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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">LmDE31</font></span>: <a NAME="T25"><span class="comment"><font color="firebrick">:: ZMODLAT3:25</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>   <a href="zmodlat1.html#V4" title="ZMODLAT1:attr.4">positive-definite</a>   <a href="zmodlat2.html#V1" title="ZMODLAT2:attr.1">RATional</a>  <a href="zmodlat1.html#NM1" title="ZMODLAT1:NM.1">Z_Lattice</a><br/>  for <font color="Olive" title="b2">b</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of  <a href="zmodlat2.html#K3" title="ZMODLAT2:func.3">EMLat</a> <font color="Olive" title="b1">L</font><br/>  for <font color="Olive" title="b3">i</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">b</font> holds <br/> ex <font color="Olive" title="b4">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="zmodul08.html#K2" title="ZMODUL08:func.2">DivisibleMod</a> <font color="Olive" title="b1">L</font></span>)</span> st <br/>( <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="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b3">i</font></span>)</span>,<font color="Olive" title="b4">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; (  for <font color="Olive" title="b5">j</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b3">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">j</font> &amp; <font color="Olive" title="b5">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b2">b</font> holds <br/><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="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Olive" title="b5">j</font></span>)</span>,<font color="Olive" title="b4">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  ) )</div></div>
