<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="nomin_1.html#K18" title="NOMIN_1:func.18">denaming</a> <a onclick="hs(this)" href="javascript:()">NOMIN_1:def 18 : <br/></a><span> for <font color="Olive" title="b1">V</font>, <font color="Olive" title="b2">A</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive">b<sub>4</sub></font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>)</span>)</span>,<span class="p1">(<span class="default"><a href="nomin_1.html#K3" title="NOMIN_1:func.3">ND</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>)</span>)</span> holds <br/> ( <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K18" title="NOMIN_1:func.18">denaming</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">v</font>) iff (  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b5">d</font> where <font color="Olive" title="b5">d</font> is    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font> : <font color="Olive" title="b3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b5">d</font> </span> } </span>  &amp; (  for <font color="Olive" title="b5">D</font> being    <a href="nomin_1.html#M3" title="NOMIN_1:mode.3">NonatomicND</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font>  st <font color="Olive" title="b5">D</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive">b<sub>4</sub></font> holds <br/><font color="Olive">b<sub>4</sub></font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nomin_1.html#K12" title="NOMIN_1:func.12">denaming</a> (<font color="Olive" title="b3">v</font>,<font color="Olive" title="b5">D</font>) ) ) );<br/></span></div>
