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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E23">Th30</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: NOMIN_2:31</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">d</font> being    <a href="nomin_1.html#M2" title="NOMIN_1:mode.2">TypeSCNominativeData</a> of <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">A</font><br/>  for <font color="Olive" title="b4">g</font> being  <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="nomin_2.html#V1" title="NOMIN_2:attr.1">-FPrg-yielding</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><br/>  for <font color="Olive" title="b5">X</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a>  st  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b5">X</font> &amp; <font color="Olive" title="b3">d</font> <a href="nomin_2.html#R1" title="NOMIN_2:pred.1">in_doms</a> <font color="Olive" title="b4">g</font> holds <br/> <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <span class="p1">(<span class="default"><a href="nomin_2.html#K4" title="NOMIN_2:func.4">NDentry</a> (<font color="Olive" title="b4">g</font>,<font color="Olive" title="b5">X</font>,<font color="Olive" title="b3">d</font>)</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <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>)</div></div>
