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

<span class="kw">thus </span><a NAME="E1:10_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="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> holds  <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">a</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rlvect_1.html#D2" title="RLVECT_1:def.2">RLVECT_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  &amp;  not  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:10_1_1"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">c</font></span>)</span>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  &amp;  not  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  )</span><br/>

<div><span class="kw">hereby </span> <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="rlvect_1.html#D4" title="RLVECT_1:def.4">RLVECT_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  &amp;  not  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  )</span>
<div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c2">t</font> =  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  ;<br/><span class="kw">let </span><font color="Maroon" title="c3">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c4">a9</font> = <font color="Maroon" title="c3">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="int_3.html#E4"><span class="lab"><font color="Green" title="E2">Lm1</font></span></a></span>;<br/><span class="lab"><font color="Green" title="E6">A1</font></span>: <a href="binop_2.html#K33" title="BINOP_2:func.33">addreal</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c2">t</font>) = 
<font color="Maroon" title="c4">a9</font> <a href="binop_2.html#K9" title="BINOP_2:func.9">+</a> <font color="Maroon" title="c2">t</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D9" title="BINOP_2:def.9">BINOP_2:def 9</a></span>
<br/>.= 
<font color="Maroon" title="c3">a</font>

;<br/><font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span> = 
<a href="binop_2.html#K33" title="BINOP_2:func.33">addreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">a</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="gr_cy_1.html#D1" title="GR_CY_1:def.1">GR_CY_1:def 1</a></span>
<br/>.= 
<a href="binop_2.html#K33" title="BINOP_2:func.33">addreal</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c3">a</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="int_3.html#E5"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a>, <a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a></span>
;<br/><span class="kw">hence </span><a NAME="E5:10_1_1_1"/>
<font color="Maroon" title="c3">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10_1_1_1"><span class="lab"><font color="Green" title="E6">A1</font></span></a></span>; <a class="txt" 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">thus </span><a NAME="E4:10_1_1"/>
 <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  &amp;  not  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="algstr_0.html#D16" title="ALGSTR_0:def.16">ALGSTR_0:def 16</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> is  <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a> </span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c3">a9</font> = <font color="Maroon" title="c2">a</font> as   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">v</font> =  <a href="binop_2.html#K19" title="BINOP_2:func.19">-</a> <font color="Maroon" title="c3">a9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">v</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="algstr_0.html#D11" title="ALGSTR_0:def.11">ALGSTR_0:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">v</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="int_3.html#K1" title="INT_3:func.1">INT.Ring</a></span><br/>

<span class="kw">thus </span><a NAME="E3:10_1_1_2"/>
<font color="Maroon" title="c2">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c4">v</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="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a></span>; <a class="txt" 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">thus </span><a NAME="E5:10_1_1"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> holds <br/> ( <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">c</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">c</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <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="b2">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">c</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">a</font></span>)</span> )
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="vectsp_1.html#D7" title="VECTSP_1:def.7">VECTSP_1:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  &amp;  not  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E6:10_1_1"/>
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> holds  <font color="Olive" title="b1">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b1">x</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_1.html#D12" title="GROUP_1:def.12">GROUP_1:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>  &amp;  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  &amp;  not  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E7:10_1_1"/>
 for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">b</font></span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">b</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b3">c</font></span>)</span>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="group_1.html#D3" title="GROUP_1:def.3">GROUP_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>  &amp;  not  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E8:10_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="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  holds <br/>(  not <font color="Olive" title="b1">a</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">b</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="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> or <font color="Olive" title="b1">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> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> or <font color="Olive" title="b2">b</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="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="int_3.html#E6"><span class="lab"><font color="Green" title="E4">Lm3</font></span></a>, <a class="ref" href="xcmplx_1.html#T6" title="XCMPLX_1:th.6">XCMPLX_1:6</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="vectsp_2.html#D1" title="VECTSP_2:def.1">VECTSP_2:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>  is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a> </span><br/>

<span class="kw">thus </span><a NAME="E9:10_1_1"/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="int_3.html#K1" title="INT_3:func.1">INT.Ring</a>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="int_3.html#E5"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a>, <a class="txt" href="int_3.html#E7"><span class="lab"><font color="Green" title="E5">Lm4</font></span></a>, <a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="struct_0.html#D8" title="STRUCT_0:def.8">STRUCT_0:def 8</a> <a class="txt" 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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