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<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: NORMSP_3:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a><br/>  for <font color="Olive" title="b2">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  ex <font color="Olive" title="b3">F</font> being   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Olive" title="b1">X</font> st <br/>( (  for <font color="Olive" title="b4">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b4">C</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">F</font> iff ( <font color="Olive" title="b4">C</font> is  <a href="nfcont_1.html#V2" title="NFCONT_1:attr.2">closed</a>  &amp; <font color="Olive" title="b2">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">C</font> ) ) ) &amp;  <a href="normsp_3.html#K1" title="NORMSP_3:func.1">Cl</a> <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <font color="Olive" title="b3">F</font> )</div></div>
