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

<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">y</font>, <font color="Olive" title="b2">w</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><br/>  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Olive" title="b2">w</font>,<font color="Olive" title="b1">y</font>)</span>)</span>  ex <font color="Olive" title="b5">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Olive" title="b2">w</font>,<font color="Olive" title="b1">y</font>)</span>)</span> st <font color="Olive" title="b5">p</font> <a href="geomtrap.html#K9" title="GEOMTRAP:func.9">#</a> <font color="Olive" title="b3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">b</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">w</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">y</font>)</span>)</span>  ex <font color="Olive" title="b3">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">y</font>)</span>)</span> st <font color="Olive" title="b3">p</font> <a href="geomtrap.html#K9" title="GEOMTRAP:func.9">#</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">b</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">y</font>)</span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">y</font>)</span>)</span> st <font color="Olive" title="b1">p</font> <a href="geomtrap.html#K9" title="GEOMTRAP:func.9">#</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font></span><br/>









<span class="kw">reconsider </span><font color="Maroon" title="c6">u</font> = <font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c7">v</font> = <font color="Maroon" title="c5">b</font> as   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">u1</font> being   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E3:87"/><span class="lab"><font color="Green" title="E76">A1</font></span>: 
<font color="Maroon" title="c6">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#T5" target="_self" title="GEOMTRAP:th.5">Th7</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">p</font> = <font color="Maroon" title="c8">u1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">y</font>)</span>)</span> ;<br/>
<a NAME="E5:87"/>
<font color="Maroon" title="c9">p</font> <a href="geomtrap.html#K9" title="GEOMTRAP:func.9">#</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">u</font> <a href="geomtrap.html#K1" title="GEOMTRAP:func.1">#</a> <font color="Maroon" title="c8">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="geomtrap.html#D8" target="_self" title="GEOMTRAP:def.8">Def8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:87"/>
 ex <font color="Olive" title="b1">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="geomtrap.html#K7" title="GEOMTRAP:func.7">DTrSpace</a> (<font color="Maroon" title="c1">V</font>,<font color="Maroon" title="c3">w</font>,<font color="Maroon" title="c2">y</font>)</span>)</span> st <font color="Olive" title="b1">p</font> <a href="geomtrap.html#K9" title="GEOMTRAP:func.9">#</a> <font color="Maroon" title="c4">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E76">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
