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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E2">Def9</font></span>   defines <a href="zmodul02.html#K9" title="ZMODUL02:func.9">lmultCoset</a> <a onclick="hs(this)" href="javascript:()">ZMODUL02:def 9 : <br/></a><span> 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">W</font> being   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive">b<sub>3</sub></font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>,<span class="p2">(<span class="default"><a href="zmodul02.html#K6" title="ZMODUL02:func.6">CosetSet</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font>)</span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<span class="p1">(<span class="default"><a href="zmodul02.html#K6" title="ZMODUL02:func.6">CosetSet</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font>)</span>)</span> holds <br/> ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zmodul02.html#K9" title="ZMODUL02:func.9">lmultCoset</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font>) iff  for <font color="Olive" title="b4">z</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><br/>  for <font color="Olive" title="b5">A</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="zmodul02.html#K6" title="ZMODUL02:func.6">CosetSet</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font>)<br/>  for <font color="Olive" title="b6">a</font> being   <a href="zmodul01.html#NM2" title="ZMODUL01:NM.2">VECTOR</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b5">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">a</font> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Olive" title="b2">W</font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Olive" title="b4">z</font>,<font color="Olive" title="b5">A</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">z</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b6">a</font></span>)</span> <a href="vectsp_4.html#K3" title="VECTSP_4:func.3">+</a> <font color="Olive" title="b2">W</font> );<br/></span></div>
