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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th43</font></span>: <a NAME="T38"><span class="comment"><font color="firebrick">:: IDEAL_2:38</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="subset_1.html#V1" title="SUBSET_1:attr.1">proper</a>  <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">x</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ideal_1.html#K17" title="IDEAL_1:func.17">sqrt</a> <font color="Olive" title="b2">I</font>  ex <font color="Olive" title="b4">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> st <br/>( <font color="Olive" title="b4">m</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b5">n</font> where <font color="Olive" title="b5">n</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  :  not <font color="Olive" title="b3">x</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <font color="Olive" title="b5">n</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> </span> } </span>  &amp; <font color="Olive" title="b3">x</font> <a href="binom.html#K2" title="BINOM:func.2">|^</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> )</div></div>
