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<b>take </b>
 <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
;<br/>

<b>thus </b><a NAME="E1:74_1_1"/>
(  <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="rlvect_1.html#V3">Abelian</a> &amp;  <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="rlvect_1.html#V4">add-associative</a> &amp;  <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="rlvect_1.html#V5">right_zeroed</a> &amp;  <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="rlvect_1.html#V6">right_complementable</a> )
 ;<br/>

<a NAME="E2:74_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">c<sub>1</sub></font><br/>for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="vectsp_1.html#NM3">Scalar</a> of <font color="Maroon">c<sub>2</sub></font><br/>for <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font> being  <a href="vectsp_2.html#NM5">Vector</a> of <span class="p1">(<span class="default"><a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">b<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>6</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>5</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>5</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>5</sub></font> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">b<sub>6</sub></font></span>)</span> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>6</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> &amp; <font color="Olive">b<sub>5</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K4">+</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>4</sub></font></span>)</span> &amp; <font color="Olive">b<sub>5</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>5</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>5</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6">*</a> <font color="Olive">b<sub>5</sub></font></span>)</span> <a href="vectsp_2.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="vectsp_2.html#E110"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:74_1_1"/>
(  <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="vectsp_2.html#V5" target="_self">RightMod-like</a> &amp;  <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="vectsp_1.html#V12">VectSp-like</a> &amp;  <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="vectsp_2.html#V6" target="_self">BiMod-like</a> &amp;  <a href="vectsp_2.html#K9" target="_self">BiModule</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> is <a href="vectsp_2.html#V4" target="_self">strict</a> )
 <b>by </b><i><a class="ref" href="vectsp_2.html#D23" target="_self">Def23</a>, <a class="ref" href="vectsp_2.html#D24" target="_self">Def24</a>, <a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/>


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