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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E12">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: COH_SP:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">l</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K5" title="COH_SP:func.5">MapsC</a> <font color="Olive" title="b1">X</font>  ex <font color="Olive" title="b3">g</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="coh_sp.html#K4" title="COH_SP:func.4">FuncsC</a> <font color="Olive" title="b1">X</font> ex <font color="Olive" title="b4">C1</font>, <font color="Olive" title="b5">C2</font> being    <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="Olive" title="b1">X</font> st <br/>( <font color="Olive" title="b2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">C1</font>,<font color="Olive" title="b5">C2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b3">g</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; (  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b5">C2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b4">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; <font color="Olive" title="b3">g</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b4">C1</font></span>)</span>,<span class="p1">(<span class="default"><a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Olive" title="b5">C2</font></span>)</span> &amp; (  for <font color="Olive" title="b6">x</font>, <font color="Olive" title="b7">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b6">x</font>,<font color="Olive" title="b7">y</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="b4">C1</font> holds <br/><span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b7">y</font></span>)</span></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="b5">C2</font> ) )</div></div>
