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<div><span class="kw">theorem </span><a NAME="T82"><span class="comment"><font color="firebrick">:: IDEAL_1:82</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V5" title="ALGSTR_0:attr.5">left_add-cancelable</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="vectsp_1.html#V2" title="VECTSP_1:attr.2">left-distributive</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">I</font>, <font color="Olive" title="b3">J</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="ideal_1.html#V1" title="IDEAL_1:attr.1">add-closed</a>   <a href="ideal_1.html#V2" title="IDEAL_1:attr.2">left-ideal</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">I</font> <a href="ideal_1.html#K11" title="IDEAL_1:func.11">+</a> <font color="Olive" title="b3">J</font></span>)</span> <a href="ideal_1.html#K14" title="IDEAL_1:func.14">*'</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">I</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Olive" title="b3">J</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">I</font> <a href="ideal_1.html#K13" title="IDEAL_1:func.13">/\</a> <font color="Olive" title="b3">J</font></div></div>
