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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">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><a NAME="E1:34"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="anproj_1.html#K2" target="_self">Proportionality_as_EqRel_of</a> <font color="Maroon">V</font>
 ;<br/>

<a NAME="E2:34"/><b>then </b>
 ex <font color="Olive">u</font>, <font color="Olive">v</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">u</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">v</font> &amp;  <a href="anproj_1.html#R1" target="_self">are_Prop</a> <font color="Olive">u</font>,<font color="Olive">v</font> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font>, <font color="Maroon">y</font> = <font color="Maroon">y</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> ;<br/>
<a NAME="E4:34"/>
( <font color="Maroon">x</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> &amp; <font color="Maroon">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> )
 
;<br/>
<b>hence </b><a NAME="E5:34"/>
( <font color="Maroon">x</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> &amp; <font color="Maroon">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">V</font> )
 ;<br/>


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