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

<b>let </b><font color="Maroon" title="c1">K</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">W</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="vectsp_2.html#L1" title="VECTSP_2:struct.1">RightModStr</a> of <font color="Maroon" title="c1">K</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c3">p</font> =  <a href="mod_4.html#K1" title="MOD_4:func.1">~</a> the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font> 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">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<span class="default"><a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c1">K</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W</font> ;<br/>
<a NAME="E2:28"/><i><font color="Green" title="E18">A1</font></i>: 
 <a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#G4" title="VECTSP_1:aggr.4">VectSpStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">W</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c2">W</font>,<font color="Maroon" title="c3">p</font> #)
 
<b>by </b><i><a class="ref" href="mod_4.html#D4" target="_self" title="MOD_4:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:28"/>
 <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">LoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rlvect_1.html#G1" title="RLVECT_1:aggr.1">LoopStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">W</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c2">W</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c2">W</font> #)
 ;<br/>

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>thus </b><a NAME="E4:28"/>
( <font color="Maroon" title="c4">x</font> is   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c2">W</font> iff <font color="Maroon" title="c4">x</font> is   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font></span>)</span> )
 <b>by </b><i><a class="txt" href="mod_4.html#E2:28"><i><font color="Green" title="E18">A1</font></i></a></i>;<br/>


</div>
