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<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">a</font>, <font color="Olive" title="b2">b</font>, <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 <font color="Maroon" title="c1">AS</font><br/> for <font color="Olive" title="b5">M</font>, <font color="Olive" title="b6">N</font>, <font color="Olive" title="b7">P</font>, <font color="Olive" title="b8">Q</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="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b5">M</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b5">M</font> &amp; <font color="Olive" title="b3">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b6">N</font> &amp; <font color="Olive" title="b4">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b6">N</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">P</font> &amp; <font color="Olive" title="b3">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">P</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">Q</font> &amp; <font color="Olive" title="b4">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">Q</font> &amp; <font color="Olive" title="b5">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">N</font> &amp; <font color="Olive" title="b5">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b6">N</font> &amp; <font color="Olive" title="b7">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b8">Q</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; not <font color="Olive" title="b7">P</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b8">Q</font> holds <br/> ex <font color="Olive" title="b9">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b9">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">P</font> &amp; <font color="Olive" title="b9">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">Q</font> )</span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <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 <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"> for <font color="Olive" title="b1">M</font>, <font color="Olive" title="b2">N</font>, <font color="Olive" title="b3">P</font>, <font color="Olive" title="b4">Q</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="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c5">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">P</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">P</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">Q</font> &amp; <font color="Maroon" title="c5">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">Q</font> &amp; <font color="Olive" title="b1">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b1">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b3">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Olive" title="b4">Q</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; not <font color="Olive" title="b3">P</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Olive" title="b4">Q</font> holds <br/> ex <font color="Olive" title="b5">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b5">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">P</font> &amp; <font color="Olive" title="b5">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">Q</font> )</span><br/><b>let </b><font color="Maroon" title="c6">M</font>, <font color="Maroon" title="c7">N</font>, <font color="Maroon" title="c8">P</font>, <font color="Maroon" title="c9">Q</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="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">M</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">M</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">N</font> &amp; <font color="Maroon" title="c5">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">N</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> &amp; <font color="Maroon" title="c5">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> &amp; <font color="Maroon" title="c6">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">N</font> &amp; <font color="Maroon" title="c6">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c7">N</font> &amp; <font color="Maroon" title="c8">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c9">Q</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; not <font color="Maroon" title="c8">P</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c9">Q</font> implies  ex <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> ) )</span><br/>

















<b>assume </b><b>that </b><br/><a NAME="E1:23"/><i><font color="Green" title="E18">A1</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">M</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">M</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">N</font> &amp; <font color="Maroon" title="c5">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">N</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> &amp; <font color="Maroon" title="c5">b'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> )
 <b>and </b><br/><a NAME="E2:23"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c6">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">N</font>
 <b>and </b><br/><a NAME="E3:23"/><i><font color="Green" title="E20">A3</font></i>: 
<font color="Maroon" title="c6">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c7">N</font>
 <b>and </b><br/><a NAME="E4:23"/><i><font color="Green" title="E21">A4</font></i>: 
( <font color="Maroon" title="c8">P</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c9">Q</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">P</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c9">Q</font> or  ex <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> ) )</span><br/>

<a NAME="E5:23"/><i><font color="Green" title="E22">A5</font></i>: 
( <font color="Maroon" title="c6">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c7">N</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 
<b>by </b><i><a class="txt" href="aff_4.html#E3:23"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="aff_1.html#T50" title="AFF_1:th.50">AFF_1:50</a></i>;<br/>
<a NAME="E6:23"/><i><font color="Green" title="E23">A6</font></i>: 
( <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a'</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b'</font> )
 
<b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E2:23"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="aff_4.html#E3:23"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1"/><i><font color="Green" title="E24">A7</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">P</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c9">Q</font> or  ex <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> ) )</span><br/><b>consider </b><font color="Maroon" title="c10">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E3:23_1"/><i><font color="Green" title="E25">A8</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c10">c</font>
 <b>and </b><br/><a NAME="E4:23_1"/><i><font color="Green" title="E26">A9</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">c</font>
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E5:23_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c7">N</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E3:23"><i><font color="Green" title="E20">A3</font></i></a>, <a class="txt" href="aff_4.html#E5:23"><i><font color="Green" title="E22">A5</font></i></a>, <a class="ref" href="aff_1.html#T57" title="AFF_1:th.57">AFF_1:57</a>, <a class="ref" href="aff_1.html#T66" title="AFF_1:th.66">AFF_1:66</a></i>;<br/><a NAME="E6:23_1"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c10">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c7">N</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23_1"><i><font color="Green" title="E24">A7</font></i></a>, <a class="txt" href="aff_4.html#E3:23_1"><i><font color="Green" title="E25">A8</font></i></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></i>;<br/><a NAME="E7:23_1"/><b>then </b><i><font color="Green" title="E27">A10</font></i>: 
<font color="Maroon" title="c10">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c7">N</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E5:23"><i><font color="Green" title="E22">A5</font></i></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></i>;<br/><a NAME="E8:23_1"/><b>then </b><i><font color="Green" title="E28">A11</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">c</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E2:23"><i><font color="Green" title="E19">A2</font></i></a>, <a class="txt" href="aff_4.html#E3:23"><i><font color="Green" title="E20">A3</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>;<br/><b>set </b><font color="Maroon" title="c11">D</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">c</font>;<br/><a NAME="E9:23_1"/><i><font color="Green" title="E29">A12</font></i>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">c</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a> 
 <b>by </b><i><a class="txt" href="aff_4.html#E8:23_1"><i><font color="Green" title="E28">A11</font></i></a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></i>;<br/><a NAME="E10:23_1"/><i><font color="Green" title="E30">A13</font></i>: 
( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">c</font> &amp; <font color="Maroon" title="c10">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">c</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:23_1_1"/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c10">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">Q</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> )</span><br/><a NAME="E2:23_1_1"/><b>then </b><i><font color="Green" title="E31">A14</font></i>: 
<font color="Maroon" title="c10">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:23"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="aff_4.html#E6:23"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="aff_4.html#E9:23_1"><i><font color="Green" title="E29">A12</font></i></a>, <a class="txt" href="aff_4.html#E10:23_1"><i><font color="Green" title="E30">A13</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/><a NAME="E3:23_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c4">a'</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E5:23"><i><font color="Green" title="E22">A5</font></i></a>, <a class="txt" href="aff_4.html#E7:23_1"><i><font color="Green" title="E27">A10</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>then consider </b><font color="Maroon" title="c12">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E5:23_1_1"/><i><font color="Green" title="E32">A15</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c12">q</font>
 <b>and </b><br/><a NAME="E6:23_1_1"/><i><font color="Green" title="E33">A16</font></i>: 
<font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c12">q</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E2:23_1_1"><i><font color="Green" title="E31">A14</font></i></a>, <a class="ref" href="aff_4.html#T1" target="_self" title="AFF_4:th.1">Th1</a></i>;<br/><a NAME="E7:23_1_1"/><i><font color="Green" title="E34">A17</font></i>: 
<font color="Maroon" title="c12">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:23"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="aff_4.html#E6:23"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="aff_4.html#E5:23_1_1"><i><font color="Green" title="E32">A15</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E8:23_1_1"/>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E4:23_1"><i><font color="Green" title="E26">A9</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E9:23_1_1"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c12">q</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E8:23_1"><i><font color="Green" title="E28">A11</font></i></a>, <a class="txt" href="aff_4.html#E6:23_1_1"><i><font color="Green" title="E33">A16</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E10:23_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c12">q</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E11:23_1_1"/><b>then </b>
<font color="Maroon" title="c12">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font>
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:23"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="aff_4.html#E6:23"><i><font color="Green" title="E23">A6</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E12:23_1_1"/>
 ex <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> )
 <b>by </b><i><a class="txt" href="aff_4.html#E7:23_1_1"><i><font color="Green" title="E34">A17</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E12:23_1"/>
( <font color="Maroon" title="c8">P</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c9">Q</font> or  ex <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> ) )
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a>, <a class="txt" href="aff_4.html#E4:23"><i><font color="Green" title="E21">A4</font></i></a>, <a class="txt" href="aff_4.html#E6:23"><i><font color="Green" title="E23">A6</font></i></a>, <a class="txt" href="aff_4.html#E4:23_1"><i><font color="Green" title="E26">A9</font></i></a>, <a class="txt" href="aff_4.html#E8:23_1"><i><font color="Green" title="E28">A11</font></i></a>, <a class="txt" href="aff_4.html#E10:23_1"><i><font color="Green" title="E30">A13</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:23"/>
( <font color="Maroon" title="c8">P</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c9">Q</font> or  ex <font color="Olive" title="b1">q</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font> st <br/>( <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c8">P</font> &amp; <font color="Olive" title="b1">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">Q</font> ) )
 <b>by </b><i><a class="txt" href="aff_4.html#E1:23"><i><font color="Green" title="E18">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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