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<b>let </b><font color="Maroon">K</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">V</font> be   <a href="vectsp_1.html#NM6">VectSp</a> of <font color="Maroon">K</font>;<br/><b>let </b><font color="Maroon">W</font> be    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">w</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">W</font>;<br/>









<b>assume </b><a NAME="E1:25"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <font color="Maroon">w</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">W1</font> =  <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">w</font></span><a href="domain_1.html#K6">}</a></span> as    <a href="vectsp_4.html#M1">Subspace</a> of <font color="Maroon">V</font> <b>by </b><i><a class="ref" href="vectsp_4.html#T34">VECTSP_4:34</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be   <a href="vectsp_1.html#NM5">Vector</a> of <font color="Maroon">V</font>;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:25_1_1"/>
<font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font>
 ;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font><b> such that </b><br/><a NAME="E3:25_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">w</font>
 <b>by </b><i/>;<br/><a NAME="E4:25_1_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">v</font>
 <b>by </b><i>, , <a class="ref" href="vectsp_4.html#T22">VECTSP_4:22</a></i>;<br/><b>hence </b><a NAME="E5:25_1_1"/>
<font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a>  <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:25_1"/>
<font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a>  <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">K</font><b> such that </b><br/><a NAME="E4:25_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">v</font>
 <b>by </b><i/>;<br/><a NAME="E5:25_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">w</font>
 <b>by </b><i>, , <a class="ref" href="vectsp_4.html#T22">VECTSP_4:22</a></i>;<br/><b>hence </b><a NAME="E6:25_1"/>
<font color="Maroon">u</font> <a href="rlvect_1.html#R1">in</a> <font color="Maroon">W1</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:25"/>
 <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">w</font></span><a href="domain_1.html#K6">}</a></span> <a href="hidden.html#R1">=</a>  <a href="vectsp_7.html#K1">Lin</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="vectsp_4.html#T38">VECTSP_4:38</a></i>;<br/>


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