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

<span class="kw">set </span><font color="Maroon" title="c4">K</font> =  <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font>;<br/>
<span class="kw">thus </span><a NAME="E1:65_1_1"/>
 <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</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"> (  <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>  &amp;  <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="65_1_1_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="65_1_1_1_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">  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 <span class="p1">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span> 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></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></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"> <font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">a</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c7">a1</font> = <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c8">b1</font> = <font color="Maroon" title="c6">b</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">b</font> = 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">b1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D6" target="_self" onmouseover="rs('field_5/D6')" onmouseout="rh()">defra</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c5">a</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D6" target="_self" onmouseover="rs('field_5/D6')" onmouseout="rh()">defra</a></span>
<br/>.= 
<font color="Maroon" title="c6">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c5">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</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="E2:65_1_1_1"/>
 <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</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><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:65_1_1"/>
 <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</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"> (  <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>  &amp;  <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="65_1_1_2"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="65_1_1_2_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">  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 <span class="p1">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span> 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></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></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"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">c</font></span>)</span></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c8">a1</font> = <font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c9">b1</font> = <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c10">c1</font> = <font color="Maroon" title="c7">c</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>;<br/><a NAME="E2:65_1_1_2_1"/><span class="lab"><font color="Green" title="E26">H</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">r</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 <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D5" target="_self" onmouseover="rs('field_5/D5')" onmouseout="rh()">defr</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">ab</font> = <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b1</font></span>)</span></span>)</span>, <font color="Maroon" title="c12">bc</font> = <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">c1</font></span>)</span></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">b</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">c</font> = 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c6">b</font></span>)</span>,<font color="Maroon" title="c7">c</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>)</span>)</span>,<font color="Maroon" title="c7">c</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b1</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c7">c</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D6" target="_self" onmouseover="rs('field_5/D6')" onmouseout="rh()">defra</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">ab</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">c1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D6" target="_self" onmouseover="rs('field_5/D6')" onmouseout="rh()">defra</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">c1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1_1_2_1"><span class="lab"><font color="Green" title="E26">H</font></span></a>, <a class="ref" href="funct_1.html#T34" onmouseover="rs('funct_1/T34')" onmouseout="rh()">FUNCT_1:34</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">c1</font></span>)</span></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" onmouseover="rs('rlvect_1/D3')" onmouseout="rh()">RLVECT_1:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">bc</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1_1_2_1"><span class="lab"><font color="Green" title="E26">H</font></span></a>, <a class="ref" href="funct_1.html#T34" onmouseover="rs('funct_1/T34')" onmouseout="rh()">FUNCT_1:34</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">b1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">c1</font></span>)</span></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D6" target="_self" onmouseover="rs('field_5/D6')" onmouseout="rh()">defra</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c6">b</font>,<font color="Maroon" title="c7">c</font>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D6" target="_self" onmouseover="rs('field_5/D6')" onmouseout="rh()">defra</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">c</font></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>
<br/>.= 
<font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">b</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c7">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</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="E2:65_1_1_2"/>
 <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</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><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E3:65_1_1"/>
 <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</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">  <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a> </span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="65_1_1_3"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="65_1_1_3_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">  for <font color="Olive" title="b1">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="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span> holds  <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"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></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"> <font color="Maroon" title="c5">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> <span class="p2">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c6">a1</font> = <font color="Maroon" title="c5">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>;<br/><a NAME="E2:65_1_1_3_1"/><span class="lab"><font color="Green" title="E26">H0</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">r</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 <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D5" target="_self" onmouseover="rs('field_5/D5')" onmouseout="rh()">defr</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">o</font> = <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/><a NAME="E4:65_1_1_3_1"/><span class="lab"><font color="Green" title="E27">H1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></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> <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:65_1_1_3_1"><span class="lab"><font color="Green" title="E26">H0</font></span></a>, <a class="ref" href="funct_1.html#T34" onmouseover="rs('funct_1/T34')" onmouseout="rh()">FUNCT_1:34</a></span>;<br/><span class="kw">thus </span><font color="Maroon" title="c5">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> <span class="p2">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p2">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">a</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">o</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D6" target="_self" onmouseover="rs('field_5/D6')" onmouseout="rh()">defra</a></span>
<br/>.= 
<font color="Maroon" title="c5">a</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65_1_1_3_1"><span class="lab"><font color="Green" title="E27">H1</font></span></a>, <a class="ref" href="funct_1.html#T35" onmouseover="rs('funct_1/T35')" onmouseout="rh()">FUNCT_1:35</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="E2:65_1_1_3"/>
 <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</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><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E4:65_1_1"/>
 <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</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><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="65_1_1_4"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="65_1_1_4_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">  for <font color="Olive" title="b1">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="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span> holds  <font color="Olive" title="b1">a</font> is  <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></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"> <font color="Maroon" title="c5">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="c6">a1</font> = <font color="Maroon" title="c5">a</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>;<br/><a NAME="E2:65_1_1_4_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a1</font> is  <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</a> 
 ;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c7">b1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">F</font><span class="kw"> such that </span><br/><a NAME="E4:65_1_1_4_1"/><span class="lab"><font color="Green" title="E26">H0</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font>
 ;<br/><a NAME="E5:65_1_1_4_1"/><span class="lab"><font color="Green" title="E27">H1</font></span>: 
 <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</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="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>;<br/><a NAME="E6:65_1_1_4_1"/><span class="lab"><font color="Green" title="E28">H2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">r</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 <font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D5" target="_self" onmouseover="rs('field_5/D5')" onmouseout="rh()">defr</a></span>;<br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">b</font> = <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:65_1_1_4_1"><span class="lab"><font color="Green" title="E27">H1</font></span></a>, <a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c9">o</font> = <font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">b1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="xtuple_0.html#K10" title="XTUPLE_0:func.10">rng</a> <font color="Maroon" title="c3">r</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:65_1_1_4_1"><span class="lab"><font color="Green" title="E28">H2</font></span></a>, <a class="ref" href="funct_1.html#T3" onmouseover="rs('funct_1/T3')" onmouseout="rh()">FUNCT_1:3</a></span>;<br/><font color="Maroon" title="c5">a</font> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <font color="Maroon" title="c8">b</font> = 
<span class="p1">(<span class="default"><a href="field_5.html#K4" title="FIELD_5:func.4">ren_add</a> <font color="Maroon" title="c3">r</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c8">b</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">a1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">r</font> <a href="field_5.html#K3" title="FIELD_5:func.3">"</a></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">o</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D6" target="_self" onmouseover="rs('field_5/D6')" onmouseout="rh()">defra</a></span>
<br/>.= 
<font color="Maroon" title="c3">r</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">F</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:65_1_1_4_1"><span class="lab"><font color="Green" title="E26">H0</font></span></a>, <a class="txt" href="#E6:65_1_1_4_1"><span class="lab"><font color="Green" title="E28">H2</font></span></a>, <a class="ref" href="funct_1.html#T34" onmouseover="rs('funct_1/T34')" onmouseout="rh()">FUNCT_1:34</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="field_5.html#D8" target="_self" onmouseover="rs('field_5/D8')" onmouseout="rh()">defrf</a></span>
;<br/><span class="kw">hence </span><a NAME="E10:65_1_1_4_1"/>
<font color="Maroon" title="c5">a</font> is  <a href="algstr_0.html#V10" title="ALGSTR_0:attr.10">right_complementable</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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:65_1_1_4"/>
 <a href="field_5.html#K6" title="FIELD_5:func.6">RenField</a> <font color="Maroon" title="c3">r</font> is  <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</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><span class="kw">end;</span></div>


</div>
