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<b>let </b><font color="Maroon" title="c1">K</font>, <font color="Maroon" title="c2">L</font> be   <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>;<br/><b>let </b><font color="Maroon" title="c3">V</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="vectsp_1.html#L4" title="VECTSP_1:struct.4">VectSpStr</a> of <font color="Maroon" title="c1">K</font>;<br/><b>let </b><font color="Maroon" title="c4">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="c2">L</font>;<br/><b>let </b><font color="Maroon" title="c5">v1</font>, <font color="Maroon" title="c6">v2</font> be   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Vector</a> of <font color="Maroon" title="c3">V</font>;<br/><b>let </b><font color="Maroon" title="c7">w1</font>, <font color="Maroon" title="c8">w2</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <font color="Maroon" title="c4">W</font>;<br/>









<b>assume </b><a NAME="E1:32"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c2">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c1">K</font> &amp; <font color="Maroon" title="c4">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="mod_4.html#K3" title="MOD_4:func.3">opp</a> <font color="Maroon" title="c3">V</font> &amp; <font color="Maroon" title="c5">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">w1</font> &amp; <font color="Maroon" title="c6">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">w2</font> )
 ;<br/>

<a NAME="E2:32"/>
 <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> <font color="Maroon" title="c3">V</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#K3" title="MOD_4:func.3">opp</a> <font color="Maroon" title="c3">V</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#K3" title="MOD_4:func.3">opp</a> <font color="Maroon" title="c3">V</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="c3">V</font>,the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c3">V</font>,the <a href="struct_0.html#U2" title="STRUCT_0:sel.2">Zero</a> of <font color="Maroon" title="c3">V</font> #)
 
<b>by </b><i><a class="ref" href="mod_4.html#T9" target="_self" title="MOD_4:th.9">Th9</a></i>;<br/>
<b>hence </b><a NAME="E3:32"/>
<font color="Maroon" title="c7">w1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c8">w2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">v1</font> <a href="rlvect_1.html#K2" title="RLVECT_1:func.2">+</a> <font color="Maroon" title="c6">v2</font>
 <b>by </b><i><a class="txt" href="mod_4.html#E1:32"><i><font color="Green" title="E23">A1</font></i></a></i>;<br/>


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