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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E5">Th6</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: IDEAL_2:3</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">F</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="ring_2.html#K2" title="RING_2:func.2">Ideals</a> <font color="Olive" title="b1">A</font> holds <br/> (  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ideal_2.html#K2" title="IDEAL_2:func.2">%</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">F</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="setfam_1.html#K6" title="SETFAM_1:func.6">meet</a> <span class="p1">(<span class="default"><a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ideal_2.html#K2" title="IDEAL_2:func.2">%</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Olive" title="b3">F</font></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">A</font> )</div></div>
