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<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#V3" title="VECTSP_1:attr.3">strict</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>set </b><font color="Maroon" title="c3">V</font> =  <a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Maroon" title="c2">W</font>;<br/>
<i><font color="Green" title="E27">A1</font></i>:  <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#K3" title="MOD_4:func.3">opp</a> <span class="p2">(<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></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#K3" title="MOD_4:func.3">opp</a> <span class="p2">(<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></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#K3" title="MOD_4:func.3">opp</a> <span class="p2">(<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></span>)</span> #) = 
 <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> #)
<b>by </b><i><a class="ref" href="mod_4.html#T9" target="_self" title="MOD_4:th.9">Th9</a></i>
<br/>.= 
 <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> #)
<b>by </b><i><a class="ref" href="mod_4.html#T12" target="_self" title="MOD_4:th.12">Th12</a></i>
;<br/>
<i><font color="Green" title="E28">A2</font></i>:  <a href="mod_4.html#K4" title="MOD_4:func.4">opp</a> the <a href="vectsp_1.html#U2" title="VECTSP_1:sel.2">lmult</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="mod_4.html#K4" title="MOD_4:func.4">opp</a> <span class="p1">(<span class="default"><a href="mod_4.html#K6" title="MOD_4:func.6">opp</a> the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font></span>)</span>
<b>by </b><i><a class="ref" href="mod_4.html#T13" target="_self" title="MOD_4:th.13">Th13</a></i>
<br/>.= 
the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font>
<b>by </b><i><a class="txt" href="mod_4.html#E33"><i><font color="Green" title="E23">Lm10</font></i></a></i>
;<br/>
<a NAME="E3:36"/>
 <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <span class="p1">(<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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">K</font>
 
<b>by </b><i><a class="txt" href="mod_4.html#E9"><i><font color="Green" title="E7">Lm6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:36"/>
 <a href="mod_4.html#K3" title="MOD_4:func.3">opp</a> <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="vectsp_2.html#G1" title="VECTSP_2:aggr.1">RightModStr</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>,the <a href="vectsp_2.html#U1" title="VECTSP_2:sel.1">rmult</a> of <font color="Maroon" title="c2">W</font> #)
 <b>by </b><i><a class="txt" href="mod_4.html#E1:36"><i><font color="Green" title="E27">A1</font></i></a>, <a class="txt" href="mod_4.html#E2:36"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="mod_4.html#T10" target="_self" title="MOD_4:th.10">Th10</a></i>;<br/>


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