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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="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="group_1.html#V7" title="GROUP_1:attr.7">commutative</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">left_unital</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">b1</font>, <font color="Maroon" title="c5">b2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">K</font>;<br/>



<b>set </b><font color="Maroon" title="c6">p</font> = <span class="p1"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font></span><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c7">q</font> = <span class="p1"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font></span><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">*&gt;</a></span>;<br/>
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1">(<span class="default"><a href="fvsum_1.html#K11" title="FVSUM_1:func.11">mlt</a> <span class="p2"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font></span><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">*&gt;</a></span>,<span class="p2"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font></span><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">*&gt;</a></span></span>)</span> = 
the <a href="rlvect_1.html#U1" title="RLVECT_1:sel.1">add</a> of <font color="Maroon" title="c1">K</font> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p1"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c4">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">a2</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span></span><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">*&gt;</a></span>
<b>by </b><i><a class="txt" href="fvsum_1.html#E92"><i><font color="Green" title="E41">Lm9</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c4">b1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a2</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span>
<b>by </b><i><a class="ref" href="finsop_1.html#T13" title="FINSOP_1:th.13">FINSOP_1:13</a></i>
;<br/>
<b>hence </b><a NAME="E2:110"/>
<span class="p1"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font></span><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">*&gt;</a></span> <a href="fvsum_1.html#K13" title="FVSUM_1:func.13">"*"</a> <span class="p1"><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">&lt;*</a><span class="default"><font color="Maroon" title="c4">b1</font>,<font color="Maroon" title="c5">b2</font></span><a href="rlvect_1.html#K7" title="RLVECT_1:func.7">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a1</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c4">b1</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">a2</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">b2</font></span>)</span>
 ;<br/>


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