<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E7">Th6</font></span>: <a NAME="T6"><span class="comment"><font color="firebrick">:: RING_1:6</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#V2" title="VECTSP_1:attr.2">left-distributive</a>   <a href="vectsp_1.html#V6" title="VECTSP_1:attr.6">left_unital</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="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b2">I</font> being   <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</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> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> holds <br/> (  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ring_1.html#K1" title="RING_1:func.1">EqRel</a> (<font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">I</font>)</span>)</span>,<font color="Olive" title="b3">a</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ring_1.html#K1" title="RING_1:func.1">EqRel</a> (<font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">I</font>)</span>)</span>,<font color="Olive" title="b4">b</font>) iff <font color="Olive" title="b3">a</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Olive" title="b4">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> )</div></div>
