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<b>take </b><font color="Maroon">c<sub>3</sub></font> =  <a href="vectsp_1.html#G4" target="_self">VectSpStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> #);<br/>

<b>thus </b><a NAME="E1:53_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font><br/>for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K2">+</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>1</sub></font> <a href="vectsp_1.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6" target="_self">*</a> <font color="Olive">b<sub>4</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" 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>1</sub></font> <a href="vectsp_1.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="vectsp_1.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</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" target="_self">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="vectsp_1.html#K6" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="vectsp_1.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font></span>)</span> &amp; <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="vectsp_1.html#K6" target="_self">*</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="vectsp_1.html#E75"><i><font color="Green">Lemma20</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="vectsp_1.html#D26" target="_self">VECTSP_1:def 26</a><br/>

<b>thus </b><a NAME="E2:53_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="rlvect_1.html#V4">add-associative</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="rlvect_1.html#V5">right_zeroed</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="rlvect_1.html#V6">right_complementable</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="rlvect_1.html#V3">Abelian</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="vectsp_1.html#V11" target="_self">strict</a> )
 <b>by </b><i><a class="txt" href="vectsp_1.html#E74"><i><font color="Green">Lemma19</font></i></a></i>;<br/>


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