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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">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>, <font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>, <font color="Maroon">b1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font>, <font color="Maroon">b2</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="rlvect_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="rlvect_1.html#K7">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">q</font> = <span class="p1"><a href="rlvect_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="rlvect_1.html#K7">*&gt;</a></span>;<br/>
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">K</font> <a href="finsop_1.html#K2">$$</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11" target="_self">mlt</a> <span class="p2"><a href="rlvect_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="rlvect_1.html#K7">*&gt;</a></span>,<span class="p2"><a href="rlvect_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="rlvect_1.html#K7">*&gt;</a></span></span>)</span> = 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">K</font> <a href="finsop_1.html#K2">$$</a> <span class="p1"><a href="rlvect_1.html#K7">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b2</font></span>)</span></span><a href="rlvect_1.html#K7">*&gt;</a></span>
<b>by </b><i><a class="ref" href="fvsum_1.html#T12" target="_self">Th12</a></i>
<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">K</font> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b2</font></span>)</span>
<b>by </b><i><a class="ref" href="finsop_1.html#T13">FINSOP_1:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b1</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b2</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T5">RLVECT_1:5</a></i>
;<br/>
<b>hence </b><a NAME="E2:111"/>
<span class="p1"><a href="rlvect_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="rlvect_1.html#K7">*&gt;</a></span> <a href="fvsum_1.html#K13" target="_self">"*"</a> <span class="p1"><a href="rlvect_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">b1</font>,<font color="Maroon">b2</font></span><a href="rlvect_1.html#K7">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">a1</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b1</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Maroon">a2</font> <a href="group_1.html#K10">*</a> <font color="Maroon">b2</font></span>)</span>
 ;<br/>


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