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

<b>consider </b><font color="Maroon">S</font> being   <a href="analoaf.html#NM1">OAffinSpace</a>;<br/>
<a NAME="E2:51_1_1"/>
(  ex <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span> st <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> &amp; ( for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font>, <font color="Olive">t</font>, <font color="Olive">u</font>, <font color="Olive">w</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span> holds <br/> ( <font color="Olive">x</font>,<font color="Olive">y</font> <a href="analoaf.html#R2">//</a> <font color="Olive">y</font>,<font color="Olive">x</font> &amp; <font color="Olive">x</font>,<font color="Olive">y</font> <a href="analoaf.html#R2">//</a> <font color="Olive">z</font>,<font color="Olive">z</font> &amp; ( <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">y</font> &amp; <font color="Olive">x</font>,<font color="Olive">y</font> <a href="analoaf.html#R2">//</a> <font color="Olive">z</font>,<font color="Olive">t</font> &amp; <font color="Olive">x</font>,<font color="Olive">y</font> <a href="analoaf.html#R2">//</a> <font color="Olive">u</font>,<font color="Olive">w</font> implies <font color="Olive">z</font>,<font color="Olive">t</font> <a href="analoaf.html#R2">//</a> <font color="Olive">u</font>,<font color="Olive">w</font> ) &amp; ( <font color="Olive">x</font>,<font color="Olive">y</font> <a href="analoaf.html#R2">//</a> <font color="Olive">x</font>,<font color="Olive">z</font> implies <font color="Olive">y</font>,<font color="Olive">x</font> <a href="analoaf.html#R2">//</a> <font color="Olive">y</font>,<font color="Olive">z</font> ) ) ) &amp; not for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span> holds  <font color="Olive">x</font>,<font color="Olive">y</font> <a href="analoaf.html#R2">//</a> <font color="Olive">x</font>,<font color="Olive">z</font> &amp; ( for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span>  ex <font color="Olive">t</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span> st <br/>( <font color="Olive">x</font>,<font color="Olive">z</font> <a href="analoaf.html#R2">//</a> <font color="Olive">y</font>,<font color="Olive">t</font> &amp; <font color="Olive">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">t</font> ) ) &amp; ( for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span>  ex <font color="Olive">t</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span> st <br/>( <font color="Olive">x</font>,<font color="Olive">y</font> <a href="analoaf.html#R2">//</a> <font color="Olive">z</font>,<font color="Olive">t</font> &amp; <font color="Olive">x</font>,<font color="Olive">z</font> <a href="analoaf.html#R2">//</a> <font color="Olive">y</font>,<font color="Olive">t</font> ) ) &amp; ( for <font color="Olive">x</font>, <font color="Olive">y</font>, <font color="Olive">z</font>, <font color="Olive">t</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span>  st <font color="Olive">z</font>,<font color="Olive">x</font> <a href="analoaf.html#R2">//</a> <font color="Olive">x</font>,<font color="Olive">t</font> &amp; <font color="Olive">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">z</font> holds <br/> ex <font color="Olive">u</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font></span>)</span> st <br/>( <font color="Olive">y</font>,<font color="Olive">x</font> <a href="analoaf.html#R2">//</a> <font color="Olive">x</font>,<font color="Olive">u</font> &amp; <font color="Olive">y</font>,<font color="Olive">z</font> <a href="analoaf.html#R2">//</a> <font color="Olive">t</font>,<font color="Olive">u</font> ) ) )
 
<b>by </b><i/>;<br/>
<a NAME="E3:51_1_1"/><b>then </b>
( not  <a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font> is <a href="realset2.html#V3">trivial</a> &amp;  <a href="diraf.html#K2" target="_self">Lambda</a> <font color="Maroon">S</font> is <a href="diraf.html#V1" target="_self">AffinSpace-like</a> )
 
<b>by </b><i>, <a class="ref" href="realset2.html#D7">REALSET2:def 7</a></i>;<br/>
<b>hence </b><a NAME="E4:51_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a>  <a href="analoaf.html#L1">AffinStruct</a>  st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="analoaf.html#V1">strict</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="realset2.html#V3">trivial</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="diraf.html#V1" target="_self">AffinSpace-like</a> )
 ;<br/>


</div>
