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<div><span class="kw">theorem </span><a NAME="T56"><span class="comment"><font color="firebrick">:: POLYRED:56</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#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">I</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#V3" title="IDEAL_1:attr.3">right-ideal</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font>  st <font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font> <a href="polyred.html#R11" title="POLYRED:pred.11">are_congruent_mod</a> <font color="Olive" title="b2">I</font> &amp; <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">d</font> <a href="polyred.html#R11" title="POLYRED:pred.11">are_congruent_mod</a> <font color="Olive" title="b2">I</font> holds <br/><font color="Olive" title="b3">a</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b4">b</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b6">d</font> <a href="polyred.html#R11" title="POLYRED:pred.11">are_congruent_mod</a> <font color="Olive" title="b2">I</font></div></div>
