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<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:5_1"/>
 <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">p</font>, <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 ;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">b</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:5_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">a</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font></span>)</span> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 )
 <b>by </b><i/>;<br/><a NAME="E4:5_1"/>
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T23">RLVECT_1:23</a></i>;<br/><b>hence </b><a NAME="E5:5_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="rlvect_1.html#T24">RLVECT_1:24</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:5"/>
(  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Maroon">p</font>, <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> iff <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">V</font> )
 ;<br/>


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