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<b>let </b><font color="Maroon" title="c4">F</font> be   <a href="vectsp_1.html#NM2" title="VECTSP_1:NM.2">Field</a>;<br/><b>let </b><font color="Maroon" title="c5">S</font> be   <a href="symsp_1.html#NM1" title="SYMSP_1:NM.1">SymSp</a> of <font color="Maroon" title="c4">F</font>;<br/><b>let </b><font color="Maroon" title="c6">a</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="c7">0V</font> =  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c5">S</font>;<br/>
<b>set </b><font color="Maroon" title="c8">0F</font> =  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font>;<br/>
<div><i><font color="Green" title="E9">A1</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1"/>
<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>
 ;<br/><a NAME="E2:13_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</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="symsp_1.html#D2" target="_self" title="SYMSP_1:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E3:13_1"/>
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c5">S</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/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_2"/>
not <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>
 ;<br/><b>then consider </b><font color="Maroon" title="c9">m</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c4">F</font><b> such that </b><br/><a NAME="E3:13_2"/><i><font color="Green" title="E10">A2</font></i>: 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c5">S</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c6">a</font></span>)</span> <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="symsp_1.html#D2" target="_self" title="SYMSP_1:def.2">Def2</a></i>;<br/><a NAME="E4:13_2"/>
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c5">S</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">m</font> <a href="vectsp_1.html#K6" title="VECTSP_1:func.6">*</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span> <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="txt" href="symsp_1.html#E3:13_2"><i><font color="Green" title="E10">A2</font></i></a>, <a class="ref" href="symsp_1.html#D2" target="_self" title="SYMSP_1:def.2">Def2</a></i>;<br/><b>hence </b><a NAME="E5:13_2"/>
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c5">S</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/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:13"/>
 <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c5">S</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="txt" href="symsp_1.html#E1:13"><i><font color="Green" title="E9">A1</font></i></a></i>;<br/>


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