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C1</font>, <font color="Olive" title="b2">C2</font> being   <a href="coh_sp.html#NM1" title="COH_SP:NM.1">Coherence_Space</a><br/>  for <font color="Olive" title="b3">X</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">C1</font>,<span class="p2">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b2">C2</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>  st (  for <font color="Olive" title="b4">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">X</font> holds <br/><font color="Olive" title="b4">x</font> <a href="xfamily.html#K1" title="XFAMILY:func.1">`1</a>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  ) &amp; (  for <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">C1</font>  st <font color="Olive" title="b4">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b5">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">C1</font> holds <br/> for <font color="Olive" title="b6">y1</font>, <font color="Olive" title="b7">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">a</font>,<font color="Olive" title="b6">y1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">X</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">b</font>,<font color="Olive" title="b7">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">X</font> holds <br/><span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b6">y1</font>,<font color="Olive" title="b7">y2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">C2</font> ) &amp; (  for <font color="Olive" title="b4">a</font>, <font color="Olive" title="b5">b</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">C1</font>  st <font color="Olive" title="b4">a</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b5">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b1">C1</font> holds <br/> for <font color="Olive" title="b6">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">a</font>,<font color="Olive" title="b6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">X</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b5">b</font>,<font color="Olive" title="b6">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">X</font> holds <br/><font color="Olive" title="b4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">b</font> ) holds <br/> ex <font color="Olive" title="b4">f</font> being   <a href="cohsp_1.html#V9" title="COHSP_1:attr.9">U-stable</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Olive" title="b1">C1</font>,<font color="Olive" title="b2">C2</font> st <font color="Olive" title="b3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cohsp_1.html#K8" title="COHSP_1:func.8">Trace</a> <font color="Olive" title="b4">f</font></div></div>
