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<b>let </b><font color="Maroon">K</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V8">left_unital</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>, <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>;<br/>



<b>set </b><font color="Maroon">p</font> = <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="matrix_2.html#K4">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">q</font> = <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">b</font></span><a href="matrix_2.html#K4">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">m</font> =  <a href="fvsum_1.html#K12" target="_self">mlt</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="matrix_2.html#K4">*&gt;</a></span>,<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">b</font></span><a href="matrix_2.html#K4">*&gt;</a></span>;<br/>
<a NAME="E1:110"/>
 <a href="fvsum_1.html#K12" target="_self">mlt</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="matrix_2.html#K4">*&gt;</a></span>,<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">b</font></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b</font></span>)</span></span><a href="matrix_2.html#K4">*&gt;</a></span>
 
<b>by </b><i><a class="ref" href="fvsum_1.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E2:110"/><b>then </b>
 <a href="fvsum_1.html#K12" target="_self">mlt</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="matrix_2.html#K4">*&gt;</a></span>,<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">b</font></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a> 1 <a href="finseqop.html#K4">|-&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T73">FINSEQ_2:73</a></i>;<br/>
<a NAME="E3:110"/><b>then </b>
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">K</font> <a href="finsop_1.html#K2">$$</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K12" target="_self">mlt</a> <span class="p2"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="matrix_2.html#K4">*&gt;</a></span>,<span class="p2"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">b</font></span><a href="matrix_2.html#K4">*&gt;</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="finsop_1.html#T17">FINSOP_1:17</a></i>;<br/>
<b>hence </b><a NAME="E4:110"/>
<span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="fvsum_1.html#K13" target="_self">"*"</a> <span class="p1"><a href="matrix_2.html#K4">&lt;*</a><span class="default"><font color="Maroon">b</font></span><a href="matrix_2.html#K4">*&gt;</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b</font>
 ;<br/>


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