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

<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">Y</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>  st <font color="Maroon" title="c1">AS</font> is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a> &amp; <font color="Olive" title="b1">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Olive" title="b2">Y</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  holds <br/><font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">Y</font></span><br/><b>let </b><font color="Maroon" title="c2">X</font>, <font color="Maroon" title="c3">Y</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">AS</font> is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a> &amp; <font color="Maroon" title="c2">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Maroon" title="c3">Y</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  implies <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Y</font> )</span><br/>





<b>assume </b><a NAME="E1:3"/>
( <font color="Maroon" title="c1">AS</font> is   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a> &amp; <font color="Maroon" title="c2">X</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  &amp; <font color="Maroon" title="c3">Y</font> <a href="aff_4.html#NR1" title="AFF_4:NR.1">is_plane</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Y</font></span><br/>

<a NAME="E2:3"/><b>then </b>
( <font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">AS</font> &amp; <font color="Maroon" title="c3">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">AS</font> )
 
<b>by </b><i><a class="ref" href="afproj.html#T2" target="_self" title="AFPROJ:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E3:3"/>
<font color="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
