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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E9">LMEQRZM1</font></span>: <a NAME="T5"><span class="comment"><font color="firebrick">:: ZMODUL04:5</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">v</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_1.html#G1" title="VECTSP_1:aggr.1">ModuleStr</a>(# <span class="p1">(<span class="default"><a href="eqrel_1.html#K8" title="EQREL_1:func.8">Class</a> <span class="p2">(<span class="default"><a href="zmodul04.html#K1" title="ZMODUL04:func.1">EQRZM</a> <font color="Olive" title="b1">V</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="zmodul04.html#K2" title="ZMODUL04:func.2">addCoset</a> <font color="Olive" title="b1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="zmodul04.html#K3" title="ZMODUL04:func.3">zeroCoset</a> <font color="Olive" title="b1">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="zmodul04.html#K4" title="ZMODUL04:func.4">lmultCoset</a> <font color="Olive" title="b1">V</font></span>)</span> #)  st <font color="Olive" title="b1">V</font> is  <a href="zmodul01.html#V1" title="ZMODUL01:attr.1">Mult-cancelable</a>  holds <br/> ex <font color="Olive" title="b3">i</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> ex <font color="Olive" title="b4">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">V</font> st <br/>( <font color="Olive" title="b3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> &amp; <font color="Olive" title="b2">v</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="zmodul04.html#K1" title="ZMODUL04:func.1">EQRZM</a> <font color="Olive" title="b1">V</font></span>)</span>,<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b4">z</font>,<font color="Olive" title="b3">i</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>) )</div></div>
