<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">V</font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">u</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">u1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">V</font>;<br/>









<a NAME="E1:22"/>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u</font>,<font color="Maroon">v</font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u1</font>,<font color="Maroon">v1</font></span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="diraf.html#K1">lambda</a> <span class="p1">(<span class="default"><a href="analoaf.html#K1">DirPar</a> <font color="Maroon">V</font></span>)</span> iff ( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u</font>,<font color="Maroon">v</font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u1</font>,<font color="Maroon">v1</font></span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="analoaf.html#K1">DirPar</a> <font color="Maroon">V</font> or <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u</font>,<font color="Maroon">v</font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">v1</font>,<font color="Maroon">u1</font></span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="analoaf.html#K1">DirPar</a> <font color="Maroon">V</font> ) )
 
<b>by </b><i><a class="ref" href="diraf.html#D1">DIRAF:def 1</a></i>;<br/>
<a NAME="E2:22"/><b>then </b>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u</font>,<font color="Maroon">v</font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u1</font>,<font color="Maroon">v1</font></span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="diraf.html#K1">lambda</a> <span class="p1">(<span class="default"><a href="analoaf.html#K1">DirPar</a> <font color="Maroon">V</font></span>)</span> iff ( <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">u1</font>,<font color="Maroon">v1</font> or <font color="Maroon">u</font>,<font color="Maroon">v</font> <a href="analoaf.html#R1">//</a> <font color="Maroon">v1</font>,<font color="Maroon">u1</font> ) )
 
<b>by </b><i><a class="ref" href="analoaf.html#T33">ANALOAF:33</a></i>;<br/>
<b>hence </b><a NAME="E3:22"/>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u</font>,<font color="Maroon">v</font></span><a href="domain_1.html#K1">]</a></span>,<span class="p2"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">u1</font>,<font color="Maroon">v1</font></span><a href="domain_1.html#K1">]</a></span></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a>  <a href="diraf.html#K1">lambda</a> <span class="p1">(<span class="default"><a href="analoaf.html#K1">DirPar</a> <font color="Maroon">V</font></span>)</span> iff  ex <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">a</font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> <a href="rlvect_1.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">v1</font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">u1</font></span>)</span> &amp; ( <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 or <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 ) ) )
 <b>by </b><i/>;<br/>


</div>
