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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E48">Th47</font></span>: <a NAME="T47"><span class="comment"><font color="firebrick">:: FVALUAT1:47</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">K</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">v</font> being    <a href="fvaluat1.html#M1" title="FVALUAT1:mode.1">Valuation</a> of <font color="Olive" title="b1">K</font><br/>  for <font color="Olive" title="b3">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">K</font> holds <br/> ( <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="fvaluat1.html#K6" title="FVALUAT1:func.6">NonNegElements</a> <font color="Olive" title="b2">v</font> iff  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">v</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">a</font> )</div></div>
