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<div><span class="kw">theorem </span><a NAME="T54"><span class="comment"><font color="firebrick">:: PARTPR_1:54</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">p</font> being   <a href="partpr_1.html#NM1" title="PARTPR_1:NM.1">PartialPredicate</a> of <font color="Olive" title="b1">D</font> holds   <a href="partpr_1.html#K7" title="PARTPR_1:func.7">PP_imp</a> (<font color="Olive" title="b2">p</font>,<span class="p1">(<span class="default"><a href="partpr_1.html#K8" title="PARTPR_1:func.8">PP_True</a> <font color="Olive" title="b1">D</font></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partpr_1.html#K8" title="PARTPR_1:func.8">PP_True</a> <font color="Olive" title="b1">D</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="partpr_1.html#T45" target="_self" onmouseover="rs('partpr_1/T45')" onmouseout="rh()">Th45</a></span>;<br/></div></div>
