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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">I</font> being   <a href="zmodul03.html#NM1" title="ZMODUL03:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="zmodlat2.html#K3" title="ZMODLAT2:func.3">EMLat</a> <font color="Maroon" title="c1">L</font></span>)</span> holds   <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="zmodlat3.html#K7" title="ZMODLAT3:func.7">DualBasis</a> <font color="Olive" title="b1">I</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="zmodul03.html#NM1" title="ZMODUL03:NM.1">Basis</a> of <span class="p1">(<span class="default"><a href="zmodlat2.html#K3" title="ZMODLAT2:func.3">EMLat</a> <font color="Maroon" title="c1">L</font></span>)</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">  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="zmodlat3.html#K7" title="ZMODLAT3:func.7">DualBasis</a> <font color="Maroon" title="c2">I</font></span>)</span></span><br/>



<a NAME="E1:47"/>
(  <a href="zmodlat3.html#K8" title="ZMODLAT3:func.8">B2DB</a> <font color="Maroon" title="c2">I</font> is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="zmodlat3.html#K8" title="ZMODLAT3:func.8">B2DB</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="zmodlat3.html#K8" title="ZMODLAT3:func.8">B2DB</a> <font color="Maroon" title="c2">I</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="zmodlat3.html#K7" title="ZMODLAT3:func.7">DualBasis</a> <font color="Maroon" title="c2">I</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="zmodlat3.html#D9" target="_self" onmouseover="rs('zmodlat3/D9')" onmouseout="rh()">defB2DB</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:47"/>
 <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="zmodlat3.html#K7" title="ZMODLAT3:func.7">DualBasis</a> <font color="Maroon" title="c2">I</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T5" onmouseover="rs('card_1/T5')" onmouseout="rh()">CARD_1:5</a>, <a class="ref" href="wellord2.html#D4" onmouseover="rs('wellord2/D4')" onmouseout="rh()">WELLORD2:def 4</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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