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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: NOMIN_9:12</font></span><br/></a><div class="add"> 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">loc</font> being  <font color="Olive">b<sub>1</sub></font> <a href="relat_1.html#V5" title="RELAT_1:attr.5">-valued</a>  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><br/>  for <font color="Olive" title="b4">d1</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  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 10 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b3">loc</font> &amp; <font color="Olive" title="b3">loc</font> <a href="nomin_7.html#R1" title="NOMIN_7:pred.1">is_valid_wrt</a> <font color="Olive" title="b4">d1</font> holds <br/><span class="p1"><a href="enumset1.html#K8" title="ENUMSET1:func.8">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 4</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 5</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 6</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 7</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 8</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 9</span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b3">loc</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 10</span>)</span></span><a href="enumset1.html#K8" title="ENUMSET1:func.8">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Olive" title="b4">d1</font></div></div>
