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

<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">mF</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c1">X</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">mo</font> being  <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <font color="Maroon" title="c1">X</font> holds <br/> (  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">mF</font>,<font color="Olive" title="b2">mo</font> #) is <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">mF</font>,<font color="Olive" title="b2">mo</font> #) is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">mF</font>,<font color="Olive" title="b2">mo</font> #) is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">mF</font>,<font color="Olive" title="b2">mo</font> #) is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> )</span><br/><b>let </b><font color="Maroon" title="c5">mF</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c1">X</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">mo</font> being  <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <font color="Maroon" title="c1">X</font> holds <br/> (  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Olive" title="b1">mo</font> #) is <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Olive" title="b1">mo</font> #) is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Olive" title="b1">mo</font> #) is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Olive" title="b1">mo</font> #) is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> )</span><br/><b>let </b><font color="Maroon" title="c6">mo</font> be   <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> )</span><br/>





<b>set </b><font color="Maroon" title="c7">H</font> =  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #);<br/>
<a NAME="E1:2"/><i><font color="Green" title="E4">A1</font></i>: 
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="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) holds  <font color="Olive" title="b1">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</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#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c8">x</font></span><br/>

<a NAME="E1:2_1"/>
( <font color="Maroon" title="c3">md</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c8">x</font>,<font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font> &amp; <font color="Maroon" title="c3">md</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c9">y</font>,<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font> )
 
<b>by </b><i><a class="txt" href="ortsp_1.html#E4"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:2_1"/>
<font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c9">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c8">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:2"/><i><font color="Green" title="E5">A2</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Olive" title="b3">z</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c9">y</font>, <font color="Maroon" title="c10">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c10">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c10">z</font></span>)</span></span><br/>

<b>reconsider </b><font color="Maroon" title="c11">x</font> = <font color="Maroon" title="c8">x</font>, <font color="Maroon" title="c12">y</font> = <font color="Maroon" title="c9">y</font>, <font color="Maroon" title="c13">z</font> = <font color="Maroon" title="c10">z</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<a NAME="E2:2_2"/>
<font color="Maroon" title="c3">md</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c11">x</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">md</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c12">y</font>,<font color="Maroon" title="c13">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="txt" href="ortsp_1.html#E4"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:2_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c9">y</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c10">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">y</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c10">z</font></span>)</span>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E4"><i><font color="Green" title="E1">Lm1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:2"/><i><font color="Green" title="E6">A3</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 <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) holds  <font color="Olive" title="b1">x</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="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #); <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</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="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font></span><br/>

<a NAME="E1:2_3"/>
<font color="Maroon" title="c3">md</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c8">x</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="txt" href="ortsp_1.html#E4"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:2_3"/>
<font color="Maroon" title="c8">x</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="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:2"/>
 <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c8">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #); <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> is <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a></span><br/>

<a NAME="E1:2_4"/><i><font color="Green" title="E7">A4</font></i>: 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="struct_0.html#D6" title="STRUCT_0:def.6">STRUCT_0:def 6</a></i>;<br/>
<b>take </b>
 <a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c8">x</font>
; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c8">x</font></span>)</span> <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="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #)</span><br/>

<b>thus </b><a NAME="E2:2_4"/>
<font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c8">x</font></span>)</span> <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="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #)
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:2_4"><i><font color="Green" title="E7">A4</font></i></a>, <a class="txt" href="ortsp_1.html#E4"><i><font color="Green" title="E1">Lm1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:2"/>
(  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a> &amp;  <a href="symsp_1.html#G1" title="SYMSP_1:aggr.1">SymStr</a>(# <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c3">md</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">mF</font>,<font color="Maroon" title="c6">mo</font> #) is <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> )
 <b>by </b><i><a class="txt" href="ortsp_1.html#E1:2"><i><font color="Green" title="E4">A1</font></i></a>, <a class="txt" href="ortsp_1.html#E2:2"><i><font color="Green" title="E5">A2</font></i></a>, <a class="txt" href="ortsp_1.html#E3:2"><i><font color="Green" title="E6">A3</font></i></a>, <a class="ref" href="rlvect_1.html#D5" title="RLVECT_1:def.5">RLVECT_1:def 5</a>, <a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a>, <a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
