<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">z</font> be   <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>; <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">zz</font> being   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</a>  st <font color="Olive" title="b1">zz</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> holds <br/>( <font color="Maroon" title="c3">z</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</a>  iff <font color="Olive" title="b1">zz</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">zz</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="c4">zz</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> implies ( <font color="Maroon" title="c3">z</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</a>  iff <font color="Maroon" title="c4">zz</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</a>  ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:103"/><span class="lab"><font color="Green" title="E43">A1</font></span>: 
<font color="Maroon" title="c4">zz</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</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"> ( <font color="Maroon" title="c3">z</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</a>  iff <font color="Maroon" title="c4">zz</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</a>  )</span><br/>

<div><span class="kw">hereby </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"> ( <font color="Maroon" title="c4">zz</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</a>  implies <font color="Maroon" title="c3">z</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</a>  )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:103_1"/><span class="lab"><font color="Green" title="E44">A2</font></span>: 
<font color="Maroon" title="c3">z</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</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="c4">zz</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</a> </span><br/><span class="kw">consider </span><font color="Maroon" title="c5">x</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="E3:103_1"/><span class="lab"><font color="Green" title="E45">A3</font></span>: 
 <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103_1"><span class="lab"><font color="Green" title="E44">A2</font></span></a>, <a class="ref" href="gcd_1.html#D1" onmouseover="rs('gcd_1/D1')" onmouseout="rh()">GCD_1:def 1</a>, <a class="ref" href="gcd_1.html#D20" onmouseover="rs('gcd_1/D20')" onmouseout="rh()">GCD_1:def 20</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c6">xx</font> = <font color="Maroon" title="c5">x</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="E5:103_1"/><span class="lab"><font color="Green" title="E46">A4</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">zz</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Maroon" title="c6">xx</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103"><span class="lab"><font color="Green" title="E43">A1</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">reconsider </span><font color="Maroon" title="c7">gintone</font> =  <a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (1,<a href="gaussint.html#K1" title="GAUSSINT:func.1">G_INT_SET</a>) as   <a href="gaussint.html#NM1" title="GAUSSINT:NM.1">G_INTEG</a> ;<br/><span class="p1">(<span class="default"><a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c4">zz</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="c6">xx</font></span>)</span> = 
 <a href="gaussint.html#K16" title="GAUSSINT:func.16">Norm</a> <font color="Maroon" title="c7">gintone</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103_1"><span class="lab"><font color="Green" title="E45">A3</font></span></a>, <a class="txt" href="#E5:103_1"><span class="lab"><font color="Green" title="E46">A4</font></span></a>, <a class="ref" href="gaussint.html#T34" target="_self" onmouseover="rs('gaussint/T34')" onmouseout="rh()">Th34</a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="complex1.html#T30" onmouseover="rs('complex1/T30')" onmouseout="rh()">COMPLEX1:30</a></span>
;<br/><span class="kw">hence </span><a NAME="E8:103_1"/>
<font color="Maroon" title="c4">zz</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</a> 
 <span class="kw">by</span> <span class="lab"><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>

<span class="kw">assume </span><a NAME="E3:103"/><span class="lab"><font color="Green" title="E44">A5</font></span>: 
<font color="Maroon" title="c4">zz</font> is  <a href="gaussint.html#V3" title="GAUSSINT:attr.3">g_int_unit</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">z</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</a> </span><br/>

<a NAME="E4:103"/>
 ex <font color="Olive" title="b1">w</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  <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b1">w</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="103_2"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_2_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="E1:103_2_1"/>
( <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 or <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 or <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  or <font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:103"><span class="lab"><font color="Green" title="E44">A5</font></span></a>, <a class="txt" href="#E1:103"><span class="lab"><font color="Green" title="E43">A1</font></span></a>, <a class="ref" href="gaussint.html#T35" target="_self" onmouseover="rs('gaussint/T35')" onmouseout="rh()">Th35</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:103_2_1_1"/><span class="lab"><font color="Green" title="E45">A6</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ; <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">  ex <font color="Olive" title="b1">w</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  <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b1">w</font></span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c5">w</font> = <font color="Maroon" title="c3">z</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="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">w</font></span><br/><span class="kw">thus </span> <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> = 
1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> 1

<br/>.= 
<font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">w</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103_2_1_1"><span class="lab"><font color="Green" title="E45">A6</font></span></a>, <a class="ref" href="gaussint.html#T6" target="_self" onmouseover="rs('gaussint/T6')" onmouseout="rh()">Th6</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:103_2_1_2"/><span class="lab"><font color="Green" title="E45">A7</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1
 ; <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">  ex <font color="Olive" title="b1">w</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  <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b1">w</font></span><br/><div class="add"><span class="kw">take </span><font color="Maroon" title="c5">w</font> = <font color="Maroon" title="c3">z</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="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">w</font></span><br/><span class="kw">thus </span> <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="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>

<br/>.= 
<font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">w</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103_2_1_2"><span class="lab"><font color="Green" title="E45">A7</font></span></a>, <a class="ref" href="gaussint.html#T6" target="_self" onmouseover="rs('gaussint/T6')" onmouseout="rh()">Th6</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_2_1_3"><span class="kw">suppose </span></a><a NAME="E1:103_2_1_3"/><span class="lab"><font color="Green" title="E45">A8</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</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">  ex <font color="Olive" title="b1">w</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  <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b1">w</font></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c5">w</font> =  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> 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/><span class="kw">take </span>
<font color="Maroon" title="c5">w</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="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">w</font></span><br/><span class="kw">thus </span> <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> = 
<a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span>

<br/>.= 
<font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">w</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103_2_1_3"><span class="lab"><font color="Green" title="E45">A8</font></span></a>, <a class="ref" href="gaussint.html#T6" target="_self" onmouseover="rs('gaussint/T6')" onmouseout="rh()">Th6</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><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="103_2_1_4"><span class="kw">suppose </span></a><a NAME="E1:103_2_1_4"/><span class="lab"><font color="Green" title="E45">A9</font></span>: 
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</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">  ex <font color="Olive" title="b1">w</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  <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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b1">w</font></span><br/><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c5">w</font> =  <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>  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="txt" href="gaussint.html#E5"><span class="lab"><font color="Green" title="E4">Lm2</font></span></a></span>;<br/><span class="kw">take </span>
<font color="Maroon" title="c5">w</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="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="gaussint.html#K6" title="GAUSSINT:func.6">Gauss_INT_Ring</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">w</font></span><br/><span class="kw">thus </span> <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="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a>

<br/>.= 
<font color="Maroon" title="c3">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c5">w</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:103_2_1_4"><span class="lab"><font color="Green" title="E45">A9</font></span></a>, <a class="ref" href="gaussint.html#T6" target="_self" onmouseover="rs('gaussint/T6')" onmouseout="rh()">Th6</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:103"/>
<font color="Maroon" title="c3">z</font> is  <a href="gcd_1.html#V1" title="GCD_1:attr.1">unital</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D2" onmouseover="rs('gcd_1/D2')" onmouseout="rh()">GCD_1:def 2</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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