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<b>consider </b><font color="Maroon">SAS</font> being   <a href="diraf.html#NM2">AffinPlane</a><b> such that </b><br/><a NAME="E2:2_1_1"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">o</font>, <font color="Olive">a</font>, <font color="Olive">a'</font>, <font color="Olive">b</font>, <font color="Olive">b'</font>, <font color="Olive">c</font>, <font color="Olive">c'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>  st not <font color="Olive">o</font>,<font color="Olive">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">b</font> &amp; not <font color="Olive">o</font>,<font color="Olive">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">c</font> &amp; <font color="Olive">o</font>,<font color="Olive">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">a'</font> &amp; <font color="Olive">o</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">b'</font> &amp; <font color="Olive">o</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">c'</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font>
 <b>and </b><br/><a NAME="E3:2_1_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">a'</font>, <font color="Olive">b</font>, <font color="Olive">b'</font>, <font color="Olive">c</font>, <font color="Olive">c'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>  st not <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a</font>,<font color="Olive">b</font> &amp; not <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a</font>,<font color="Olive">c</font> &amp; <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">c'</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font>
 <b>and </b><br/><a NAME="E4:2_1_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">a1</font>, <font color="Olive">a2</font>, <font color="Olive">a3</font>, <font color="Olive">b1</font>, <font color="Olive">b2</font>, <font color="Olive">b3</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>  st <font color="Olive">a1</font>,<font color="Olive">a2</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a1</font>,<font color="Olive">a3</font> &amp; <font color="Olive">b1</font>,<font color="Olive">b2</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b1</font>,<font color="Olive">b3</font> &amp; <font color="Olive">a1</font>,<font color="Olive">b2</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a2</font>,<font color="Olive">b1</font> &amp; <font color="Olive">a2</font>,<font color="Olive">b3</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a3</font>,<font color="Olive">b2</font> holds <br/><font color="Olive">a3</font>,<font color="Olive">b1</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a1</font>,<font color="Olive">b3</font>
 <b>and </b><br/><a NAME="E5:2_1_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">SAS</font>  st not <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a</font>,<font color="Olive">c</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">d</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">d</font> holds <br/> not <font color="Olive">a</font>,<font color="Olive">d</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">c</font>
 <b>by </b><i><a class="ref" href="pardepap.html#T5">PARDEPAP:5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">AS</font> = <font color="Maroon">SAS</font> as  non <a href="struct_0.html#V3">empty</a>  <a href="analoaf.html#L1">AffinStruct</a>  ;<br/>
<b>take </b>
<font color="Maroon">AS</font>
;<br/>

<b>thus </b><a NAME="E7:2_1_1"/>
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> holds  <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">a</font>
 <b>by </b><i><a class="ref" href="diraf.html#T47">DIRAF:47</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="semi_af1.html#D1" target="_self">SEMI_AF1:def 1</a><br/>

<b>thus </b><a NAME="E8:2_1_1"/>
( ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> holds  <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">c</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">p</font>, <font color="Olive">q</font>, <font color="Olive">r</font>, <font color="Olive">s</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  st <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">p</font>,<font color="Olive">q</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">r</font>,<font color="Olive">s</font> holds <br/><font color="Olive">p</font>,<font color="Olive">q</font> <a href="analoaf.html#R2">//</a> <font color="Olive">r</font>,<font color="Olive">s</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  st <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a</font>,<font color="Olive">c</font> holds <br/><font color="Olive">b</font>,<font color="Olive">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">c</font> ) &amp; not for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> holds  <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a</font>,<font color="Olive">c</font> &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  ex <font color="Olive">q</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>( <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">p</font>,<font color="Olive">q</font> &amp; <font color="Olive">a</font>,<font color="Olive">p</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">q</font> ) ) &amp; ( for <font color="Olive">o</font>, <font color="Olive">a</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  ex <font color="Olive">p</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>for <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> holds <br/> ( <font color="Olive">o</font>,<font color="Olive">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">p</font> &amp;  ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font> st <br/>( <font color="Olive">o</font>,<font color="Olive">p</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">b</font> implies ( <font color="Olive">o</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">d</font> &amp; <font color="Olive">p</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">d</font> ) ) ) ) &amp; ( for <font color="Olive">o</font>, <font color="Olive">a</font>, <font color="Olive">a'</font>, <font color="Olive">b</font>, <font color="Olive">b'</font>, <font color="Olive">c</font>, <font color="Olive">c'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  st not <font color="Olive">o</font>,<font color="Olive">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">b</font> &amp; not <font color="Olive">o</font>,<font color="Olive">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">c</font> &amp; <font color="Olive">o</font>,<font color="Olive">a</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">a'</font> &amp; <font color="Olive">o</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">b'</font> &amp; <font color="Olive">o</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">o</font>,<font color="Olive">c'</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">a'</font>, <font color="Olive">b</font>, <font color="Olive">b'</font>, <font color="Olive">c</font>, <font color="Olive">c'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  st not <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a</font>,<font color="Olive">b</font> &amp; not <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a</font>,<font color="Olive">c</font> &amp; <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">a'</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">c'</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">b'</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a'</font>,<font color="Olive">c'</font> holds <br/><font color="Olive">b</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b'</font>,<font color="Olive">c'</font> ) &amp; ( for <font color="Olive">a1</font>, <font color="Olive">a2</font>, <font color="Olive">a3</font>, <font color="Olive">b1</font>, <font color="Olive">b2</font>, <font color="Olive">b3</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  st <font color="Olive">a1</font>,<font color="Olive">a2</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a1</font>,<font color="Olive">a3</font> &amp; <font color="Olive">b1</font>,<font color="Olive">b2</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b1</font>,<font color="Olive">b3</font> &amp; <font color="Olive">a1</font>,<font color="Olive">b2</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a2</font>,<font color="Olive">b1</font> &amp; <font color="Olive">a2</font>,<font color="Olive">b3</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a3</font>,<font color="Olive">b2</font> holds <br/><font color="Olive">a3</font>,<font color="Olive">b1</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a1</font>,<font color="Olive">b3</font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">AS</font>  st not <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">a</font>,<font color="Olive">c</font> &amp; <font color="Olive">a</font>,<font color="Olive">b</font> <a href="analoaf.html#R2">//</a> <font color="Olive">c</font>,<font color="Olive">d</font> &amp; <font color="Olive">a</font>,<font color="Olive">c</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">d</font> holds <br/> not <font color="Olive">a</font>,<font color="Olive">d</font> <a href="analoaf.html#R2">//</a> <font color="Olive">b</font>,<font color="Olive">c</font> ) )
 <b>by </b><i>, , , , <a class="ref" href="diraf.html#T47">DIRAF:47</a>, <a class="ref" href="pardepap.html#T6">PARDEPAP:6</a></i>;<br/>


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