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

<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">distributive</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/>

<b>consider </b><font color="Maroon" title="c2">A</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c1">L</font></span>)</span><b> such that </b><br/><a NAME="E2:51"/><i><font color="Green" title="E28">A1</font></i>: 
( <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> &amp;  <a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyalg1.html#K2" title="POLYALG1:func.2">GenAlg</a> <font color="Maroon" title="c2">A</font> )
 <b>by </b><i><a class="ref" href="polyalg1.html#D6" target="_self" title="POLYALG1:def.6">Def6</a></i>;<br/>
<a NAME="E3:51"/><i><font color="Green" title="E29">A2</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="polyalg1.html#V3" title="POLYALG1:attr.3">opers_closed</a>
 
<b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyalg1.html#T23" target="_self" title="POLYALG1:th.23">Th23</a></i>;<br/>
<a NAME="E4:51"/><b>then </b><i><font color="Green" title="E30">A3</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyalg1.html#T22" target="_self" title="POLYALG1:th.22">Th22</a></i>;<br/>
<a NAME="E5:51"/><i><font color="Green" title="E31">A4</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self" title="POLYALG1:def.3">Def3</a></i>;<br/>
<a NAME="E6:51"/><i><font color="Green" title="E32">A5</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span><br/> for <font color="Olive" title="b2">y</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#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> holds  the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>;<br/>



<b>reconsider </b><font color="Maroon" title="c5">x1</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="polyalg1.html#E3:51"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="polyalg1.html#T22" target="_self" title="POLYALG1:th.22">Th22</a></i>;<br/>
<b>reconsider </b><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 <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="polyalg1.html#E3:51"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="polyalg1.html#T22" target="_self" title="POLYALG1:th.22">Th22</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">x'</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyalg1.html#E5:51"><i><font color="Green" title="E31">A4</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">y'</font> = <font color="Maroon" title="c6">y1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c3">x</font> as   <a href="algseq_1.html#NM1" title="ALGSEQ_1:NM.1">AlgSequence</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="polyalg1.html#E4:51"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">q</font> = <font color="Maroon" title="c4">y</font> as   <a href="algseq_1.html#NM1" title="ALGSEQ_1:NM.1">AlgSequence</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>;<br/>
<b>thus </b>the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> = 
<font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c6">y1</font>

<br/>.= 
<font color="Maroon" title="c7">x'</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c8">y'</font>
<b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyalg1.html#T15" target="_self" title="POLYALG1:th.15">Th15</a></i>
<br/>.= 
<font color="Maroon" title="c9">p</font> <a href="polynom3.html#K8" title="POLYNOM3:func.8">+</a> <font color="Maroon" title="c10">q</font>
<b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c5">x1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c4">y</font>
<b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>
<br/>.= 
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>

;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="51_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon" title="c5">x1</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="polyalg1.html#E3:51"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="polyalg1.html#T22" target="_self" title="POLYALG1:th.22">Th22</a></i>;<br/><b>reconsider </b><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 <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="polyalg1.html#E3:51"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="polyalg1.html#T22" target="_self" title="POLYALG1:th.22">Th22</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c7">x'</font> = <font color="Maroon" title="c3">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyalg1.html#E5:51"><i><font color="Green" title="E31">A4</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">y'</font> = <font color="Maroon" title="c6">y1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c1">L</font></span>)</span> <b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c3">x</font> as   <a href="algseq_1.html#NM1" title="ALGSEQ_1:NM.1">AlgSequence</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="txt" href="polyalg1.html#E4:51"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c10">q</font> = <font color="Maroon" title="c4">y</font> as   <a href="algseq_1.html#NM1" title="ALGSEQ_1:NM.1">AlgSequence</a> of <font color="Maroon" title="c1">L</font> <b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>;<br/><b>thus </b>the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> = 
<font color="Maroon" title="c3">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c6">y1</font>

<br/>.= 
<font color="Maroon" title="c7">x'</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c8">y'</font>
<b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyalg1.html#T16" target="_self" title="POLYALG1:th.16">Th16</a></i>
<br/>.= 
<font color="Maroon" title="c9">p</font> <a href="polynom3.html#K14" title="POLYNOM3:func.14">*'</a> <font color="Maroon" title="c10">q</font>
<b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c5">x1</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">y</font>
<b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>
<br/>.= 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>

;<br/></div><b>end;</b></div>
<a NAME="E8:51"/><b>then </b><i><font color="Green" title="E33">A6</font></i>: 
the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>
 
<b>by </b><i><a class="txt" href="polyalg1.html#E4:51"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>
<i><font color="Green" title="E34">A7</font></i>: the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> = 
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span>

<br/>.= 
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self" title="POLYALG1:def.3">Def3</a></i>
<br/>.= 
 <a href="polynom3.html#K12" title="POLYNOM3:func.12">0_.</a> <font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>
<br/>.= 
the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>

;<br/>
the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> = 
 <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">1_</a> <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span>

<br/>.= 
 <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">1_</a> <span class="p1">(<span class="default"><a href="polyalg1.html#K1" title="POLYALG1:func.1">Formal-Series</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="txt" href="polyalg1.html#E2:51"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self" title="POLYALG1:def.3">Def3</a></i>
<br/>.= 
 <a href="polynom3.html#K13" title="POLYNOM3:func.13">1_.</a> <font color="Maroon" title="c1">L</font>
<b>by </b><i><a class="ref" href="polyalg1.html#D2" target="_self" title="POLYALG1:def.2">Def2</a></i>
<br/>.= 
 <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">1_</a> <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D12" title="POLYNOM3:def.12">POLYNOM3:def 12</a></i>
<br/>.= 
the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font></span>)</span>

;<br/>
<b>hence </b><a NAME="E11:51"/>
 <a href="vectsp_1.html#G3" title="VECTSP_1:aggr.3">doubleLoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span>,the <a href="group_1.html#U1" title="GROUP_1:sel.1">mult</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span>,the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">unity</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <span class="p1">(<span class="default"><a href="polyalg1.html#K3" title="POLYALG1:func.3">Polynom-Algebra</a> <font color="Maroon" title="c1">L</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polynom3.html#K16" title="POLYNOM3:func.16">Polynom-Ring</a> <font color="Maroon" title="c1">L</font>
 <b>by </b><i><a class="txt" href="polyalg1.html#E4:51"><i><font color="Green" title="E30">A3</font></i></a>, <a class="txt" href="polyalg1.html#E6:51"><i><font color="Green" title="E32">A5</font></i></a>, <a class="txt" href="polyalg1.html#E8:51"><i><font color="Green" title="E33">A6</font></i></a>, <a class="txt" href="polyalg1.html#E9:51"><i><font color="Green" title="E34">A7</font></i></a>, <a class="ref" href="binop_1.html#T2" title="BINOP_1:th.2">BINOP_1:2</a></i>;<br/>


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