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<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/><b>let </b><font color="Maroon" title="c5">S</font> be   <a href="ortsp_1.html#NM1" title="ORTSP_1:NM.1">OrtSp</a> of <font color="Maroon" title="c4">F</font>;<br/><b>let </b><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c5">S</font>;<br/>







<b>set </b><font color="Maroon" title="c8">0V</font> =  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c5">S</font>;<br/>
<b>assume </b><a NAME="E1:16"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c7">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">b</font> )
 ;<br/>

<a NAME="E2:16"/><b>then </b>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><a href="group_1.html#K2" title="GROUP_1:func.2">1_</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="vectsp_1.html#K5" title="VECTSP_1:func.5">*</a> <font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="ortsp_1.html#D2" target="_self" title="ORTSP_1:def.2">Def2</a></i>;<br/>
<a NAME="E3:16"/><b>then </b>
 <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#T59" title="VECTSP_1:th.59">VECTSP_1:59</a></i>;<br/>
<a NAME="E4:16"/><b>then </b>
<font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a>  <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="ortsp_1.html#T12" target="_self" title="ORTSP_1:th.12">Th12</a></i>;<br/>
<a NAME="E5:16"/><b>then </b>
<font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c5">S</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>;<br/>
<a NAME="E6:16"/><b>then </b>
<font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">b</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></i>;<br/>
<a NAME="E7:16"/><b>then </b>
<font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>;<br/>
<a NAME="E8:16"/><b>then </b>
<font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c6">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></i>;<br/>
<a NAME="E9:16"/><b>then </b>
<font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#T64" title="VECTSP_1:th.64">VECTSP_1:64</a></i>;<br/>
<a NAME="E10:16"/><b>then </b><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c6">a</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">b</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></i>;<br/>
<a NAME="E11:16"/>
<font color="Maroon" title="c7">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c5">S</font></span>)</span>
 
<b>by </b><i><a class="txt" href="ortsp_1.html#E1:16"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="rlvect_1.html#T10" title="RLVECT_1:th.10">RLVECT_1:10</a></i>;<br/>
<a NAME="E12:16"/><b>then </b>
<font color="Maroon" title="c7">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T16" title="RLVECT_1:th.16">RLVECT_1:16</a></i>;<br/>
<a NAME="E13:16"/><b>then </b>
<font color="Maroon" title="c7">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">b</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c6">a</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c6">a</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D6" title="RLVECT_1:def.6">RLVECT_1:def 6</a></i>;<br/>
<a NAME="E14:16"/><b>then </b>
<font color="Maroon" title="c7">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">b</font></span>)</span> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c6">a</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#D11" title="RLVECT_1:def.11">RLVECT_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E15:16"/>
<font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c7">b</font> <a href="symsp_1.html#R1" title="SYMSP_1:pred.1">_|_</a> <font color="Maroon" title="c6">a</font> <a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c7">b</font>
 <b>by </b><i><a class="txt" href="ortsp_1.html#E10:16"><i><font color="Green" title="E17">A2</font></i></a>, <a class="ref" href="ortsp_1.html#D2" target="_self" title="ORTSP_1:def.2">Def2</a></i>;<br/>


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