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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <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>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">b</font> being    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of  <a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font> holds   <a href="zmodlat1.html#K22" title="ZMODLAT1:func.22">GramMatrix</a> (<span class="p1">(<span class="default"><a href="zmodlat1.html#K24" title="ZMODLAT1:func.24">InnerProduct</a> <span class="p2">(<span class="default"><a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>,<font color="Olive" title="b1">b</font>) is   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of  <a href="zmodlat1.html#NK4" title="ZMODLAT1:NK.4">dim</a> <font color="Maroon" title="c1">L</font>,<a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a></span><br/><span class="kw">let </span><font color="Maroon" title="c2">b</font> be    <a href="zmatrlin.html#M1" title="ZMATRLIN:mode.1">OrdBasis</a> of  <a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="zmodlat1.html#K22" title="ZMODLAT1:func.22">GramMatrix</a> (<span class="p1">(<span class="default"><a href="zmodlat1.html#K24" title="ZMODLAT1:func.24">InnerProduct</a> <span class="p2">(<span class="default"><a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">b</font>) is   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of  <a href="zmodlat1.html#NK4" title="ZMODLAT1:NK.4">dim</a> <font color="Maroon" title="c1">L</font>,<a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a></span><br/>



<a NAME="E1:72"/><span class="lab"><font color="Green" title="E54">A1</font></span>: 
 the <a href="zmodlat1.html#U1" title="ZMODLAT1:sel.1">scalar</a> of <span class="p1">(<span class="default"><a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font></span>)</span> <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="Maroon" title="c1">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 <span class="p1">(<span class="default"><a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodlat3.html#D10" target="_self" onmouseover="rs('zmodlat3/D10')" onmouseout="rh()">defDualLat</a></span>;<br/>
<a NAME="E2:72"/><span class="lab"><font color="Green" title="E55">A2</font></span>: 
 <a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font> is   <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="Maroon" title="c1">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodlat3.html#T35" target="_self" onmouseover="rs('zmodlat3/T35')" onmouseout="rh()">ThDL2</a></span>;<br/>
<a NAME="E3:72"/>
 <a href="zmodlat1.html#NK4" title="ZMODLAT1:NK.4">dim</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zmodlat1.html#NK4" title="ZMODLAT1:NK.4">dim</a> <span class="p1">(<span class="default"><a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodlat3.html#T43" target="_self" onmouseover="rs('zmodlat3/T43')" onmouseout="rh()">ThRankDL</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:72"/>
 <a href="zmodlat1.html#K22" title="ZMODLAT1:func.22">GramMatrix</a> (<span class="p1">(<span class="default"><a href="zmodlat1.html#K24" title="ZMODLAT1:func.24">InnerProduct</a> <span class="p2">(<span class="default"><a href="zmodlat3.html#K9" title="ZMODLAT3:func.9">DualLat</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">b</font>) is   <a href="matrix_1.html#NM2" title="MATRIX_1:NM.2">Matrix</a> of  <a href="zmodlat1.html#NK4" title="ZMODLAT1:NK.4">dim</a> <font color="Maroon" title="c1">L</font>,<a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:72"><span class="lab"><font color="Green" title="E54">A1</font></span></a>, <a class="txt" href="#E2:72"><span class="lab"><font color="Green" title="E55">A2</font></span></a>, <a class="ref" href="zmodlat3.html#T50" target="_self" onmouseover="rs('zmodlat3/T50')" onmouseout="rh()">ThSLGM2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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