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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V1" title="CONMETR1:attr.1">satisfying_minor_Scherungssatz</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:12"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V1" title="CONMETR1:attr.1">satisfying_minor_Scherungssatz</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c5">a4</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c9">b4</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font>, <font color="Olive" title="b2">N</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c2">a1</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">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c8">b3</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">a2</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">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp;  not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp;  not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp;  not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp;  not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> holds <br/><font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c11">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp;  not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp;  not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp;  not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp;  not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp;  not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp;  not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp;  not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp;  not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> implies <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:12_1"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<font color="Maroon" title="c10">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E2:12_1"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E3:12_1"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E4:12_1"/><span class="lab"><font color="Green" title="E16">A5</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E5:12_1"/><span class="lab"><font color="Green" title="E17">A6</font></span>: 
<font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E6:12_1"/><span class="lab"><font color="Green" title="E18">A7</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E7:12_1"/><span class="lab"><font color="Green" title="E19">A8</font></span>: 
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E8:12_1"/><span class="lab"><font color="Green" title="E20">A9</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E9:12_1"/><span class="lab"><font color="Green" title="E21">A10</font></span>: 
<font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E10:12_1"/><span class="lab"><font color="Green" title="E22">A11</font></span>: 
 not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E11:12_1"/><span class="lab"><font color="Green" title="E23">A12</font></span>: 
 not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E12:12_1"/><span class="lab"><font color="Green" title="E24">A13</font></span>: 
 not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E13:12_1"/>
 not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E14:12_1"/><span class="lab"><font color="Green" title="E25">A14</font></span>: 
 not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E15:12_1"/><span class="lab"><font color="Green" title="E26">A15</font></span>: 
 not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E16:12_1"/><span class="lab"><font color="Green" title="E27">A16</font></span>: 
 not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E17:12_1"/>
 not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E18:12_1"/><span class="lab"><font color="Green" title="E28">A17</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">and </span><br/><a NAME="E19:12_1"/><span class="lab"><font color="Green" title="E29">A18</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E20:12_1"/><span class="lab"><font color="Green" title="E30">A19</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E21:12_1"/><span class="lab"><font color="Green" title="E31">A20</font></span>: 
<font color="Maroon" title="c10">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="aff_1.html#T36" title="AFF_1:th.36">AFF_1:36</a></span>;<br/><a NAME="E22:12_1"/><span class="lab"><font color="Green" title="E32">A21</font></span>: 
<font color="Maroon" title="c11">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="ref" href="aff_1.html#T36" title="AFF_1:th.36">AFF_1:36</a></span>;<br/><div><span class="lab"><font color="Green" title="E33">A22</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:12_1_1"/><span class="lab"><font color="Green" title="E34">A23</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a3</font>
 <span class="kw">and </span><br/><a NAME="E2:12_1_1"/><span class="lab"><font color="Green" title="E35">A24</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><span class="lab"><font color="Green" title="E36">A25</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:12_1_1_1"/>
 ex <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:12_1_1_1"/><span class="lab"><font color="Green" title="E37">A26</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">and </span><br/><a NAME="E4:12_1_1_1"/><span class="lab"><font color="Green" title="E38">A27</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 <span class="kw">and </span><br/><a NAME="E5:12_1_1_1"/><span class="lab"><font color="Green" title="E39">A28</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="translac.html#T1" title="TRANSLAC:th.1">TRANSLAC:1</a></span>;<br/><a NAME="E6:12_1_1_1"/><span class="lab"><font color="Green" title="E40">A29</font></span>: 
 ex <font color="Olive" title="b1">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b1">Y</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">M</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c13">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:12_1_1_1_1"/><span class="lab"><font color="Green" title="E41">A30</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font>
 <span class="kw">and </span><br/><a NAME="E3:12_1_1_1_1"/><span class="lab"><font color="Green" title="E42">A31</font></span>: 
<font color="Maroon" title="c10">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c13">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c13">Y</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c13">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font> &amp; <font color="Maroon" title="c13">Y</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">M</font> )</span><br/>

<span class="kw">thus </span><a NAME="E4:12_1_1_1_1"/>
( <font color="Maroon" title="c13">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font> &amp; <font color="Maroon" title="c13">Y</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">M</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_1_1_1"><span class="lab"><font color="Green" title="E41">A30</font></span></a>, <a class="txt" href="#E3:12_1_1_1_1"><span class="lab"><font color="Green" title="E42">A31</font></span></a>, <a class="ref" href="aff_1.html#T36" title="AFF_1:th.36">AFF_1:36</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E7:12_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_1_1"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E8:12_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E9:12_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A32</font></span>: 
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E10:12_1_1_1"/><span class="lab"><font color="Green" title="E42">A33</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:12_1"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c13">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E12:12_1_1_1"/><span class="lab"><font color="Green" title="E43">A34</font></span>: 
<font color="Maroon" title="c13">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E13:12_1_1_1"/><span class="lab"><font color="Green" title="E44">A35</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font>
 <span class="kw">and </span><br/><a NAME="E14:12_1_1_1"/><span class="lab"><font color="Green" title="E45">A36</font></span>: 
<font color="Maroon" title="c13">Y</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1_1_1"><span class="lab"><font color="Green" title="E40">A29</font></span></a></span>;<br/><a NAME="E15:12_1_1_1"/><span class="lab"><font color="Green" title="E46">A37</font></span>: 
<font color="Maroon" title="c13">Y</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E14:12_1_1_1"><span class="lab"><font color="Green" title="E45">A36</font></span></a>, <a class="ref" href="aff_1.html#T44" title="AFF_1:th.44">AFF_1:44</a></span>;<br/><a NAME="E16:12_1_1_1"/><span class="lab"><font color="Green" title="E47">A38</font></span>: 
( <font color="Maroon" title="c11">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c11">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Y</font> &amp; <font color="Maroon" title="c13">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">M</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1_2"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E48">A39</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:12_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c2">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_1_1"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E2:12_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A40</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E3:12_1_1_1_2_1"/>
<font color="Maroon" title="c11">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">Y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:12_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E12:12_1_1_1"><span class="lab"><font color="Green" title="E43">A34</font></span></a>, <a class="txt" href="#E13:12_1_1_1"><span class="lab"><font color="Green" title="E44">A35</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E5:12_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:12_1_1_1"><span class="lab"><font color="Green" title="E39">A28</font></span></a>, <a class="txt" href="#E2:12_1_1_1_2_1"><span class="lab"><font color="Green" title="E49">A40</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E6:12_1_1_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c2">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:12_1_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E14:12_1"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E22:12_1"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E2:12_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E49">A41</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:12_1_1_1_2_2"/>
<font color="Maroon" title="c13">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:12_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A42</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E13:12_1_1_1"><span class="lab"><font color="Green" title="E44">A35</font></span></a>, <a class="txt" href="#E14:12_1_1_1"><span class="lab"><font color="Green" title="E45">A36</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E3:12_1_1_1_2_2"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_1_1"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E4:12_1_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1_1_1"><span class="lab"><font color="Green" title="E38">A27</font></span></a>, <a class="txt" href="#E2:12_1_1_1_2_2"><span class="lab"><font color="Green" title="E50">A42</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E5:12_1_1_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:12_1_1_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E1:12_1_1"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:12_1_1_1_2"/>
(  not <font color="Maroon" title="c11">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">M</font> or  not <font color="Maroon" title="c11">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Y</font> or  not <font color="Maroon" title="c13">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">M</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:12_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E1:12_1_1_1_2"><span class="lab"><font color="Green" title="E48">A39</font></span></a>, <a class="txt" href="#E2:12_1_1_1_2"><span class="lab"><font color="Green" title="E49">A41</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E17:12_1_1_1"/><span class="lab"><font color="Green" title="E48">A43</font></span>: 
<font color="Maroon" title="c13">Y</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c13">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:12_1_1_1"><span class="lab"><font color="Green" title="E43">A34</font></span></a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E18:12_1_1_1"/>
 ex <font color="Olive" title="b1">d1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font> &amp; <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Olive" title="b1">d1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c14">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:12_1_1_1_3"/><span class="lab"><font color="Green" title="E49">A44</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:12_1_1_1_3"/><span class="lab"><font color="Green" title="E50">A45</font></span>: 
<font color="Maroon" title="c14">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:12_1_1_1"><span class="lab"><font color="Green" title="E43">A34</font></span></a>, <a class="ref" href="aff_1.html#T20" title="AFF_1:th.20">AFF_1:20</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:12_1_1_1_3"/><span class="lab"><font color="Green" title="E51">A46</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c15">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:12_1_1_1_3"/><span class="lab"><font color="Green" title="E52">A47</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/>
<a NAME="E7:12_1_1_1_3"/>
 not <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c15">e2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:12_1_1_1_3_1"/>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c15">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:12_1_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:12_1_1_1_3"><span class="lab"><font color="Green" title="E51">A46</font></span></a>, <a class="txt" href="#E6:12_1_1_1_3"><span class="lab"><font color="Green" title="E52">A47</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E3:12_1_1_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A48</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:12_1_1_1"><span class="lab"><font color="Green" title="E44">A35</font></span></a>, <a class="txt" href="#E17:12_1_1_1"><span class="lab"><font color="Green" title="E48">A43</font></span></a>, <a class="txt" href="#E2:12_1_1_1_3"><span class="lab"><font color="Green" title="E49">A44</font></span></a>, <a class="txt" href="#E3:12_1_1_1_3"><span class="lab"><font color="Green" title="E50">A45</font></span></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/>
<a NAME="E4:12_1_1_1_3_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E14:12_1_1_1"><span class="lab"><font color="Green" title="E45">A36</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/>
<a NAME="E5:12_1_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:12_1_1_1"><span class="lab"><font color="Green" title="E43">A34</font></span></a>, <a class="txt" href="#E3:12_1_1_1_3_1"><span class="lab"><font color="Green" title="E53">A48</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/>
<a NAME="E6:12_1_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E7:12_1_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E12:12_1"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E8:12_1_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E9:12_1_1_1_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:12_1_1_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E1:12_1_1"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">d1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E9:12_1_1_1_3"/><span class="lab"><font color="Green" title="E53">A49</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e1</font>,<font color="Maroon" title="c16">d1</font>
 <span class="kw">and </span><br/><a NAME="E10:12_1_1_1_3"/><span class="lab"><font color="Green" title="E54">A50</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c15">e2</font>,<font color="Maroon" title="c16">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" title="AFF_1:th.60">AFF_1:60</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c16">d1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c16">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font> &amp; <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c16">d1</font> )</span><br/>

<a NAME="E11:12_1_1_1_3"/>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c15">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c16">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:12_1_1_1_3"><span class="lab"><font color="Green" title="E54">A50</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:12_1_1_1_3"/>
( <font color="Maroon" title="c16">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font> &amp; <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c16">d1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:12_1_1_1"><span class="lab"><font color="Green" title="E43">A34</font></span></a>, <a class="txt" href="#E13:12_1_1_1"><span class="lab"><font color="Green" title="E44">A35</font></span></a>, <a class="txt" href="#E2:12_1_1_1_3"><span class="lab"><font color="Green" title="E49">A44</font></span></a>, <a class="txt" href="#E3:12_1_1_1_3"><span class="lab"><font color="Green" title="E50">A45</font></span></a>, <a class="txt" href="#E5:12_1_1_1_3"><span class="lab"><font color="Green" title="E51">A46</font></span></a>, <a class="txt" href="#E6:12_1_1_1_3"><span class="lab"><font color="Green" title="E52">A47</font></span></a>, <a class="txt" href="#E9:12_1_1_1_3"><span class="lab"><font color="Green" title="E53">A49</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">d1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E20:12_1_1_1"/><span class="lab"><font color="Green" title="E49">A51</font></span>: 
<font color="Maroon" title="c14">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Y</font>
 <span class="kw">and </span><br/><a NAME="E21:12_1_1_1"/><span class="lab"><font color="Green" title="E50">A52</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c14">d1</font>
 ;<br/><a NAME="E22:12_1_1_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_1_1"><span class="lab"><font color="Green" title="E37">A26</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E23:12_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E24:12_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E25:12_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E26:12_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c14">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E12:12_1"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E21:12_1_1_1"><span class="lab"><font color="Green" title="E50">A52</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E27:12_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A53</font></span>: 
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E9:12_1"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E20:12_1"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E22:12_1"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E12:12_1_1_1"><span class="lab"><font color="Green" title="E43">A34</font></span></a>, <a class="txt" href="#E13:12_1_1_1"><span class="lab"><font color="Green" title="E44">A35</font></span></a>, <a class="txt" href="#E14:12_1_1_1"><span class="lab"><font color="Green" title="E45">A36</font></span></a>, <a class="txt" href="#E20:12_1_1_1"><span class="lab"><font color="Green" title="E49">A51</font></span></a>, <a class="txt" href="#E16:12_1_1_1"><span class="lab"><font color="Green" title="E47">A38</font></span></a>, <a class="ref" href="aff_2.html#D11" title="AFF_2:def.11">AFF_2:def 11</a></span>;<br/><a NAME="E28:12_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c14">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:12_1_1_1"><span class="lab"><font color="Green" title="E50">A52</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E29:12_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c14">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E30:12_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c14">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E31:12_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A54</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c14">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E12:12_1"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E9:12_1_1_1"><span class="lab"><font color="Green" title="E41">A32</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E32:12_1_1_1"/>
<font color="Maroon" title="c11">N</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c13">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E14:12_1_1_1"><span class="lab"><font color="Green" title="E45">A36</font></span></a>, <a class="ref" href="aff_1.html#T44" title="AFF_1:th.44">AFF_1:44</a></span>;<br/><a NAME="E33:12_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E8:12_1"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E22:12_1"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E12:12_1_1_1"><span class="lab"><font color="Green" title="E43">A34</font></span></a>, <a class="txt" href="#E13:12_1_1_1"><span class="lab"><font color="Green" title="E44">A35</font></span></a>, <a class="txt" href="#E20:12_1_1_1"><span class="lab"><font color="Green" title="E49">A51</font></span></a>, <a class="txt" href="#E16:12_1_1_1"><span class="lab"><font color="Green" title="E47">A38</font></span></a>, <a class="txt" href="#E31:12_1_1_1"><span class="lab"><font color="Green" title="E52">A54</font></span></a>, <a class="txt" href="#E10:12_1_1_1"><span class="lab"><font color="Green" title="E42">A33</font></span></a>, <a class="ref" href="aff_2.html#D11" title="AFF_2:def.11">AFF_2:def 11</a></span>;<br/><span class="kw">hence </span><a NAME="E34:12_1_1_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E9:12_1"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="txt" href="#E22:12_1"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="txt" href="#E12:12_1_1_1"><span class="lab"><font color="Green" title="E43">A34</font></span></a>, <a class="txt" href="#E13:12_1_1_1"><span class="lab"><font color="Green" title="E44">A35</font></span></a>, <a class="txt" href="#E14:12_1_1_1"><span class="lab"><font color="Green" title="E45">A36</font></span></a>, <a class="txt" href="#E20:12_1_1_1"><span class="lab"><font color="Green" title="E49">A51</font></span></a>, <a class="txt" href="#E16:12_1_1_1"><span class="lab"><font color="Green" title="E47">A38</font></span></a>, <a class="txt" href="#E27:12_1_1_1"><span class="lab"><font color="Green" title="E51">A53</font></span></a>, <a class="txt" href="#E15:12_1_1_1"><span class="lab"><font color="Green" title="E46">A37</font></span></a>, <a class="ref" href="aff_2.html#D11" title="AFF_2:def.11">AFF_2:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:12_1_1_2"/><span class="lab"><font color="Green" title="E37">A55</font></span>: 
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  holds <br/>(  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> or  not <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> or  not <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> or  not <font color="Olive" title="b2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><span class="lab"><font color="Green" title="E38">A56</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:12_1_1_2_1"/><span class="lab"><font color="Green" title="E39">A57</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:12_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A58</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:12_1"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E3:12_1_1_2_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="txt" href="#E1:12_1_1_2_1"><span class="lab"><font color="Green" title="E39">A57</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E4:12_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A59</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E5:12_1_1_2_1"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E8:12_1"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/><a NAME="E6:12_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E4:12_1_1_2_1"><span class="lab"><font color="Green" title="E41">A59</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></span>;<br/><a NAME="E7:12_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:12_1"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E8:12_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A60</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E9:12_1_1_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/><a NAME="E10:12_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A61</font></span>: 
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E15:12_1"><span class="lab"><font color="Green" title="E26">A15</font></span></a>, <a class="txt" href="#E8:12_1_1_2_1"><span class="lab"><font color="Green" title="E42">A60</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></span>;<br/><a NAME="E11:12_1_1_2_1"/>
<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c9">b4</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E9:12_1"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/><a NAME="E12:12_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E2:12_1_1_2_1"><span class="lab"><font color="Green" title="E40">A58</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></span>;<br/><span class="kw">hence </span><a NAME="E13:12_1_1_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:12_1_1_2_1"><span class="lab"><font color="Green" title="E43">A61</font></span></a>, <a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E39">A62</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:12_1_1_2_2"/><span class="lab"><font color="Green" title="E40">A63</font></span>: 
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><span class="lab"><font color="Green" title="E41">A64</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:12_1_1_2_2_1"/><span class="lab"><font color="Green" title="E42">A65</font></span>: 
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:12_1_1_2_2_1_1"/>
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:12_1_1_2_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:12_1"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E3:12_1_1_2_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A66</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E4:12_1_1_2_2_1_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:12_1_1_2_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E14:12_1"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E1:12_1_1"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E1:12_1_1_2_2"><span class="lab"><font color="Green" title="E40">A63</font></span></a>, <a class="txt" href="#E3:12_1_1_2_2_1_1"><span class="lab"><font color="Green" title="E43">A66</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:12_1_1_2_2_1"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E9:12_1"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="txt" href="#E22:12_1"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E3:12_1_1_2_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E4:12_1_1_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A67</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E1:12_1_1_2"><span class="lab"><font color="Green" title="E37">A55</font></span></a>, <a class="txt" href="#E1:12_1_1_2_2_1"><span class="lab"><font color="Green" title="E42">A65</font></span></a></span>;<br/><span class="kw">assume </span><a NAME="E5:12_1_1_2_2_1"/><span class="lab"><font color="Green" title="E44">A68</font></span>: 
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E6:12_1_1_2_2_1"/><span class="lab"><font color="Green" title="E45">A69</font></span>: 
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2_2_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:12_1_1_2_2_1_2"/>
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:12_1_1_2_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A70</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:12_1"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:12_1_1_2_2_1_2"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E8:12_1"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:12_1_1_2_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E2:12_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E5:12_1_1_2_2_1"><span class="lab"><font color="Green" title="E44">A68</font></span></a>, <a class="txt" href="#E2:12_1_1_2_2_1_2"><span class="lab"><font color="Green" title="E46">A70</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E7:12_1_1_2_2_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E8:12_1_1_2_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E9:12_1_1_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A71</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_1"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E1:12_1_1_2"><span class="lab"><font color="Green" title="E37">A55</font></span></a>, <a class="txt" href="#E6:12_1_1_2_2_1"><span class="lab"><font color="Green" title="E45">A69</font></span></a></span>;<br/><a NAME="E10:12_1_1_2_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_1_2_2"><span class="lab"><font color="Green" title="E40">A63</font></span></a>, <a class="txt" href="#E5:12_1_1_2_2_1"><span class="lab"><font color="Green" title="E44">A68</font></span></a>, <a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/><a NAME="E11:12_1_1_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E12:12_1"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><span class="kw">hence </span><a NAME="E12:12_1_1_2_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:12_1_1_2_2_1"><span class="lab"><font color="Green" title="E46">A71</font></span></a>, <a class="txt" href="#E4:12_1_1_2_2_1"><span class="lab"><font color="Green" title="E43">A67</font></span></a>, <a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E42">A72</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_1_2_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:12_1_1_2_2_2"/>
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:12_1_1_2_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A73</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E3:12_1_1_2_2_2"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/><span class="kw">hence </span><a NAME="E4:12_1_1_2_2_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E14:12_1"><span class="lab"><font color="Green" title="E25">A14</font></span></a>, <a class="txt" href="#E2:12_1_1_2"><span class="lab"><font color="Green" title="E38">A56</font></span></a>, <a class="txt" href="#E2:12_1_1_2_2_2"><span class="lab"><font color="Green" title="E43">A73</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:12_1_1_2_2"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:12_1"><span class="lab"><font color="Green" title="E18">A7</font></span></a>, <a class="txt" href="#E7:12_1"><span class="lab"><font color="Green" title="E19">A8</font></span></a>, <a class="txt" href="#E8:12_1"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E22:12_1"><span class="lab"><font color="Green" title="E32">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E5:12_1_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:12_1_1_2_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1_1"><span class="lab"><font color="Green" title="E35">A24</font></span></a>, <a class="txt" href="#E1:12_1_1_2"><span class="lab"><font color="Green" title="E37">A55</font></span></a>, <a class="txt" href="#E2:12_1_1_2_2"><span class="lab"><font color="Green" title="E41">A64</font></span></a>, <a class="txt" href="#E3:12_1_1_2_2"><span class="lab"><font color="Green" title="E42">A72</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:12_1_1_2"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E21:12_1"><span class="lab"><font color="Green" title="E31">A20</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E5:12_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:12_1_1_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_1"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="txt" href="#E1:12_1_1_2"><span class="lab"><font color="Green" title="E37">A55</font></span></a>, <a class="txt" href="#E2:12_1_1_2"><span class="lab"><font color="Green" title="E38">A56</font></span></a>, <a class="txt" href="#E3:12_1_1_2"><span class="lab"><font color="Green" title="E39">A62</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:12_1_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1_1"><span class="lab"><font color="Green" title="E36">A25</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E34">A74</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:12_1_2_1"/><span class="lab"><font color="Green" title="E35">A75</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:12_1_2_1"/>
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:12_1_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_2_1"><span class="lab"><font color="Green" title="E35">A75</font></span></a>, <a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/>
<a NAME="E2:12_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:12_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E4:12_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E5:12_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:12_1"><span class="lab"><font color="Green" title="E15">A4</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E18:12_1"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E6:12_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E7:12_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A76</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E8:12_1_2_1_1"/><span class="lab"><font color="Green" title="E37">A77</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E9:12_1_2_1_1"/>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">b3</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c11">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E5:12_1"><span class="lab"><font color="Green" title="E17">A6</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:12_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:12_1"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E16:12_1"><span class="lab"><font color="Green" title="E27">A16</font></span></a>, <a class="txt" href="#E8:12_1_2_1_1"><span class="lab"><font color="Green" title="E37">A77</font></span></a>, <a class="txt" href="#E7:12_1_2_1_1"><span class="lab"><font color="Green" title="E36">A76</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:12_1_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:12_1"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="txt" href="#E1:12_1_2_1"><span class="lab"><font color="Green" title="E35">A75</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E35">A78</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="12_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:12_1_2_2"/><span class="lab"><font color="Green" title="E36">A79</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:12_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/><a NAME="E3:12_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E4:12_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E10:12_1"><span class="lab"><font color="Green" title="E22">A11</font></span></a>, <a class="txt" href="#E20:12_1"><span class="lab"><font color="Green" title="E30">A19</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E5:12_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E6:12_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:12_1"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E11:12_1"><span class="lab"><font color="Green" title="E23">A12</font></span></a>, <a class="txt" href="#E19:12_1"><span class="lab"><font color="Green" title="E29">A18</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E7:12_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E8:12_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A80</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E9:12_1_2_2"/>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c9">b4</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E8:12_1"><span class="lab"><font color="Green" title="E20">A9</font></span></a>, <a class="txt" href="#E9:12_1"><span class="lab"><font color="Green" title="E21">A10</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a></span>;<br/><span class="kw">hence </span><a NAME="E10:12_1_2_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:12_1"><span class="lab"><font color="Green" title="E16">A5</font></span></a>, <a class="txt" href="#E12:12_1"><span class="lab"><font color="Green" title="E24">A13</font></span></a>, <a class="txt" href="#E18:12_1"><span class="lab"><font color="Green" title="E28">A17</font></span></a>, <a class="txt" href="#E1:12_1_2_2"><span class="lab"><font color="Green" title="E36">A79</font></span></a>, <a class="txt" href="#E8:12_1_2_2"><span class="lab"><font color="Green" title="E37">A80</font></span></a>, <a class="ref" href="aff_1.html#T46" title="AFF_1:th.46">AFF_1:46</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E3:12_1_2"/>
( <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a3</font> or <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><span class="kw">hence </span><a NAME="E4:12_1_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_2"><span class="lab"><font color="Green" title="E34">A74</font></span></a>, <a class="txt" href="#E2:12_1_2"><span class="lab"><font color="Green" title="E35">A78</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E25:12_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:12_1"><span class="lab"><font color="Green" title="E33">A22</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:12"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V1" title="CONMETR1:attr.1">satisfying_minor_Scherungssatz</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr1.html#D1" target="_self" title="CONMETR1:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
