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

<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c2">V</font> be   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c3">V1</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">V</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:36"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c3">V1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c3">V1</font> is <a href="rmod_2.html#V1" title="RMOD_2:attr.1">linearly-closed</a>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">VV</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">D</font> = <font color="Maroon" title="c3">V1</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="txt" href="rmod_2.html#E1:36"><i><font color="Green" title="E25">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c6">A</font> = the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c5">D</font>;<br/>
<a NAME="E4:36"/><i><font color="Green" title="E27">A3</font></i>: 
( <font color="Maroon" title="c3">V1</font> <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 <font color="Maroon" title="c2">V</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">V</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:36"/>
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c5">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <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="c2">V</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">V</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E6:36"/><b>then </b><i><font color="Green" title="E28">A4</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c5">D</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E4:36"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E7:36"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:36_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c5">D</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c8">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:36_1"/><i><font color="Green" title="E29">A5</font></i>: 
<font color="Maroon" title="c8">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c5">D</font></span>)</span>
 <b>and </b><br/><a NAME="E4:36_1"/><i><font color="Green" title="E30">A6</font></i>: 
<span class="p1">(<span class="default">the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">x</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c9">y1</font>, <font color="Maroon" title="c10">y2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:36_1"/><i><font color="Green" title="E31">A7</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c9">y1</font>,<font color="Maroon" title="c10">y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">y</font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E6:36"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_1"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></i>;<br/>
<a NAME="E7:36_1"/><i><font color="Green" title="E32">A8</font></i>: 
( <font color="Maroon" title="c9">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font> &amp; <font color="Maroon" title="c10">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font> &amp; <font color="Maroon" title="c5">D</font> <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 <font color="Maroon" title="c2">V</font> )
 
<b>by </b><i><a class="txt" href="rmod_2.html#E6:36"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_1"><i><font color="Green" title="E29">A5</font></i></a>, <a class="txt" href="rmod_2.html#E6:36_1"><i><font color="Green" title="E31">A7</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c11">y1</font> = <font color="Maroon" title="c9">y1</font>, <font color="Maroon" title="c12">y2</font> = <font color="Maroon" title="c10">y2</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> ;<br/>
<a NAME="E9:36_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">y1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c12">y2</font>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E3:36_1"><i><font color="Green" title="E29">A5</font></i></a>, <a class="txt" href="rmod_2.html#E4:36_1"><i><font color="Green" title="E30">A6</font></i></a>, <a class="txt" href="rmod_2.html#E6:36_1"><i><font color="Green" title="E31">A7</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<b>hence </b><a NAME="E10:36_1"/>
<font color="Maroon" title="c7">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E2:36"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="rmod_2.html#E7:36_1"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="rmod_2.html#D1" target="_self" title="RMOD_2:def.1">Def1</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c7">A</font> = the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">V</font> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <font color="Maroon" title="c5">D</font> as   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <font color="Maroon" title="c5">D</font> <b>by </b><i><a class="txt" href="rmod_2.html#E6:36"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>set </b><font color="Maroon" title="c8">C</font> = <span class="p1">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c5">D</font>;<br/>
<a NAME="E9:36"/>
( <font color="Maroon" title="c3">V1</font> <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 <font color="Maroon" title="c2">V</font> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</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 <font color="Maroon" title="c2">V</font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E10:36"/><b>then </b><i><font color="Green" title="E29">A9</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">D</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E11:36"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c9">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:36_2"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c5">D</font></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c10">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:36_2"/><i><font color="Green" title="E30">A10</font></i>: 
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c5">D</font></span>)</span>
 <b>and </b><br/><a NAME="E4:36_2"/><i><font color="Green" title="E31">A11</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">x</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">y</font> = <font color="Maroon" title="c10">y</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="txt" href="rmod_2.html#E10:36"><i><font color="Green" title="E29">A9</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_2"><i><font color="Green" title="E30">A10</font></i></a></i>;<br/>
<font color="Maroon" title="c9">x</font> = 
<span class="p1">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">y</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E3:36_2"><i><font color="Green" title="E30">A10</font></i></a>, <a class="txt" href="rmod_2.html#E4:36_2"><i><font color="Green" title="E31">A11</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c11">y</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#D25" title="VECTSP_1:def.25">VECTSP_1:def 25</a></i>
;<br/>
<b>hence </b><a NAME="E7:36_2"/>
<font color="Maroon" title="c9">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E2:36"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="rmod_2.html#E10:36"><i><font color="Green" title="E29">A9</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_2"><i><font color="Green" title="E30">A10</font></i></a>, <a class="ref" href="rmod_2.html#T5" target="_self" title="RMOD_2:th.5">Th5</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c9">C</font> = <span class="p1">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c5">D</font> as   <a href="binop_1.html#NM1" title="BINOP_1:NM.1">UnOp</a> of <font color="Maroon" title="c5">D</font> <b>by </b><i><a class="txt" href="rmod_2.html#E10:36"><i><font color="Green" title="E29">A9</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">M</font> = the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">V</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">d</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c5">D</font> <b>by </b><i><a class="txt" href="rmod_2.html#E2:36"><i><font color="Green" title="E26">A2</font></i></a>, <a class="ref" href="rmod_2.html#T4" target="_self" title="RMOD_2:th.4">Th4</a></i>;<br/>
<a NAME="E14:36"/><i><font color="Green" title="E30">A12</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">V</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c2">V</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E15:36"/>
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <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="c2">V</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T119" title="ZFMISC_1:th.119">ZFMISC_1:119</a></i>;<br/>
<a NAME="E16:36"/><b>then </b><i><font color="Green" title="E31">A13</font></i>: 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">V</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E14:36"><i><font color="Green" title="E30">A12</font></i></a>, <a class="ref" href="relat_1.html#T91" title="RELAT_1:th.91">RELAT_1:91</a></i>;<br/>
<a NAME="E17:36"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">V</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c12">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:36_3"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default">the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">V</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c13">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:36_3"/><i><font color="Green" title="E32">A14</font></i>: 
<font color="Maroon" title="c13">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default">the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">V</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span>
 <b>and </b><br/><a NAME="E4:36_3"/><i><font color="Green" title="E33">A15</font></i>: 
<span class="p1">(<span class="default">the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">V</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p2"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c13">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">x</font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c14">y2</font>, <font color="Maroon" title="c15">y1</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E6:36_3"/><i><font color="Green" title="E34">A16</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c14">y2</font>,<font color="Maroon" title="c15">y1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">y</font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E16:36"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_3"><i><font color="Green" title="E32">A14</font></i></a>, <a class="ref" href="relat_1.html#D1" title="RELAT_1:def.1">RELAT_1:def 1</a></i>;<br/>
<a NAME="E7:36_3"/><i><font color="Green" title="E35">A17</font></i>: 
( <font color="Maroon" title="c15">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c14">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">V1</font> )
 
<b>by </b><i><a class="txt" href="rmod_2.html#E16:36"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_3"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="rmod_2.html#E6:36_3"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">y1</font> = <font color="Maroon" title="c15">y1</font> as   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="txt" href="rmod_2.html#E16:36"><i><font color="Green" title="E31">A13</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_3"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="rmod_2.html#E6:36_3"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">y2</font> = <font color="Maroon" title="c14">y2</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="txt" href="rmod_2.html#E7:36_3"><i><font color="Green" title="E35">A17</font></i></a></i>;<br/>
<a NAME="E10:36_3"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">y2</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c16">y1</font>
 
<b>by </b><i><a class="txt" href="rmod_2.html#E3:36_3"><i><font color="Green" title="E32">A14</font></i></a>, <a class="txt" href="rmod_2.html#E4:36_3"><i><font color="Green" title="E33">A15</font></i></a>, <a class="txt" href="rmod_2.html#E6:36_3"><i><font color="Green" title="E34">A16</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<b>hence </b><a NAME="E11:36_3"/>
<font color="Maroon" title="c12">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E2:36"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="rmod_2.html#E7:36_3"><i><font color="Green" title="E35">A17</font></i></a>, <a class="ref" href="rmod_2.html#D1" target="_self" title="RMOD_2:def.1">Def1</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c12">M</font> = the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">V</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> as   <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"><font color="Maroon" title="c5">D</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<font color="Maroon" title="c5">D</font> <b>by </b><i><a class="txt" href="rmod_2.html#E16:36"><i><font color="Green" title="E31">A13</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>set </b><font color="Maroon" title="c13">W</font> =  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #);<br/>
<a NAME="E19:36"/><i><font color="Green" title="E32">A18</font></i>: 
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="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #)<br/> for <font color="Olive" title="b3">x</font>, <font color="Olive" title="b4">y</font> being  <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>  st <font color="Olive" title="b3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">y</font> holds <br/><font color="Olive" title="b1">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c15">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #);<br/><b>let </b><font color="Maroon" title="c16">x</font>, <font color="Maroon" title="c17">y</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/>



<b>assume </b><a NAME="E1:36_4"/><i><font color="Green" title="E33">A19</font></i>: 
( <font color="Maroon" title="c16">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">a</font> &amp; <font color="Maroon" title="c15">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">y</font> )
 ;<br/>

<b>thus </b><font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c15">b</font> = 
<font color="Maroon" title="c7">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c14">a</font>,<font color="Maroon" title="c15">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>

<br/>.= 
<font color="Maroon" title="c16">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c17">y</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E6:36"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="rmod_2.html#E1:36_4"><i><font color="Green" title="E33">A19</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E20:36"/><i><font color="Green" title="E33">A20</font></i>: 
(  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #) is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> &amp;  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #) is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> &amp;  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #) is <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> &amp;  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #) is <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_5"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:36_5"/>
 <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #) is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c15">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #); <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D5" title="RLVECT_1:def.5">RLVECT_1:def 5</a><br/>

<b>reconsider </b><font color="Maroon" title="c16">x</font> = <font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c17">y</font> = <font color="Maroon" title="c15">b</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c15">b</font> = 
<font color="Maroon" title="c17">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c16">x</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c15">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c14">a</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a></i>
;<br/>


</div><b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a>
<div class="add"><b>let </b><font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c15">b</font>, <font color="Maroon" title="c16">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #);<br/><b>reconsider </b><font color="Maroon" title="c17">x</font> = <font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c18">y</font> = <font color="Maroon" title="c15">b</font>, <font color="Maroon" title="c19">z</font> = <font color="Maroon" title="c16">c</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><a NAME="E2:36_5_2"/><i><font color="Green" title="E34">A21</font></i>: 
( <font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c15">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c18">y</font> &amp; <font color="Maroon" title="c15">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c16">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c19">z</font> )
 <b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c15">b</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c16">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c17">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c18">y</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c19">z</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c17">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">y</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c19">z</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>
<br/>.= 
<font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">b</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c16">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a>, <a class="txt" href="rmod_2.html#E2:36_5_2"><i><font color="Green" title="E34">A21</font></i></a></i>
;<br/><br/></div>
<b>end;</b></div>

<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a>
<div class="add"><b>let </b><font color="Maroon" title="c14">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #);<br/><b>reconsider </b><font color="Maroon" title="c15">x</font> = <font color="Maroon" title="c14">a</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/><b>thus </b><font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #)</span>)</span> = 
<font color="Maroon" title="c15">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c14">a</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#D7" title="RLVECT_1:def.7">RLVECT_1:def 7</a></i>
;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c14">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #); <i><font color="Red">:: according to </font></i><a class="ref" href="rlvect_1.html#D8" title="RLVECT_1:def.8">RLVECT_1:def 8</a><br/>

<b>reconsider </b><font color="Maroon" title="c15">x</font> = <font color="Maroon" title="c14">a</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">b'</font> = <span class="p1">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">x</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> ;<br/>
<a NAME="E6:36_5"/>
<font color="Maroon" title="c9">C</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">D</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T7" title="FUNCT_2:th.7">FUNCT_2:7</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c17">b</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp_1.html#K6" title="VECTSP_1:func.6">comp</a> <font color="Maroon" title="c2">V</font></span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> <font color="Maroon" title="c5">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c15">x</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #) ;<br/>
<a NAME="E8:36_5"/><i><font color="Green" title="E34">A22</font></i>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">b'</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c17">b</font>
;<br/>

<b>thus </b><font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c17">b</font> = 
<font color="Maroon" title="c15">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c16">b'</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a>, <a class="txt" href="rmod_2.html#E8:36_5"><i><font color="Green" title="E34">A22</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c15">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c15">x</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D25" title="VECTSP_1:def.25">VECTSP_1:def 25</a></i>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #)
<b>by </b><i><a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></i>
;<br/>


</div><b>end;</b></div>
<a NAME="E21:36"/>
 <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #) is <a href="vectsp_2.html#V4" title="VECTSP_2:attr.4">RightMod-like</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_6"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c14">a</font>, <font color="Maroon" title="c15">b</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_2.html#D23" title="VECTSP_2:def.23">VECTSP_2:def 23</a><br/><b>let </b><font color="Maroon" title="c16">v</font>, <font color="Maroon" title="c17">w</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #);<br/>



<b>reconsider </b><font color="Maroon" title="c18">x</font> = <font color="Maroon" title="c16">v</font>, <font color="Maroon" title="c19">y</font> = <font color="Maroon" title="c17">w</font> as   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<div><i><font color="Green" title="E34">A23</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_6_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c20">a</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R</font>;<br/><b>let </b><font color="Maroon" title="c21">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #);<br/><b>let </b><font color="Maroon" title="c22">y</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">V</font>;<br/><b>assume </b><a NAME="E1:36_6_1"/><i><font color="Green" title="E35">A24</font></i>: 
<font color="Maroon" title="c22">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">x</font>
 ;<br/><a NAME="E2:36_6_1"/>
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c21">x</font>,<font color="Maroon" title="c20">a</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c12">M</font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E16:36"><i><font color="Green" title="E31">A13</font></i></a></i>;<br/><b>hence </b><a NAME="E3:36_6_1"/>
<font color="Maroon" title="c21">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c20">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">y</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c20">a</font>
 <b>by </b><i><a class="txt" href="rmod_2.html#E1:36_6_1"><i><font color="Green" title="E35">A24</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/></div><b>end;</b></div>
<a NAME="E3:36_6"/><b>then </b><i><font color="Green" title="E35">A25</font></i>: 
( <font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c15">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c15">b</font> &amp; <font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font> &amp; <font color="Maroon" title="c17">w</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">y</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font> )
 
;<br/>
<a NAME="E4:36_6"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">w</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">y</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span> &amp; <font color="Maroon" title="c16">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c17">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c19">y</font> )
 
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c16">v</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <font color="Maroon" title="c17">w</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c19">y</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E2:36_6"><i><font color="Green" title="E34">A23</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c19">y</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_2.html#D23" title="VECTSP_2:def.23">VECTSP_2:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">w</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_6"><i><font color="Green" title="E35">A25</font></i></a></i>
;<br/><br/>

<b>thus </b><font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c15">b</font></span>)</span> = 
<font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c14">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c15">b</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_2.html#E2:36_6"><i><font color="Green" title="E34">A23</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c15">b</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_2.html#D23" title="VECTSP_2:def.23">VECTSP_2:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font></span>)</span> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c15">b</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_2.html#E19:36"><i><font color="Green" title="E32">A18</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_6"><i><font color="Green" title="E35">A25</font></i></a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c14">a</font></span>)</span> = 
<font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">b</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c14">a</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_2.html#E2:36_6"><i><font color="Green" title="E34">A23</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c15">b</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font>
<b>by </b><i><a class="ref" href="vectsp_2.html#D23" title="VECTSP_2:def.23">VECTSP_2:def 23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c15">b</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Maroon" title="c14">a</font>
<b>by </b><i><a class="txt" href="rmod_2.html#E2:36_6"><i><font color="Green" title="E34">A23</font></i></a>, <a class="txt" href="rmod_2.html#E3:36_6"><i><font color="Green" title="E35">A25</font></i></a></i>
;<br/>

<b>thus </b><font color="Maroon" title="c16">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">R</font></span>)</span> = 
<font color="Maroon" title="c18">x</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">R</font></span>)</span>
<b>by </b><i><a class="txt" href="rmod_2.html#E2:36_6"><i><font color="Green" title="E34">A23</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c16">v</font>
<b>by </b><i><a class="ref" href="vectsp_2.html#D23" title="VECTSP_2:def.23">VECTSP_2:def 23</a></i>
;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c14">W</font> =  <a href="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</a>(# <font color="Maroon" title="c5">D</font>,<font color="Maroon" title="c7">A</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">M</font> #) as   <a href="vectsp_2.html#NM7" title="VECTSP_2:NM.7">RightMod</a> of <font color="Maroon" title="c1">R</font> <b>by </b><i><a class="txt" href="rmod_2.html#E20:36"><i><font color="Green" title="E33">A20</font></i></a></i>;<br/>
<a NAME="E23:36"/>
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c14">W</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="c2">V</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c15">W</font> = <font color="Maroon" title="c14">W</font> as  <a href="vectsp_2.html#V2" title="VECTSP_2:attr.2">strict</a>  <a href="rmod_2.html#M1" title="RMOD_2:mode.1">Submodule</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="ref" href="rmod_2.html#D2" target="_self" title="RMOD_2:def.2">Def2</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c15">W</font>
;<br/>

<b>thus </b><a NAME="E25:36"/>
<font color="Maroon" title="c3">V1</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="c15">W</font>
 ;<br/>


</div>
