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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E20">ThEQRZMV4</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: ZMODUL04:12</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">I</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font><br/>  for <font color="Olive" title="b3">l</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b2">I</font><br/>  for <font color="Olive" title="b4">IQ</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="zmodul04.html#K5" title="ZMODUL04:func.5">Z_MQ_VectSp</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>  &amp; <font color="Olive" title="b4">IQ</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zmodul04.html#K6" title="ZMODUL04:func.6">MorphsZQ</a> <font color="Olive" title="b1">V</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Olive" title="b2">I</font> holds <br/> ex <font color="Olive" title="b5">lq</font> being    <a href="vectsp_6.html#M2" title="VECTSP_6:mode.2">Linear_Combination</a> of <font color="Olive" title="b4">IQ</font> st <br/>( <font color="Olive" title="b3">l</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">lq</font> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <span class="p1">(<span class="default"><a href="zmodul04.html#K6" title="ZMODUL04:func.6">MorphsZQ</a> <font color="Olive" title="b1">V</font></span>)</span> &amp;  <a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Olive" title="b5">lq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zmodul04.html#K6" title="ZMODUL04:func.6">MorphsZQ</a> <font color="Olive" title="b1">V</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <span class="p1">(<span class="default"><a href="vectsp_6.html#K1" title="VECTSP_6:func.1">Carrier</a> <font color="Olive" title="b3">l</font></span>)</span> )</div></div>
