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

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   non  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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">p</font> being    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p2">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> holds   the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Olive" title="b1">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p2">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></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">  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> </span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">F</font> =  <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">FX</font> =  <a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">I</font> = <span class="p1"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">K</font> = <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p2">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p1">(<span class="default"><span class="p2"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">x</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span></span>)</span>;<br/>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="42_1"><span class="kw">now </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">  not  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:42_1"/><span class="lab"><font color="Green" title="E19">AS</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</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/><span class="kw">reconsider </span><font color="Maroon" title="c8">x</font> =  the    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span></span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1"><span class="lab"><font color="Green" title="E19">AS</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">q</font> = <font color="Maroon" title="c8">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42_1"><span class="lab"><font color="Green" title="E19">AS</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c10">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p2">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span><span class="kw"> such that </span><br/><a NAME="E5:42_1"/><span class="lab"><font color="Green" title="E20">A1</font></span>: 
<font color="Maroon" title="c9">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="eqrel_1.html#K6" title="EQREL_1:func.6">Class</a> (<span class="p1">(<span class="default"><a href="ring_1.html#K1" title="RING_1:func.1">EqRel</a> (<span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span>)</span>)</span>,<font color="Maroon" title="c10">a</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ring_1.html#T11" onmouseover="rs('ring_1/T11')" onmouseout="rh()">RING_1:11</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c11">pa</font> = <font color="Maroon" title="c10">a</font> as   <a href="polynom3.html#NM1" title="POLYNOM3:NM.1">Polynomial</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="polynom3.html#D10" onmouseover="rs('polynom3/D10')" onmouseout="rh()">POLYNOM3:def 10</a></span>;<br/><a NAME="E7:42_1"/>
<font color="Maroon" title="c10">a</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p2">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#T15" onmouseover="rs('rlvect_1/T15')" onmouseout="rh()">RLVECT_1:15</a></span>;<br/><a NAME="E8:42_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A2</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c9">q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42_1"><span class="lab"><font color="Green" title="E20">A1</font></span></a>, <a class="ref" href="ring_1.html#T5" onmouseover="rs('ring_1/T5')" onmouseout="rh()">RING_1:5</a>, <a class="ref" href="ideal_1.html#T3" onmouseover="rs('ideal_1/T3')" onmouseout="rh()">IDEAL_1:3</a></span>;<br/><a NAME="E9:42_1"/>
 <a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G6" title="ALGSTR_0:aggr.6">doubleLoopStr</a>(# <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="gr_cy_1.html#K3" title="GR_CY_1:func.3">addint</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="int_3.html#K7" title="INT_3:func.7">multint</a> <font color="Maroon" title="c1">n</font></span>)</span>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (1,<span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">In</a> (<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,<span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c1">n</font></span>)</span>)</span>)</span> #)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_3.html#D12" onmouseover="rs('int_3/D12')" onmouseout="rh()">INT_3:def 12</a></span>;<br/><a NAME="E10:42_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="card_1.html#K5" title="CARD_1:func.5">Segm</a> <font color="Maroon" title="c1">n</font>
 ;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c12">k</font> = <font color="Maroon" title="c8">x</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  ;<br/><a NAME="E12:42_1"/>
<font color="Maroon" title="c12">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">m</font> where <font color="Olive" title="b1">m</font> is   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> : <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">k</font> </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="axioms.html#T4" onmouseover="rs('axioms/T4')" onmouseout="rh()">AXIOMS:4</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">m</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E14:42_1"/><span class="lab"><font color="Green" title="E22">B1</font></span>: 
( <font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">m</font> &amp; <font color="Maroon" title="c13">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">k</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:42_1"><span class="lab"><font color="Green" title="E21">A2</font></span></a></span>;<br/><a NAME="E15:42_1"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c11">pa</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E16:42_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:42_1"><span class="lab"><font color="Green" title="E22">B1</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="E2:42"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <span class="p3">(<span class="default"><a href="ring_3.html#NK1" title="RING_3:NK.1">Z/</a> <font color="Maroon" title="c1">n</font></span>)</span></span>)</span> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <span class="p2">(<span class="default"><span class="p3"><a href="ring_4.html#K1" title="RING_4:func.1">{</a><span class="default"><font color="Maroon" title="c2">p</font></span><a href="ring_4.html#K1" title="RING_4:func.1">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</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"> verum</span><br/>


</div>
