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<b>let </b><font color="Maroon" title="c1">AFP</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</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">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">b</font>, <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</font>, <font color="Olive" title="b7">p'</font>, <font color="Olive" title="b8">q</font>, <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">AFP</font>  st not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">p</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b5">x</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b2">a</font>,<font color="Olive" title="b6">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">p</font>,<font color="Olive" title="b7">p'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">p</font>,<font color="Olive" title="b8">q</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">o</font>,<font color="Olive" title="b3">p</font>,<font color="Olive" title="b9">q'</font> &amp; <font color="Olive" title="b3">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b8">q</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">x</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b8">q</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">x</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b</font>,<font color="Olive" title="b7">p'</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b8">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b</font>,<font color="Olive" title="b9">q'</font> &amp; <font color="Olive" title="b5">x</font>,<font color="Olive" title="b3">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">y</font>,<font color="Olive" title="b7">p'</font> &amp; <font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a>  holds <br/><font color="Olive" title="b5">x</font>,<font color="Olive" title="b8">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">y</font>,<font color="Olive" title="b9">q'</font></span><br/><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">p</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font>, <font color="Maroon" title="c8">p'</font>, <font color="Maroon" title="c9">q</font>, <font color="Maroon" title="c10">q'</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">x</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c8">p'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c9">q</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c10">q'</font> &amp; <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">q</font> &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">q</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c8">p'</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c10">q'</font> &amp; <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c8">p'</font> &amp; <font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a>  implies <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c10">q'</font> )</span><br/>



















<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green" title="E6">A1</font></i>: 
( not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">x</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">y</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c8">p'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c9">q</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c10">q'</font> )
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green" title="E7">A2</font></i>: 
( <font color="Maroon" title="c4">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">q</font> &amp; <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">q</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x</font> )
 <b>and </b><br/><a NAME="E3:5"/><i><font color="Green" title="E8">A3</font></i>: 
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c8">p'</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c10">q'</font> &amp; <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c8">p'</font> )
 <b>and </b><br/><a NAME="E4:5"/><i><font color="Green" title="E9">A4</font></i>: 
<font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR4" title="AFF_2:NR.4">satisfies_DES</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c10">q'</font></span><br/>

<a NAME="E5:5"/><i><font color="Green" title="E10">A5</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">p</font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><b> such that </b><br/><a NAME="E7:5"/><i><font color="Green" title="E11">A6</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c11">d</font> &amp; <font color="Maroon" title="c11">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c11">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">p</font> )
 <b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E2:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="translac.html#T2" title="TRANSLAC:th.2">TRANSLAC:2</a></i>;<br/>
<b>set </b><font color="Maroon" title="c12">K</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>;<br/>
<b>set </b><font color="Maroon" title="c13">A</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>;<br/>
<b>set </b><font color="Maroon" title="c14">B'</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>;<br/>
<a NAME="E8:5"/><i><font color="Green" title="E12">A7</font></i>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c6">x</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="c6">x</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c4">p</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="c6">x</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c11">d</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="c6">x</font>,<font color="Maroon" title="c4">p</font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E7:5"><i><font color="Green" title="E11">A6</font></i></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></i>;<br/>
<a NAME="E9:5"/><i><font color="Green" title="E13">A8</font></i>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c2">o</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="c2">o</font>,<font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c3">a</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="c2">o</font>,<font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c6">x</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="c2">o</font>,<font color="Maroon" title="c3">a</font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E5:5"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></i>;<br/>
<a NAME="E10:5"/><i><font color="Green" title="E14">A9</font></i>: 
(  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c2">o</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="c2">o</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c4">p</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="c2">o</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c9">q</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="c2">o</font>,<font color="Maroon" title="c4">p</font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E5:5"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="aff_1.html#T26" title="AFF_1:th.26">AFF_1:26</a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c15">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AFP</font><b> such that </b><br/><a NAME="E12:5"/><i><font color="Green" title="E15">A10</font></i>: 
( <font color="Maroon" title="c7">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">M</font> &amp;  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c15">M</font> )
 <b>by </b><i><a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="aff_1.html#T63" title="AFF_1:th.63">AFF_1:63</a></i>;<br/>
<a NAME="E13:5"/><i><font color="Green" title="E16">A11</font></i>: 
<font color="Maroon" title="c15">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a> 
 
<b>by </b><i><a class="txt" href="homothet.html#E12:5"><i><font color="Green" title="E15">A10</font></i></a>, <a class="ref" href="aff_1.html#T50" title="AFF_1:th.50">AFF_1:50</a></i>;<br/>
<a NAME="E14:5"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c15">M</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c15">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:5_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E12:5"><i><font color="Green" title="E15">A10</font></i></a>, <a class="ref" href="aff_1.html#T57" title="AFF_1:th.57">AFF_1:57</a></i>;<br/>
<a NAME="E3:5_1"/><b>then </b>
<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c2">o</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T48" title="AFF_1:th.48">AFF_1:48</a></i>;<br/>
<a NAME="E4:5_1"/><b>then </b>
<font color="Maroon" title="c2">o</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="c6">x</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></i>;<br/>
<a NAME="E5:5_1"/><b>then </b>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E2:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E9:5"><i><font color="Green" title="E13">A8</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E6:5_1"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</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>then consider </b><font color="Maroon" title="c16">d'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><b> such that </b><br/><a NAME="E16:5"/><i><font color="Green" title="E17">A12</font></i>: 
( <font color="Maroon" title="c16">d'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">M</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c16">d'</font> )
 <b>by </b><i><a class="txt" href="homothet.html#E13:5"><i><font color="Green" title="E16">A11</font></i></a>, <a class="ref" href="aff_1.html#T73" title="AFF_1:th.73">AFF_1:73</a></i>;<br/>
<a NAME="E17:5"/><i><font color="Green" title="E18">A13</font></i>: 
<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c6">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">d'</font>,<font color="Maroon" title="c7">y</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E12:5"><i><font color="Green" title="E15">A10</font></i></a>, <a class="txt" href="homothet.html#E16:5"><i><font color="Green" title="E17">A12</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E18:5"/><i><font color="Green" title="E19">A14</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c9">q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<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"> contradiction</span><br/>

<a NAME="E2:5_2"/><b>then </b>
<font color="Maroon" title="c9">q</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="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<a NAME="E3:5_2"/><b>then </b>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E2:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="homothet.html#E9:5"><i><font color="Green" title="E13">A8</font></i></a>, <a class="txt" href="homothet.html#E10:5"><i><font color="Green" title="E14">A9</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E4:5_2"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E10:5"><i><font color="Green" title="E14">A9</font></i></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</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>
<a NAME="E19:5"/><i><font color="Green" title="E20">A15</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c11">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c11">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:5_3"/><b>then </b>
<font color="Maroon" title="c11">d</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="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<a NAME="E3:5_3"/><b>then </b>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E7:5"><i><font color="Green" title="E11">A6</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E9:5"><i><font color="Green" title="E13">A8</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E4:5_3"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</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>
<a NAME="E20:5"/><i><font color="Green" title="E21">A16</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c9">q</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">d</font>,<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"> contradiction</span><br/>

<a NAME="E2:5_4"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c4">p</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c2">o</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c11">d</font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<a NAME="E3:5_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c11">d</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E2:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<a NAME="E4:5_4"/><b>then </b>
<font color="Maroon" title="c11">d</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="c2">o</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<a NAME="E5:5_4"/><b>then </b>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E7:5"><i><font color="Green" title="E11">A6</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E10:5"><i><font color="Green" title="E14">A9</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<a NAME="E6:5_4"/><b>then </b>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E2:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E9:5"><i><font color="Green" title="E13">A8</font></i></a>, <a class="txt" href="homothet.html#E10:5"><i><font color="Green" title="E14">A9</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E7:5_4"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E10:5"><i><font color="Green" title="E14">A9</font></i></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</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>
<a NAME="E21:5"/><i><font color="Green" title="E22">A17</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c6">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_5"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c6">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:5_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c11">d</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:5_5"/><b>then </b>
<font color="Maroon" title="c11">d</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="c2">o</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E2:5"><i><font color="Green" title="E7">A2</font></i></a>, <a class="txt" href="homothet.html#E9:5"><i><font color="Green" title="E13">A8</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:5_5"/><b>then </b>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E7:5"><i><font color="Green" title="E11">A6</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E9:5"><i><font color="Green" title="E13">A8</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E5:5_5"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</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>
<a NAME="E22:5"/><i><font color="Green" title="E23">A18</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c11">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:5_6"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c11">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:5_6"/><b>then </b>
<font color="Maroon" title="c11">d</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="c2">o</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<a NAME="E3:5_6"/><b>then </b>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E7:5"><i><font color="Green" title="E11">A6</font></i></a>, <a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E10:5"><i><font color="Green" title="E14">A9</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>;<br/>
<b>hence </b><a NAME="E4:5_6"/>
contradiction
 <b>by </b><i><a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E10:5"><i><font color="Green" title="E14">A9</font></i></a>, <a class="txt" href="homothet.html#E21:5"><i><font color="Green" title="E22">A17</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</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>
<a NAME="E23:5"/><i><font color="Green" title="E24">A19</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E24:5"/><i><font color="Green" title="E25">A20</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c10">q'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_7"><b>proof </b></a><div class="add">

<a NAME="E1:5_7"/>
( <font color="Maroon" title="c9">q</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="c2">o</font>,<font color="Maroon" title="c4">p</font> &amp; <font color="Maroon" title="c10">q'</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="c2">o</font>,<font color="Maroon" title="c4">p</font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:5_7"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">q</font>,<font color="Maroon" title="c10">q'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E10:5"><i><font color="Green" title="E14">A9</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</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>
<a NAME="E25:5"/><i><font color="Green" title="E26">A21</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_8"><b>proof </b></a><div class="add">

<a NAME="E1:5_8"/>
( <font color="Maroon" title="c6">x</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="c2">o</font>,<font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c7">y</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="c2">o</font>,<font color="Maroon" title="c3">a</font> )
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="aff_1.html#D2" title="AFF_1:def.2">AFF_1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E2:5_8"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>
 <b>by </b><i><a class="txt" href="homothet.html#E9:5"><i><font color="Green" title="E13">A8</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</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>
<a NAME="E26:5"/><i><font color="Green" title="E27">A22</font></i>: 
<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c11">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">p'</font>,<font color="Maroon" title="c16">d'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_9"><b>proof </b></a><div class="add">

<a NAME="E1:5_9"/>
<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></i>;<br/>
<a NAME="E2:5_9"/><b>then </b>
<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">p</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c15">M</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E12:5"><i><font color="Green" title="E15">A10</font></i></a>, <a class="ref" href="aff_1.html#T57" title="AFF_1:th.57">AFF_1:57</a></i>;<br/>
<a NAME="E3:5_9"/><b>then </b>
<font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c8">p'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c15">M</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E3:5"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></i>;<br/>
<a NAME="E4:5_9"/><b>then </b>
<font color="Maroon" title="c8">p'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c15">M</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E12:5"><i><font color="Green" title="E15">A10</font></i></a>, <a class="txt" href="homothet.html#E13:5"><i><font color="Green" title="E16">A11</font></i></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></i>;<br/>
<b>hence </b><a NAME="E5:5_9"/>
<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c11">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">p'</font>,<font color="Maroon" title="c16">d'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E8:5"><i><font color="Green" title="E12">A7</font></i></a>, <a class="txt" href="homothet.html#E12:5"><i><font color="Green" title="E15">A10</font></i></a>, <a class="txt" href="homothet.html#E16:5"><i><font color="Green" title="E17">A12</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</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>
<a NAME="E27:5"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c11">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c16">d'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_10"><b>proof </b></a><div class="add">

<a NAME="E1:5_10"/>
<font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">p'</font>,<font color="Maroon" title="c5">b</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E3:5"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E2:5_10"/>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c11">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c16">d'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E4:5"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="homothet.html#E16:5"><i><font color="Green" title="E17">A12</font></i></a>, <a class="txt" href="homothet.html#E22:5"><i><font color="Green" title="E23">A18</font></i></a>, <a class="txt" href="homothet.html#E23:5"><i><font color="Green" title="E24">A19</font></i></a>, <a class="txt" href="homothet.html#E26:5"><i><font color="Green" title="E27">A22</font></i></a>, <a class="txt" href="homothet.html#E1"><i><font color="Green" title="E1">Lm1</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>
<a NAME="E28:5"/><b>then </b>
<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">d'</font>,<font color="Maroon" title="c10">q'</font>
 
<b>by </b><i><a class="txt" href="homothet.html#E1:5"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="homothet.html#E3:5"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="homothet.html#E4:5"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="homothet.html#E16:5"><i><font color="Green" title="E17">A12</font></i></a>, <a class="txt" href="homothet.html#E18:5"><i><font color="Green" title="E19">A14</font></i></a>, <a class="txt" href="homothet.html#E19:5"><i><font color="Green" title="E20">A15</font></i></a>, <a class="txt" href="homothet.html#E24:5"><i><font color="Green" title="E25">A20</font></i></a>, <a class="txt" href="homothet.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E29:5"/>
<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c9">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c10">q'</font>
 <b>by </b><i><a class="txt" href="homothet.html#E4:5"><i><font color="Green" title="E9">A4</font></i></a>, <a class="txt" href="homothet.html#E16:5"><i><font color="Green" title="E17">A12</font></i></a>, <a class="txt" href="homothet.html#E17:5"><i><font color="Green" title="E18">A13</font></i></a>, <a class="txt" href="homothet.html#E20:5"><i><font color="Green" title="E21">A16</font></i></a>, <a class="txt" href="homothet.html#E21:5"><i><font color="Green" title="E22">A17</font></i></a>, <a class="txt" href="homothet.html#E24:5"><i><font color="Green" title="E25">A20</font></i></a>, <a class="txt" href="homothet.html#E25:5"><i><font color="Green" title="E26">A21</font></i></a>, <a class="txt" href="homothet.html#E1"><i><font color="Green" title="E1">Lm1</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>
