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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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V2" title="CONMETR1:attr.2">satisfying_major_Scherungssatz</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:13"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V2" title="CONMETR1:attr.2">satisfying_major_Scherungssatz</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c6">a4</font>, <font color="Maroon" title="c7">b1</font>, <font color="Maroon" title="c8">b2</font>, <font color="Maroon" title="c9">b3</font>, <font color="Maroon" title="c10">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="Red">::  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> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b2">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c3">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="c5">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="c7">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="c9">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="c4">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="c6">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="c8">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="c10">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="c6">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="c4">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="c8">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="c10">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="c3">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="c5">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="c7">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="c9">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="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font> holds <br/><font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><span class="kw">let </span><font color="Maroon" title="c11">M</font>, <font color="Maroon" title="c12">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c11">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c12">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font> implies <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13_1"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
<font color="Maroon" title="c11">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E2:13_1"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
<font color="Maroon" title="c12">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E3:13_1"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E4:13_1"/><span class="lab"><font color="Green" title="E17">A5</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E5:13_1"/><span class="lab"><font color="Green" title="E18">A6</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E6:13_1"/><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E7:13_1"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E8:13_1"/><span class="lab"><font color="Green" title="E21">A9</font></span>: 
<font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E9:13_1"/><span class="lab"><font color="Green" title="E22">A10</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E10:13_1"/><span class="lab"><font color="Green" title="E23">A11</font></span>: 
<font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E11:13_1"/><span class="lab"><font color="Green" title="E24">A12</font></span>: 
<font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E12:13_1"/><span class="lab"><font color="Green" title="E25">A13</font></span>: 
<font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E13:13_1"/><span class="lab"><font color="Green" title="E26">A14</font></span>: 
not <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E14:13_1"/><span class="lab"><font color="Green" title="E27">A15</font></span>: 
not <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E15:13_1"/><span class="lab"><font color="Green" title="E28">A16</font></span>: 
not <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E16:13_1"/>
not <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font>
 <span class="kw">and </span><br/><a NAME="E17:13_1"/><span class="lab"><font color="Green" title="E29">A17</font></span>: 
not <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E18:13_1"/><span class="lab"><font color="Green" title="E30">A18</font></span>: 
not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E19:13_1"/><span class="lab"><font color="Green" title="E31">A19</font></span>: 
not <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E20:13_1"/>
not <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font>
 <span class="kw">and </span><br/><a NAME="E21:13_1"/><span class="lab"><font color="Green" title="E32">A20</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font>
 <span class="kw">and </span><br/><a NAME="E22:13_1"/><span class="lab"><font color="Green" title="E33">A21</font></span>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>
 <span class="kw">and </span><br/><a NAME="E23:13_1"/><span class="lab"><font color="Green" title="E34">A22</font></span>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><div><span class="lab"><font color="Green" title="E35">A23</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E36">A24</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">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="E3:13_1_1_1"/><span class="lab"><font color="Green" title="E37">A25</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">and </span><br/><a NAME="E4:13_1_1_1"/><span class="lab"><font color="Green" title="E38">A26</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 <span class="kw">and </span><br/><a NAME="E5:13_1_1_1"/><span class="lab"><font color="Green" title="E39">A27</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="translac.html#T2" title="TRANSLAC:th.2">TRANSLAC:2</a></span>;<br/><a NAME="E6:13_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c14">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="E8:13_1_1_1"/><span class="lab"><font color="Green" title="E40">A28</font></span>: 
<font color="Maroon" title="c14">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="E9:13_1_1_1"/><span class="lab"><font color="Green" title="E41">A29</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font>
 <span class="kw">and </span><br/><a NAME="E10:13_1_1_1"/><span class="lab"><font color="Green" title="E42">A30</font></span>: 
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font>
 <span class="kw">and </span><br/><a NAME="E11:13_1_1_1"/>
<font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><a NAME="E12:13_1_1_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</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="E13:13_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E14:13_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A31</font></span>: 
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><a NAME="E15:13_1_1_1"/><span class="lab"><font color="Green" title="E44">A32</font></span>: 
( <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> &amp; <font color="Maroon" title="c11">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E45">A33</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_1_1_1_1_1"/><span class="lab"><font color="Green" title="E46">A34</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">assume </span><a NAME="E2:13_1_1_1_1_1"/><span class="lab"><font color="Green" title="E47">A35</font></span>: 
( <font color="Maroon" title="c12">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y</font> or <font color="Maroon" title="c11">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:13_1_1_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E4:13_1_1_1"><span class="lab"><font color="Green" title="E38">A26</font></span></a>, <a class="txt" href="#E5:13_1_1_1"><span class="lab"><font color="Green" title="E39">A27</font></span></a>, <a class="txt" href="#E10:13_1_1_1"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E2:13_1_1_1_1_1"><span class="lab"><font color="Green" title="E47">A35</font></span></a>, <a class="txt" href="#E1:13_1_1_1_1_1"><span class="lab"><font color="Green" title="E46">A34</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:13_1_1_1_1"/>
(  not <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">M</font> or  not <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> or  not <font color="Maroon" title="c11">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E3:13_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E13:13_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="txt" href="#E1:13_1_1_1_1"><span class="lab"><font color="Green" title="E45">A33</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E16:13_1_1_1"/><span class="lab"><font color="Green" title="E45">A36</font></span>: 
 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/>(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Olive" title="b1">d1</font> &amp; <font color="Olive" title="b1">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:13_1_1_1_2"/>
not <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:13_1_1_1_2_1"/><span class="lab"><font color="Green" title="E46">A37</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1_1_1_2_1_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_1_1_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:13_1_1_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:13_1_1_1_2_1"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E4:13_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A38</font></span>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E5:13_1_1_1_2_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</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="E6:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E7:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E4:13_1_1_1_2_1"><span class="lab"><font color="Green" title="E47">A38</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E8:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E9:13_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="c13">d</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">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/>
<a NAME="E10:13_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="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E11:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">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/>
<a NAME="E12:13_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A39</font></span>: 
<font color="Maroon" title="c14">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c11">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E8:13_1_1_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E9:13_1_1_1"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="txt" href="#E10:13_1_1_1"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E1:13_1_1_1_2_1"><span class="lab"><font color="Green" title="E46">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></span>;<br/>
<a NAME="E13:13_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E14:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">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="E15:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E4:13_1_1_1_2_1"><span class="lab"><font color="Green" title="E47">A38</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E16:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E17:13_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="c13">d</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</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="E18:13_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="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E19:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">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="E20:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E8:13_1_1_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E9:13_1_1_1"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="txt" href="#E10:13_1_1_1"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E1:13_1_1_1_2_1"><span class="lab"><font color="Green" title="E46">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></span>;<br/>
<a NAME="E21:13_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_1_1_1_2_1"><span class="lab"><font color="Green" title="E48">A39</font></span></a>, <a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:13_1_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E13:13_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">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="E3:13_1_1_1_2"/><span class="lab"><font color="Green" title="E46">A40</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">and </span><br/><a NAME="E4:13_1_1_1_2"/><span class="lab"><font color="Green" title="E47">A41</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c15">d1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font> &amp; <font color="Maroon" title="c15">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )</span><br/>

<a NAME="E5:13_1_1_1_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1_1_1_2_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_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">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:13_1_1_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E6:13_1_1_1_2"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font> &amp; <font color="Maroon" title="c15">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_1_1_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E9:13_1_1_1"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="txt" href="#E10:13_1_1_1"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E3:13_1_1_1_2"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E4:13_1_1_1_2"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E17:13_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E18:13_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">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="E19:13_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A42</font></span>: 
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><a NAME="E20:13_1_1_1"/><span class="lab"><font color="Green" title="E47">A43</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1_1_1_3"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1_1"><span class="lab"><font color="Green" title="E37">A25</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:13_1_1_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">consider </span><font color="Maroon" title="c15">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="E22:13_1_1_1"/><span class="lab"><font color="Green" title="E48">A44</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">and </span><br/><a NAME="E23:13_1_1_1"/><span class="lab"><font color="Green" title="E49">A45</font></span>: 
<font color="Maroon" title="c15">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:13_1_1_1"><span class="lab"><font color="Green" title="E45">A36</font></span></a></span>;<br/><a NAME="E24:13_1_1_1"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13_1_1_1"><span class="lab"><font color="Green" title="E48">A44</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="E25:13_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E26:13_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E14:13_1_1_1"><span class="lab"><font color="Green" title="E43">A31</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><a NAME="E27:13_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A46</font></span>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">d1</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="txt" href="#E13:13_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E23:13_1"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="txt" href="#E8:13_1_1_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E9:13_1_1_1"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="txt" href="#E10:13_1_1_1"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E23:13_1_1_1"><span class="lab"><font color="Green" title="E49">A45</font></span></a>, <a class="txt" href="#E20:13_1_1_1"><span class="lab"><font color="Green" title="E47">A43</font></span></a>, <a class="txt" href="#E15:13_1_1_1"><span class="lab"><font color="Green" title="E44">A32</font></span></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></span>;<br/><a NAME="E28:13_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13_1_1_1"><span class="lab"><font color="Green" title="E48">A44</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E29:13_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">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="E30:13_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A47</font></span>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E19:13_1_1_1"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><a NAME="E31:13_1_1_1"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13_1"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E32:13_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">d1</font>,<font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E18:13_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="txt" href="#E8:13_1_1_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E9:13_1_1_1"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="txt" href="#E10:13_1_1_1"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E23:13_1_1_1"><span class="lab"><font color="Green" title="E49">A45</font></span></a>, <a class="txt" href="#E20:13_1_1_1"><span class="lab"><font color="Green" title="E47">A43</font></span></a>, <a class="txt" href="#E15:13_1_1_1"><span class="lab"><font color="Green" title="E44">A32</font></span></a>, <a class="txt" href="#E30:13_1_1_1"><span class="lab"><font color="Green" title="E51">A47</font></span></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></span>;<br/><span class="kw">hence </span><a NAME="E33:13_1_1_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="txt" href="#E13:13_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="txt" href="#E18:13_1"><span class="lab"><font color="Green" title="E30">A18</font></span></a>, <a class="txt" href="#E8:13_1_1_1"><span class="lab"><font color="Green" title="E40">A28</font></span></a>, <a class="txt" href="#E9:13_1_1_1"><span class="lab"><font color="Green" title="E41">A29</font></span></a>, <a class="txt" href="#E10:13_1_1_1"><span class="lab"><font color="Green" title="E42">A30</font></span></a>, <a class="txt" href="#E23:13_1_1_1"><span class="lab"><font color="Green" title="E49">A45</font></span></a>, <a class="txt" href="#E20:13_1_1_1"><span class="lab"><font color="Green" title="E47">A43</font></span></a>, <a class="txt" href="#E15:13_1_1_1"><span class="lab"><font color="Green" title="E44">A32</font></span></a>, <a class="txt" href="#E27:13_1_1_1"><span class="lab"><font color="Green" title="E50">A46</font></span></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:13_1_1"/><span class="lab"><font color="Green" title="E37">A48</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 <span class="kw">and </span><br/><a NAME="E3:13_1_1"/><span class="lab"><font color="Green" title="E38">A49</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_1_2"/><span class="lab"><font color="Green" title="E39">A50</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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><div><span class="lab"><font color="Green" title="E40">A51</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_1_2_1"/><span class="lab"><font color="Green" title="E41">A52</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E2:13_1_1_2_1"/><span class="lab"><font color="Green" title="E42">A53</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1_1_2_1_1"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_1_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:13_1"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="txt" href="#E1:13_1_1_2_1"><span class="lab"><font color="Green" title="E41">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="E3:13_1_1_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:13_1_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E3:13_1_1"><span class="lab"><font color="Green" title="E38">A49</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:13_1_1_2_1"/><span class="lab"><font color="Green" title="E43">A54</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1_1_2_1_2"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_1_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13_1"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="txt" href="#E1:13_1_1_2_1"><span class="lab"><font color="Green" title="E41">A52</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E3:13_1_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A55</font></span>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E4:13_1_1_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:13_1_1_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E17:13_1"><span class="lab"><font color="Green" title="E29">A17</font></span></a>, <a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E37">A48</font></span></a>, <a class="txt" href="#E3:13_1_1_2_1_2"><span class="lab"><font color="Green" title="E44">A55</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E4:13_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><a NAME="E5:13_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A56</font></span>: 
( <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font> or <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1"><span class="lab"><font color="Green" title="E38">A49</font></span></a>, <a class="txt" href="#E1:13_1_1_2"><span class="lab"><font color="Green" title="E39">A50</font></span></a></span>;<br/><a NAME="E6:13_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><a NAME="E7:13_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E37">A48</font></span></a>, <a class="txt" href="#E1:13_1_1_2"><span class="lab"><font color="Green" title="E39">A50</font></span></a>, <a class="txt" href="#E3:13_1_1_2_1"><span class="lab"><font color="Green" title="E43">A54</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_1_1_2_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1_1_2_1"><span class="lab"><font color="Green" title="E44">A56</font></span></a>, <a class="txt" href="#E2:13_1_1_2_1"><span class="lab"><font color="Green" title="E42">A53</font></span></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E41">A57</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_1_2_2"/><span class="lab"><font color="Green" title="E42">A58</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E2:13_1_1_2_2"/><span class="lab"><font color="Green" title="E43">A59</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1_1_2_2_1"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_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="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="txt" href="#E1:13_1_1_2_2"><span class="lab"><font color="Green" title="E42">A58</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="E3:13_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">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:13_1_1_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E37">A48</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:13_1_1_2_2"/><span class="lab"><font color="Green" title="E44">A60</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1_1_2_2_2"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_1_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13_1"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="txt" href="#E1:13_1_1_2_2"><span class="lab"><font color="Green" title="E42">A58</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E3:13_1_1_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/>
<a NAME="E4:13_1_1_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E5:13_1_1_2_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">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/>
<a NAME="E6:13_1_1_2_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">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:13_1_1_2_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E37">A48</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E4:13_1_1_2_2"/><span class="lab"><font color="Green" title="E45">A61</font></span>: 
<font color="Maroon" title="c6">a4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2_2_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1_1_2_2_3"/>
<font color="Maroon" title="c6">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_1_2_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:13_1"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="txt" href="#E1:13_1_1_2_2"><span class="lab"><font color="Green" title="E42">A58</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E3:13_1_1_2_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">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="E4:13_1_1_2_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:13_1_1_2_2_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E13:13_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E37">A48</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:13_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><a NAME="E6:13_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A62</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1"><span class="lab"><font color="Green" title="E38">A49</font></span></a>, <a class="txt" href="#E1:13_1_1_2"><span class="lab"><font color="Green" title="E39">A50</font></span></a>, <a class="txt" href="#E4:13_1_1_2_2"><span class="lab"><font color="Green" title="E45">A61</font></span></a></span>;<br/><a NAME="E7:13_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c8">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E9:13_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E10:13_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><a NAME="E8:13_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1_1"><span class="lab"><font color="Green" title="E38">A49</font></span></a>, <a class="txt" href="#E1:13_1_1_2"><span class="lab"><font color="Green" title="E39">A50</font></span></a>, <a class="txt" href="#E2:13_1_1_2_2"><span class="lab"><font color="Green" title="E43">A59</font></span></a></span>;<br/><a NAME="E9:13_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A63</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1_2_2"><span class="lab"><font color="Green" title="E42">A58</font></span></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></span>;<br/><a NAME="E10:13_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><a NAME="E11:13_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E37">A48</font></span></a>, <a class="txt" href="#E1:13_1_1_2"><span class="lab"><font color="Green" title="E39">A50</font></span></a>, <a class="txt" href="#E3:13_1_1_2_2"><span class="lab"><font color="Green" title="E44">A60</font></span></a></span>;<br/><a NAME="E12:13_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b4</font>,<font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="txt" href="#E6:13_1_1_2_2"><span class="lab"><font color="Green" title="E46">A62</font></span></a>, <a class="txt" href="#E9:13_1_1_2_2"><span class="lab"><font color="Green" title="E47">A63</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E13:13_1_1_2_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:13_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E6:13_1"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_1_1_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_1"><span class="lab"><font color="Green" title="E37">A48</font></span></a>, <a class="txt" href="#E1:13_1_1_2"><span class="lab"><font color="Green" title="E39">A50</font></span></a>, <a class="txt" href="#E2:13_1_1_2"><span class="lab"><font color="Green" title="E40">A51</font></span></a>, <a class="txt" href="#E3:13_1_1_2"><span class="lab"><font color="Green" title="E41">A57</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:13_1_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1_1"><span class="lab"><font color="Green" title="E36">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E36">A64</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_1_2_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E12:13_1"><span class="lab"><font color="Green" title="E25">A13</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E2:13_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A65</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c10">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/><span class="kw">assume </span><a NAME="E3:13_1_2_1"/><span class="lab"><font color="Green" title="E38">A66</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E4:13_1_2_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E5:13_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E13:13_1"><span class="lab"><font color="Green" title="E26">A14</font></span></a>, <a class="txt" href="#E23:13_1"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="txt" href="#E3:13_1_2_1"><span class="lab"><font color="Green" title="E38">A66</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E6:13_1_2_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E19:13_1"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="txt" href="#E21:13_1"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="txt" href="#E3:13_1_2_1"><span class="lab"><font color="Green" title="E38">A66</font></span></a>, <a class="txt" href="#E2:13_1_2_1"><span class="lab"><font color="Green" title="E37">A65</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E37">A67</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_1_2_2"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E7:13_1"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E8:13_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E2:13_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A68</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">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="E3:13_1_2_2"/><span class="lab"><font color="Green" title="E39">A69</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E4:13_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13_1"><span class="lab"><font color="Green" title="E32">A20</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E5:13_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_1"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="txt" href="#E14:13_1"><span class="lab"><font color="Green" title="E27">A15</font></span></a>, <a class="txt" href="#E22:13_1"><span class="lab"><font color="Green" title="E33">A21</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E6:13_1_2_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E11:13_1"><span class="lab"><font color="Green" title="E24">A12</font></span></a>, <a class="txt" href="#E15:13_1"><span class="lab"><font color="Green" title="E28">A16</font></span></a>, <a class="txt" href="#E19:13_1"><span class="lab"><font color="Green" title="E31">A19</font></span></a>, <a class="txt" href="#E23:13_1"><span class="lab"><font color="Green" title="E34">A22</font></span></a>, <a class="txt" href="#E3:13_1_2_2"><span class="lab"><font color="Green" title="E39">A69</font></span></a>, <a class="txt" href="#E2:13_1_2_2"><span class="lab"><font color="Green" title="E38">A68</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E3:13_1_2"/>
( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font> or <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><span class="kw">hence </span><a NAME="E4:13_1_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_1_2"><span class="lab"><font color="Green" title="E37">A67</font></span></a>, <a class="txt" href="#E1:13_1_2"><span class="lab"><font color="Green" title="E36">A64</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E26:13_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:13_1"><span class="lab"><font color="Green" title="E35">A23</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:13"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V2" title="CONMETR1:attr.2">satisfying_major_Scherungssatz</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr1.html#D2" target="_self" title="CONMETR1:def.2">Def2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
