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<a NAME="E1:66_1_1"/>
<font color="Maroon">W1</font> <a href="vectsp_5.html#K1" target="_self">+</a> <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G4">VectSpStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">M</font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">M</font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">M</font>,the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">M</font> #)
 
<b>by </b><i><a class="txt" href="vectsp_5.html#E11"><i><font color="Green">Lemma48</font></i></a>, <a class="txt" href="vectsp_5.html#E2"><i><font color="Green">Lemma37</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">v1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font>, <font color="Maroon">v2</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">M</font><b> such that </b><br/><a NAME="E3:66_1_1"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">v1</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font> &amp; <font color="Maroon">v2</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W2</font> &amp; <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">v2</font> )
 <b>by </b><i/>;<br/>
<b>take </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K1">]</a></span>
;<br/>

<a NAME="E4:66_1_1"/>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K2">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">v1</font> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K3">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font> )
 
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>;<br/>
<b>hence </b><a NAME="E5:66_1_1"/>
( <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K2">`1</a> </span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K3">`2</a> </span>)</span> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K2">`1</a>  <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font> &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">v2</font></span><a href="domain_1.html#K1">]</a></span> <a href="domain_1.html#K3">`2</a>  <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W2</font> )
 <b>by </b><i><a class="txt" href="vectsp_5.html#E12"><i><font color="Green">Lemma49</font></i></a></i>;<br/>


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