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<span class="kw">consider </span><font color="Maroon" title="c3">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a>,<a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a><span class="kw"> such that </span><br/><a NAME="E2:118_1_1"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
 for <font color="Olive" title="b1">x</font> being   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</a> holds  <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Olive" title="b1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="gaussint.html#E82"><span class="lab"><font color="Green" title="E49">Lm13</font></span></a></span>;<br/>
<a NAME="E3:118_1_1"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a>  st <font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a> holds <br/> ex <font color="Olive" title="b3">q</font>, <font color="Olive" title="b4">r</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a> st <br/>( <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">q</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">r</font> &amp; ( <font color="Olive" title="b4">r</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a> or <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">b</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="gaussint.html#E85"><span class="lab"><font color="Green" title="E52">Lm14</font></span></a>, <a class="txt" href="#E2:118_1_1"><span class="lab"><font color="Green" title="E53">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:118_1_1"/>
 <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a>  is  <a href="int_3.html#V1" title="INT_3:attr.1">Euclidian</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_3.html#D8" onmouseover="rs('int_3/D8')" onmouseout="rh()">INT_3:def 8</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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