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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E18">SB02</font></span>: <a NAME="T20"><span class="comment"><font color="firebrick">:: ZMODUL08:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="zmodul06.html#V3" title="ZMODUL06:attr.3">torsion-free</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a> holds <br/> ( (  for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</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="b2">v</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="zmodul08.html#K1" title="ZMODUL08:func.1">EMbedding</a> <font color="Olive" title="b1">V</font> &amp; <font color="Olive" title="b3">w</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="zmodul08.html#K1" title="ZMODUL08:func.1">EMbedding</a> <font color="Olive" title="b1">V</font> holds <br/><font color="Olive" title="b2">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">w</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="zmodul08.html#K1" title="ZMODUL08:func.1">EMbedding</a> <font color="Olive" title="b1">V</font> ) &amp; (  for <font color="Olive" title="b2">j</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a><br/>  for <font color="Olive" title="b3">v</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</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="b2">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp; <font color="Olive" title="b3">v</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="zmodul08.html#K1" title="ZMODUL08:func.1">EMbedding</a> <font color="Olive" title="b1">V</font> holds <br/><font color="Olive" title="b2">j</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b3">v</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="zmodul08.html#K1" title="ZMODUL08:func.1">EMbedding</a> <font color="Olive" title="b1">V</font> ) )</div></div>
