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<b>take </b>
 <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font>
;<br/>

<b>thus </b><a NAME="E1:71_1_1"/>
(  <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> is <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">Abelian</a> &amp;  <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> is <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> &amp;  <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> is <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> &amp;  <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> is <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> )
 ;<br/>

<a NAME="E2:71_1_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">R1</font><br/> for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c2">R2</font><br/> for <font color="Olive" title="b5">v</font>, <font color="Olive" title="b6">w</font> being  <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b6">w</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b5">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b6">w</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b5">v</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b5">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b5">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c1">R1</font></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b5">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b6">w</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b3">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">w</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b3">p</font></span>)</span> &amp; <font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">p</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b4">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b4">q</font></span>)</span> &amp; <font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">q</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b4">q</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b3">p</font> &amp; <font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c2">R2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b5">v</font> &amp; <font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">v</font> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b3">p</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Olive" title="b5">v</font></span>)</span> <a href="vectsp_2.html#K6" title="VECTSP_2:func.6">*</a> <font color="Olive" title="b3">p</font> )
 
<b>by </b><i><a class="txt" href="vectsp_2.html#E110"><i><font color="Green" title="E28">Lm10</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:71_1_1"/>
(  <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> is <a href="vectsp_2.html#V4" title="VECTSP_2:attr.4">RightMod-like</a> &amp;  <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> is <a href="vectsp_1.html#V12" title="VECTSP_1:attr.12">VectSp-like</a> &amp;  <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> is <a href="vectsp_2.html#V5" title="VECTSP_2:attr.5">BiMod-like</a> &amp;  <a href="vectsp_2.html#K9" title="VECTSP_2:func.9">BiModule</a> <font color="Maroon" title="c1">R1</font>,<font color="Maroon" title="c2">R2</font> is <a href="vectsp_2.html#V3" title="VECTSP_2:attr.3">strict</a> )
 <b>by </b><i><a class="ref" href="vectsp_2.html#D23" target="_self" title="VECTSP_2:def.23">Def23</a>, <a class="ref" href="vectsp_2.html#D24" target="_self" title="VECTSP_2:def.24">Def24</a>, <a class="ref" href="vectsp_1.html#D26" title="VECTSP_1:def.26">VECTSP_1:def 26</a></i>;<br/>


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