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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E30">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: AOFA_000:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   <a href="unialg_1.html#NM1" title="UNIALG_1:NM.1">Universal_Algebra</a><br/>  for <font color="Olive" title="b2">G</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">A</font> holds <br/> ( <font color="Olive" title="b2">G</font> is    <a href="freealg.html#M1" title="FREEALG:mode.1">GeneratorSet</a> of <font color="Olive" title="b1">A</font> iff  for <font color="Olive" title="b3">I</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font>  ex <font color="Olive" title="b4">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <font color="Olive" title="b3">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">G</font> <a href="aofa_000.html#K9" title="AOFA_000:func.9">|^</a> <font color="Olive" title="b4">n</font> )</div></div>
