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<b>let </b><font color="Maroon" title="c1">K</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">W</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="vectsp_2.html#L1" title="VECTSP_2:struct.1">RightModStr</a> of <font color="Maroon" title="c1">K</font> holds  the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">lmult</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K5" title="MOD_4:func.5">opp</a> <font color="Olive" title="b1">W</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <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="Olive" title="b1">W</font></span><br/><b>let </b><font color="Maroon" title="c2">W</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="vectsp_2.html#L1" title="VECTSP_2:struct.1">RightModStr</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <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><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="E2:34"/>
 <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#G1" title="VECTSP_1:aggr.1">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="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Maroon" title="c2">W</font>,<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">W</font></span>)</span>,<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="E3:34"/>
the <a href="vectsp_1.html#U1" title="VECTSP_1:sel.1">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="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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