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<span class="kw">consider </span><font color="Maroon" title="c1">SAS</font> being   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a><span class="kw"> such that </span><br/><a NAME="E2:2_1_1"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
( ( for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">a9</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c</font>, <font color="Olive" title="b7">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>  st not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b</font> &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">c</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">a9</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b7">c9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a9</font>,<font color="Olive" title="b7">c9</font> holds <br/><font color="Olive" title="b4">b</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b7">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">a9</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b9</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>  st not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> &amp; not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">c9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>  st <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">a3</font> &amp; <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b6">b3</font> &amp; <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b6">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b5">b2</font> holds <br/><font color="Olive" title="b3">a3</font>,<font color="Olive" title="b4">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b6">b3</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">SAS</font>  st not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> holds <br/> not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pardepap.html#T5" title="PARDEPAP:th.5">PARDEPAP:5</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c2">AS</font> = <font color="Maroon" title="c1">SAS</font> as  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="analoaf.html#L1" title="ANALOAF:struct.1">AffinStruct</a>  ;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c2">AS</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">AS</font> is  <a href="semi_af1.html#V1" title="SEMI_AF1:attr.1">Semi_Affine_Space-like</a> </span><br/>

<span class="kw">thus </span><a NAME="E4:2_1_1"/>
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 <font color="Maroon" title="c2">AS</font> holds  <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="semi_af1.html#D1" target="_self" title="SEMI_AF1:def.1">SEMI_AF1:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> holds  <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">r</font>, <font color="Olive" title="b6">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">r</font>,<font color="Olive" title="b6">s</font> holds <br/><font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">r</font>,<font color="Olive" title="b6">s</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp; not for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> holds  <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  ex <font color="Olive" title="b4">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">q</font> ) ) &amp; ( for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  ex <font color="Olive" title="b3">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> st <br/>for <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> holds <br/> ( <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">p</font> &amp;  ex <font color="Olive" title="b6">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> st <br/>( <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b</font> implies ( <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">d</font> &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b</font>,<font color="Olive" title="b6">d</font> ) ) ) ) &amp; ( for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">a9</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c</font>, <font color="Olive" title="b7">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b</font> &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">c</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">a9</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b7">c9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a9</font>,<font color="Olive" title="b7">c9</font> holds <br/><font color="Olive" title="b4">b</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b7">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">a9</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b9</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> &amp; not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">c9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">a3</font> &amp; <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b6">b3</font> &amp; <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b6">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b5">b2</font> holds <br/><font color="Olive" title="b3">a3</font>,<font color="Olive" title="b4">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b6">b3</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> holds <br/> not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) )</span><br/>

<span class="kw">thus </span><a NAME="E5:2_1_1"/>
( ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> holds  <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b3">c</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font>, <font color="Olive" title="b5">r</font>, <font color="Olive" title="b6">s</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">r</font>,<font color="Olive" title="b6">s</font> holds <br/><font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">r</font>,<font color="Olive" title="b6">s</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) &amp; not for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> holds  <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  ex <font color="Olive" title="b4">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> st <br/>( <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">q</font> ) ) &amp; ( for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  ex <font color="Olive" title="b3">p</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> st <br/>for <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> holds <br/> ( <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">p</font> &amp;  ex <font color="Olive" title="b6">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font> st <br/>( <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b</font> implies ( <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">d</font> &amp; <font color="Olive" title="b3">p</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b</font>,<font color="Olive" title="b6">d</font> ) ) ) ) &amp; ( for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">a9</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c</font>, <font color="Olive" title="b7">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b</font> &amp; not <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">c</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">a9</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">o</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b7">c9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a9</font>,<font color="Olive" title="b7">c9</font> holds <br/><font color="Olive" title="b4">b</font>,<font color="Olive" title="b6">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b7">c9</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">a9</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b9</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">c9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> &amp; not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">c</font>,<font color="Olive" title="b6">c9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b4">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b9</font>,<font color="Olive" title="b6">c9</font> ) &amp; ( for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b2">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b3">a3</font> &amp; <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b6">b3</font> &amp; <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b6">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b5">b2</font> holds <br/><font color="Olive" title="b3">a3</font>,<font color="Olive" title="b4">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b6">b3</font> ) &amp; ( for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">AS</font>  st not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> holds <br/> not <font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:2_1_1"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a>, <a class="ref" href="pardepap.html#T6" title="PARDEPAP:th.6">PARDEPAP:6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
