<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="armstrng.html#R6" title="ARMSTRNG:pred.6">is_p_i_w_ncv_of</a> <a onclick="hs(this)" href="javascript:()">ARMSTRNG:def 32 : <br/></a><span> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">K</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b3">F</font> being   <a href="armstrng.html#NM2" title="ARMSTRNG:NM.2">Dependency-set</a> of <font color="Olive" title="b1">A</font> holds <br/> ( <font color="Olive" title="b2">K</font> <a href="armstrng.html#R6" title="ARMSTRNG:pred.6">is_p_i_w_ncv_of</a> <font color="Olive" title="b3">F</font> iff ( (  for <font color="Olive" title="b4">a</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b2">K</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b4">a</font> &amp; <font color="Olive" title="b4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b4">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="armstrng.html#K14" title="ARMSTRNG:func.14">charact_set</a> <font color="Olive" title="b3">F</font> ) &amp; (  for <font color="Olive" title="b4">k</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b4">k</font> <a href="xboole_0.html#R2" title="XBOOLE_0:pred.2">c&lt;</a> <font color="Olive" title="b2">K</font> holds <br/> ex <font color="Olive" title="b5">a</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">A</font> st <br/>( <font color="Olive" title="b4">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b5">a</font> &amp; <font color="Olive" title="b5">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">A</font> &amp;  not <font color="Olive" title="b5">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="armstrng.html#K14" title="ARMSTRNG:func.14">charact_set</a> <font color="Olive" title="b3">F</font> ) ) ) );<br/></span></div>
