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<b>let </b><font color="Maroon">F</font> be   <a href="vectsp_1.html#NM2">Field</a>;<br/><b>let </b><font color="Maroon">S</font> be   <a href="symsp_1.html#NM1">SymSp</a> of <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">l</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">F</font>;<br/>











<b>assume </b><a NAME="E1:28"/><i><font color="Green">E27</font></i>: 
not <font color="Maroon">b</font> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font>
 ;<br/>

<b>set </b><font color="Maroon">L</font> = <font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font></span>)</span>;<br/>
<a NAME="E2:28"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font>
 
<b>by </b><i>, </i>;<br/>
<font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="rlvect_1.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">x</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#T70">VECTSP_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">x</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font></span>)</span>
<b>by </b><i><a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>
;<br/>
<a NAME="E4:28"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">x</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="group_1.html#K10">*</a> <span class="p3">(<span class="default"><a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:28"/>
<span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">x</font></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">b</font></span>)</span> <a href="symsp_1.html#R1" target="_self">_|_</a> <font color="Maroon">a</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:28"/>
 <a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">l</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="symsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font></span>)</span>
 <b>by </b><i>, , </i>;<br/>


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