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<span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</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"> ( <font color="Maroon" title="c3">x</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c4">y</font> implies  <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c3">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="Maroon" title="c4">y</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:102"/><span class="lab"><font color="Green" title="E42">A1</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="gaussint.html#R2" title="GAUSSINT:pred.2">is_associated_to</a> <font color="Maroon" title="c4">y</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="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c3">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="Maroon" title="c4">y</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c5">x1</font> = <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c6">y1</font> = <font color="Maroon" title="c4">y</font> as   <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> <span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T3" target="_self" onmouseover="rs('gaussint/T3')" onmouseout="rh()">Th3</a></span>;<br/>
<a NAME="E3:102"/><span class="lab"><font color="Green" title="E43">A2</font></span>: 
<font color="Maroon" title="c5">x1</font> <a href="gcd_1.html#R4" title="GCD_1:pred.4">is_associated_to</a> <font color="Maroon" title="c6">y1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:102"><span class="lab"><font color="Green" title="E42">A1</font></span></a>, <a class="ref" href="gaussint.html#T38" target="_self" onmouseover="rs('gaussint/T38')" onmouseout="rh()">Th38</a></span>;<br/>
<a NAME="E4:102"/>
<font color="Maroon" title="c5">x1</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c6">y1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:102"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="gcd_1.html#D3" onmouseover="rs('gcd_1/D3')" onmouseout="rh()">GCD_1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">z1</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><span class="kw"> such that </span><br/><a NAME="E6:102"/><span class="lab"><font color="Green" title="E44">A3</font></span>: 
<font color="Maroon" title="c6">y1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">z1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D1" onmouseover="rs('gcd_1/D1')" onmouseout="rh()">GCD_1:def 1</a></span>;<br/>
<a NAME="E7:102"/>
<font color="Maroon" title="c6">y1</font> <a href="gcd_1.html#R2" title="GCD_1:pred.2">divides</a> <font color="Maroon" title="c5">x1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:102"><span class="lab"><font color="Green" title="E43">A2</font></span></a>, <a class="ref" href="gcd_1.html#D3" onmouseover="rs('gcd_1/D3')" onmouseout="rh()">GCD_1:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">z2</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><span class="kw"> such that </span><br/><a NAME="E9:102"/><span class="lab"><font color="Green" title="E45">A4</font></span>: 
<font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">y1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c8">z2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D1" onmouseover="rs('gcd_1/D1')" onmouseout="rh()">GCD_1:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">z3</font> = <font color="Maroon" title="c7">z1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c8">z2</font> as   <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> ;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:102_1"/>
( <font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c6">y1</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> or <font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c6">y1</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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_1"><span class="kw">suppose </span></a><a NAME="E1:102_1_1"/><span class="lab"><font color="Green" title="E46">A5</font></span>: 
<font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c6">y1</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>
 ; <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="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c3">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="Maroon" title="c4">y</font></span><br/><div class="add"><font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c6">y1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">z1</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c8">z2</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:102"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="txt" href="#E9:102"><span class="lab"><font color="Green" title="E45">A4</font></span></a>, <a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c7">z1</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c8">z2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c6">y1</font></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c9">z3</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="group_1.html#D3" onmouseover="rs('group_1/D3')" onmouseout="rh()">GROUP_1:def 3</a></span>
;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A6</font></span>: <font color="Maroon" title="c9">z3</font> = 
 <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:102_1_1"><span class="lab"><font color="Green" title="E46">A5</font></span></a>, <a class="ref" href="gcd_1.html#T17" onmouseover="rs('gcd_1/T17')" onmouseout="rh()">GCD_1:17</a></span>
<br/>.= 
1

;<br/><span class="kw">reconsider </span><font color="Maroon" title="c10">zz1</font> = <font color="Maroon" title="c7">z1</font>, <font color="Maroon" title="c11">zz2</font> = <font color="Maroon" title="c8">z2</font> as   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T2" target="_self" onmouseover="rs('gaussint/T2')" onmouseout="rh()">Th2</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c12">zz3</font> = <font color="Maroon" title="c9">z3</font> as   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</a> <span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T2" target="_self" onmouseover="rs('gaussint/T2')" onmouseout="rh()">Th2</a></span>;<br/><a NAME="E6:102_1_1"/><span class="lab"><font color="Green" title="E48">A7</font></span>: 
 <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c10">zz1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="102_1_1_3"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:102_1_1_3"/>
<font color="Maroon" title="c12">zz3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">zz1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c11">zz2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T6" target="_self" onmouseover="rs('gaussint/T6')" onmouseout="rh()">Th6</a></span>;<br/>
<a NAME="E2:102_1_1_3"/><span class="kw">then </span>
 <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c12">zz3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c10">zz1</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c11">zz2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T34" target="_self" onmouseover="rs('gaussint/T34')" onmouseout="rh()">Th34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:102_1_1_3"/>
 <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c10">zz1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:102_1_1"><span class="lab"><font color="Green" title="E47">A6</font></span></a>, <a class="ref" href="complex1.html#T30" onmouseover="rs('complex1/T30')" onmouseout="rh()">COMPLEX1:30</a>, <a class="ref" href="nat_1.html#T15" onmouseover="rs('nat_1/T15')" onmouseout="rh()">NAT_1:15</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/>


</div><span class="kw">end;</span></div><a NAME="E7:102_1_1"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c10">zz1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:102"><span class="lab"><font color="Green" title="E44">A3</font></span></a>, <a class="ref" href="gaussint.html#T6" target="_self" onmouseover="rs('gaussint/T6')" onmouseout="rh()">Th6</a></span>;<br/><span class="kw">hence </span> <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c4">y</font> = 
<span class="p1">(<span class="default"><a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c3">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c10">zz1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="gaussint.html#T34" target="_self" onmouseover="rs('gaussint/T34')" onmouseout="rh()">Th34</a></span>
<br/>.= 
 <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c3">x</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:102_1_1"><span class="lab"><font color="Green" title="E48">A7</font></span></a></span>
;<br/> <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/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="102_1_2"><span class="kw">suppose </span></a><a NAME="E1:102_1_2"/><span class="lab"><font color="Green" title="E46">A8</font></span>: 
<font color="Maroon" title="c5">x1</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c6">y1</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>
 ; <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="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c3">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="Maroon" title="c4">y</font></span><br/><div class="add"><a NAME="E2:102_1_2"/><span class="lab"><font color="Green" title="E47">A9</font></span>: 
<font color="Maroon" title="c5">x1</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>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="102_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:102_1_2_1"/><span class="lab"><font color="Green" title="E48">A10</font></span>: 
 not <font color="Maroon" title="c5">x1</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>
 ; <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"> contradiction</span><br/>

<a NAME="E2:102_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">y1</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:102_1_2"><span class="lab"><font color="Green" title="E46">A8</font></span></a>, <a class="ref" href="vectsp_2.html#D1" onmouseover="rs('vectsp_2/D1')" onmouseout="rh()">VECTSP_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:102_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:102_1_2_1"><span class="lab"><font color="Green" title="E48">A10</font></span></a>, <a class="txt" href="#E9:102"><span class="lab"><font color="Green" title="E45">A4</font></span></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/>


</div><span class="kw">end;</span></div><a NAME="E3:102_1_2"/>
<font color="Maroon" title="c6">y1</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>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="102_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:102_1_2_2"/><span class="lab"><font color="Green" title="E48">A11</font></span>: 
 not <font color="Maroon" title="c6">y1</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>
 ; <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"> contradiction</span><br/>

<a NAME="E2:102_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">x1</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:102_1_2"><span class="lab"><font color="Green" title="E46">A8</font></span></a>, <a class="ref" href="vectsp_2.html#D1" onmouseover="rs('vectsp_2/D1')" onmouseout="rh()">VECTSP_2:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:102_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:102_1_2_2"><span class="lab"><font color="Green" title="E48">A11</font></span></a>, <a class="txt" href="#E6:102"><span class="lab"><font color="Green" title="E44">A3</font></span></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/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:102_1_2"/>
 <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c3">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="Maroon" title="c4">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:102_1_2"><span class="lab"><font color="Green" title="E47">A9</font></span></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/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div>
