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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="ortsp_1.html#NM1">OrtSp</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="E1:23"/><i><font color="Green">E22</font></i>: 
( not <font color="Maroon">b</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">a</font> &amp; <font color="Maroon">l</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">F</font> )
 ;<br/>

<a NAME="E2:23"/><b>then </b>
not <font color="Maroon">b</font> <a href="symsp_1.html#R1">_|_</a> <font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:23"/><b>then </b><i><font color="Green">E26</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="ortsp_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">_|_</a> <font color="Maroon">a</font> &amp; <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="ortsp_1.html#K1" target="_self">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span>,<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">_|_</a> <font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:23"/><b>then </b>
<font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font> <a href="symsp_1.html#R1">_|_</a> <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="ortsp_1.html#K1" target="_self">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span>,<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>
 
<b>by </b><i/>;<br/>
<a NAME="E5:23"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="vectsp_1.html#K6">*</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span> <a href="symsp_1.html#R1">_|_</a> <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="ortsp_1.html#K1" target="_self">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span>,<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>
 
<b>by </b><i/>;<br/>
<a NAME="E6:23"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K4">"</a> </span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">l</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font> <a href="symsp_1.html#R1">_|_</a> <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="ortsp_1.html#K1" target="_self">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span>,<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>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/>
<a NAME="E7:23"/><b>then </b>
<span class="p1">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">F</font></span>)</span> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font> <a href="symsp_1.html#R1">_|_</a> <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="ortsp_1.html#K1" target="_self">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span>,<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>
 
<b>by </b><i>, <a class="ref" href="vectsp_1.html#D22">VECTSP_1:def 22</a></i>;<br/>
<a NAME="E8:23"/><b>then </b>
<font color="Maroon">a</font> <a href="symsp_1.html#R1">_|_</a> <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="ortsp_1.html#K1" target="_self">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span>,<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>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D26">VECTSP_1:def 26</a></i>;<br/>
<a NAME="E9:23"/><b>then </b>
<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="ortsp_1.html#K1" target="_self">ProJ</a> <span class="p3">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span>,<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">_|_</a> <font color="Maroon">a</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E10:23"/>
 <a href="ortsp_1.html#K1" target="_self">ProJ</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="vectsp_1.html#K6">*</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">b</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ortsp_1.html#K1" target="_self">ProJ</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">x</font>
 <b>by </b><i>, <a class="txt" href="ortsp_1.html#E1:23"><i><font color="Green">E22</font></i></a>, </i>;<br/>


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