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<div><span class="kw">theorem </span><a NAME="T27"><span class="comment"><font color="firebrick">:: ZMODLAT2:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="zmodlat1.html#V4" title="ZMODLAT1:attr.4">positive-definite</a>  <a href="zmodlat1.html#NM1" title="ZMODLAT1:NM.1">Z_Lattice</a><br/>  for <font color="Olive" title="b2">Z</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="zmodlat1.html#L1" title="ZMODLAT1:struct.1">LatticeStr</a> over  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>   st <font color="Olive" title="b2">Z</font> is   <a href="zmodul03.html#V2" title="ZMODUL03:attr.2">finitely-generated</a>  <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of  <a href="zmodul08.html#K2" title="ZMODUL08:func.2">DivisibleMod</a> <font color="Olive" title="b1">L</font> &amp;  the <a href="zmodlat1.html#U1" title="ZMODLAT1:sel.1">scalar</a> of <font color="Olive" title="b2">Z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="zmodlat2.html#K2" title="ZMODLAT2:func.2">ScProductDM</a> <font color="Olive" title="b1">L</font></span>)</span> <a href="realset1.html#K1" title="REALSET1:func.1">||</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b2">Z</font> holds <br/><font color="Olive" title="b2">Z</font> is   <a href="zmodlat1.html#NM1" title="ZMODLAT1:NM.1">Z_Lattice</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="zmodlat2.html#T26" target="_self" onmouseover="rs('zmodlat2/T26')" onmouseout="rh()">ThSLX2</a></span>;<br/></div></div>
