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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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a>  iff <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a>  )</span><br/>

<a NAME="E1:14"/><span class="lab"><font color="Green" title="E7">A1</font></span>: 
( <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a>  )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1"/><span class="lab"><font color="Green" title="E8">A2</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Y</font>, <font color="Olive" title="b2">Z</font>, <font color="Olive" title="b3">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b4">o</font>, <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font>, <font color="Olive" title="b7">c</font>, <font color="Olive" title="b8">a1</font>, <font color="Olive" title="b9">b1</font>, <font color="Olive" title="b10">c1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">a</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">b</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">c</font> &amp; <font color="Olive" title="b5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b8">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Olive" title="b9">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Olive" title="b7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b10">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b1">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b2">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b3">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b1">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Olive" title="b1">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">a1</font>,<font color="Olive" title="b9">b1</font> &amp; <font color="Olive" title="b5">a</font>,<font color="Olive" title="b7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">a1</font>,<font color="Olive" title="b10">c1</font> holds <br/><font color="Olive" title="b6">b</font>,<font color="Olive" title="b7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">b1</font>,<font color="Olive" title="b10">c1</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">Y</font>, <font color="Maroon" title="c3">Z</font>, <font color="Maroon" title="c4">M</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">c1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Olive" title="b5">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Olive" title="b6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b7">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c2">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c3">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c4">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b6">b1</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b7">c1</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">c1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">o</font>, <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c9">a1</font>, <font color="Maroon" title="c10">b1</font>, <font color="Maroon" title="c11">c1</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font> &amp; <font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c9">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c11">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c2">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c3">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c4">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">Z</font> &amp; <font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">M</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font> implies <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14_1_1"/><span class="lab"><font color="Green" title="E9">A3</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">and </span><br/><a NAME="E2:14_1_1"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1"/><span class="lab"><font color="Green" title="E11">A5</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">and </span><br/><a NAME="E4:14_1_1"/><span class="lab"><font color="Green" title="E12">A6</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a</font>
 <span class="kw">and </span><br/><a NAME="E5:14_1_1"/><span class="lab"><font color="Green" title="E13">A7</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1"/><span class="lab"><font color="Green" title="E14">A8</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 <span class="kw">and </span><br/><a NAME="E7:14_1_1"/><span class="lab"><font color="Green" title="E15">A9</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">and </span><br/><a NAME="E8:14_1_1"/><span class="lab"><font color="Green" title="E16">A10</font></span>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">and </span><br/><a NAME="E9:14_1_1"/><span class="lab"><font color="Green" title="E17">A11</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 <span class="kw">and </span><br/><a NAME="E10:14_1_1"/><span class="lab"><font color="Green" title="E18">A12</font></span>: 
<font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 <span class="kw">and </span><br/><a NAME="E11:14_1_1"/><span class="lab"><font color="Green" title="E19">A13</font></span>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">and </span><br/><a NAME="E12:14_1_1"/><span class="lab"><font color="Green" title="E20">A14</font></span>: 
<font color="Maroon" title="c11">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">and </span><br/><a NAME="E13:14_1_1"/><span class="lab"><font color="Green" title="E21">A15</font></span>: 
<font color="Maroon" title="c2">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="E14:14_1_1"/><span class="lab"><font color="Green" title="E22">A16</font></span>: 
<font color="Maroon" title="c3">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E15:14_1_1"/><span class="lab"><font color="Green" title="E23">A17</font></span>: 
<font color="Maroon" title="c4">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="E16:14_1_1"/><span class="lab"><font color="Green" title="E24">A18</font></span>: 
<font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">Z</font>
 <span class="kw">and </span><br/><a NAME="E17:14_1_1"/><span class="lab"><font color="Green" title="E25">A19</font></span>: 
<font color="Maroon" title="c2">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">and </span><br/><a NAME="E18:14_1_1"/><span class="lab"><font color="Green" title="E26">A20</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 <span class="kw">and </span><br/><a NAME="E19:14_1_1"/><span class="lab"><font color="Green" title="E27">A21</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font></span><br/><span class="kw">assume </span><a NAME="E20:14_1_1"/><span class="lab"><font color="Green" title="E28">A22</font></span>: 
 not <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div><span class="lab"><font color="Green" title="E29">A23</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Y</font>, <font color="Olive" title="b2">Z</font>, <font color="Olive" title="b3">M</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b4">o</font>, <font color="Olive" title="b5">a</font>, <font color="Olive" title="b6">b</font>, <font color="Olive" title="b7">c</font>, <font color="Olive" title="b8">a1</font>, <font color="Olive" title="b9">b1</font>, <font color="Olive" title="b10">c1</font>, <font color="Olive" title="b11">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a>  &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">a</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">b</font> &amp; <font color="Olive" title="b4">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b7">c</font> &amp; <font color="Olive" title="b5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b8">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Olive" title="b9">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Olive" title="b7">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b10">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b1">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b2">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b3">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Olive" title="b1">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">Z</font> &amp; <font color="Olive" title="b1">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">M</font> &amp; <font color="Olive" title="b5">a</font>,<font color="Olive" title="b6">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">a1</font>,<font color="Olive" title="b9">b1</font> &amp; <font color="Olive" title="b5">a</font>,<font color="Olive" title="b7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b8">a1</font>,<font color="Olive" title="b10">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b6">b</font>,<font color="Olive" title="b7">c</font>,<font color="Olive" title="b11">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b9">b1</font>,<font color="Olive" title="b10">c1</font>,<font color="Olive" title="b11">d</font> &amp;  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b5">a</font>,<font color="Olive" title="b8">a1</font>,<font color="Olive" title="b11">d</font> holds <br/><font color="Olive" title="b6">b</font>,<font color="Olive" title="b7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b9">b1</font>,<font color="Olive" title="b10">c1</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c12">Y</font>, <font color="Maroon" title="c13">Z</font>, <font color="Maroon" title="c14">M</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">o</font>, <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font>, <font color="Olive" title="b5">a1</font>, <font color="Olive" title="b6">b1</font>, <font color="Olive" title="b7">c1</font>, <font color="Olive" title="b8">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a>  &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b1">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">c</font> &amp; <font color="Olive" title="b2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Olive" title="b5">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Olive" title="b3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Olive" title="b6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Olive" title="b4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Olive" title="b7">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c12">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c13">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c14">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b6">b1</font> &amp; <font color="Olive" title="b2">a</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">a1</font>,<font color="Olive" title="b7">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>,<font color="Olive" title="b8">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">c1</font>,<font color="Olive" title="b8">d</font> &amp;  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b5">a1</font>,<font color="Olive" title="b8">d</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b1</font>,<font color="Olive" title="b7">c1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c15">o</font>, <font color="Maroon" title="c16">a</font>, <font color="Maroon" title="c17">b</font>, <font color="Maroon" title="c18">c</font>, <font color="Maroon" title="c19">a1</font>, <font color="Maroon" title="c20">b1</font>, <font color="Maroon" title="c21">c1</font>, <font color="Maroon" title="c22">d</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a>  &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">a</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c12">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c13">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c14">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c22">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c22">d</font> &amp;  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> implies <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )</span><br/><span class="kw">assume </span><a NAME="E1:14_1_1_1"/><span class="lab"><font color="Green" title="E30">A24</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">a</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> &amp; <font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c12">Y</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c13">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c14">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Z</font> &amp; <font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">M</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c22">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c22">d</font> &amp;  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> implies <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:14_1_1_1"/><span class="lab"><font color="Green" title="E31">A25</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1_1"/><span class="lab"><font color="Green" title="E32">A26</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font>
 <span class="kw">and </span><br/><a NAME="E4:14_1_1_1"/><span class="lab"><font color="Green" title="E33">A27</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font>
 <span class="kw">and </span><br/><a NAME="E5:14_1_1_1"/><span class="lab"><font color="Green" title="E34">A28</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">a</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_1"/><span class="lab"><font color="Green" title="E35">A29</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font>
 <span class="kw">and </span><br/><a NAME="E7:14_1_1_1"/><span class="lab"><font color="Green" title="E36">A30</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font>
 <span class="kw">and </span><br/><a NAME="E8:14_1_1_1"/><span class="lab"><font color="Green" title="E37">A31</font></span>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">and </span><br/><a NAME="E9:14_1_1_1"/><span class="lab"><font color="Green" title="E38">A32</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">and </span><br/><a NAME="E10:14_1_1_1"/><span class="lab"><font color="Green" title="E39">A33</font></span>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font>
 <span class="kw">and </span><br/><a NAME="E11:14_1_1_1"/><span class="lab"><font color="Green" title="E40">A34</font></span>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font>
 <span class="kw">and </span><br/><a NAME="E12:14_1_1_1"/><span class="lab"><font color="Green" title="E41">A35</font></span>: 
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font>
 <span class="kw">and </span><br/><a NAME="E13:14_1_1_1"/><span class="lab"><font color="Green" title="E42">A36</font></span>: 
<font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font>
 <span class="kw">and </span><br/><a NAME="E14:14_1_1_1"/><span class="lab"><font color="Green" title="E43">A37</font></span>: 
<font color="Maroon" title="c12">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="E15:14_1_1_1"/><span class="lab"><font color="Green" title="E44">A38</font></span>: 
<font color="Maroon" title="c13">Z</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E16:14_1_1_1"/><span class="lab"><font color="Green" title="E45">A39</font></span>: 
<font color="Maroon" title="c14">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="E17:14_1_1_1"/><span class="lab"><font color="Green" title="E46">A40</font></span>: 
<font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">Z</font>
 <span class="kw">and </span><br/><a NAME="E18:14_1_1_1"/><span class="lab"><font color="Green" title="E47">A41</font></span>: 
<font color="Maroon" title="c12">Y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">M</font>
 <span class="kw">and </span><br/><a NAME="E19:14_1_1_1"/><span class="lab"><font color="Green" title="E48">A42</font></span>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">and </span><br/><a NAME="E20:14_1_1_1"/><span class="lab"><font color="Green" title="E49">A43</font></span>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">and </span><br/><a NAME="E21:14_1_1_1"/><span class="lab"><font color="Green" title="E50">A44</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c22">d</font>
 <span class="kw">and </span><br/><a NAME="E22:14_1_1_1"/><span class="lab"><font color="Green" title="E51">A45</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c22">d</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> or <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )</span><br/><a NAME="E23:14_1_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> or <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14_1_1_1_1"/><span class="lab"><font color="Green" title="E52">A46</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font>
 <span class="kw">and </span><br/><a NAME="E2:14_1_1_1_1"/><span class="lab"><font color="Green" title="E53">A47</font></span>: 
 not <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_1_1"/><span class="lab"><font color="Green" title="E54">A48</font></span>: 
( <font color="Maroon" title="c18">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a1</font> &amp; <font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E55">A49</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c17">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E56">A50</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A51</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E57">A51</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_1_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A52</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E4:14_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E58">A53</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A54</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E59">A54</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:14_1_1_1_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E6:14_1_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A55</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E7:14_1_1_1_1_1_1"/><span class="lab"><font color="Green" title="E60">A56</font></span>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E8:14_1_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E9:14_1_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E58">A53</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E59">A55</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>;<br/><a NAME="E10:14_1_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E56">A50</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E57">A52</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E11:14_1_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E7:14_1_1_1_1_1_1"><span class="lab"><font color="Green" title="E60">A56</font></span></a>, <a class="ref" href="aff_1.html#T2" onmouseover="rs('aff_1/T2')" onmouseout="rh()">AFF_1:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E56">A57</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c18">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E57">A58</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A59</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E58">A59</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_1_1_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A60</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E4:14_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E59">A61</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A62</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_1_2_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E60">A62</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:14_1_1_1_1_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E6:14_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A63</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E7:14_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E61">A64</font></span>: 
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E8:14_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E9:14_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E59">A61</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E60">A63</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>;<br/><a NAME="E10:14_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E57">A58</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E58">A60</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E11:14_1_1_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E7:14_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E61">A64</font></span></a>, <a class="ref" href="aff_1.html#T2" onmouseover="rs('aff_1/T2')" onmouseout="rh()">AFF_1:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E57">A65</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_1_3"/><span class="lab"><font color="Green" title="E58">A66</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_1_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A67</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_1_3_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_3_1"><span class="lab"><font color="Green" title="E59">A67</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_1_1_1_3"/><span class="lab"><font color="Green" title="E59">A68</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_1_3_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_1_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A69</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_1_3_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_1_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_3_2"><span class="lab"><font color="Green" title="E60">A69</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E3:14_1_1_1_1_1_3"/><span class="lab"><font color="Green" title="E60">A70</font></span>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:14_1_1_1_1_1_3"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E5:14_1_1_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="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E6:14_1_1_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A71</font></span>: 
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_3"><span class="lab"><font color="Green" title="E60">A70</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_1_3"><span class="lab"><font color="Green" title="E58">A66</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>;<br/><a NAME="E7:14_1_1_1_1_1_3"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E8:14_1_1_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="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E9:14_1_1_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1_3"><span class="lab"><font color="Green" title="E60">A70</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_1_3"><span class="lab"><font color="Green" title="E59">A68</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E10:14_1_1_1_1_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_1_3"><span class="lab"><font color="Green" title="E61">A71</font></span></a>, <a class="ref" href="aff_1.html#T2" onmouseover="rs('aff_1/T2')" onmouseout="rh()">AFF_1:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E4:14_1_1_1_1_1"/>
(  not <font color="Maroon" title="c18">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> or  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a1</font> or  not <font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_1"><span class="lab"><font color="Green" title="E56">A57</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_1"><span class="lab"><font color="Green" title="E57">A65</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_1"><span class="lab"><font color="Green" title="E55">A49</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2"/><span class="lab"><font color="Green" title="E55">A72</font></span>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><div><span class="lab"><font color="Green" title="E56">A73</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">o</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E57">A74</font></span>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E58">A75</font></span>: 
( <font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font> &amp; <font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E59">A76</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_2_1_1_1"/><span class="lab"><font color="Green" title="E60">A77</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_1_1_1"/><span class="lab"><font color="Green" title="E61">A78</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_1_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_1_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A79</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_1_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_1_1_1_1"><span class="lab"><font color="Green" title="E62">A79</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:14_1_1_1_1_2_1_1_1_1"/><span class="lab"><font color="Green" title="E62">A80</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:14_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E62">A80</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E62">A80</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A81</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:14_1_1_1_1_2_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E61">A78</font></span></a>, <a class="txt" href="#E11:14_1_1_1_1_2_1_1_1_1"><span class="lab"><font color="Green" title="E63">A81</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_1_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A82</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><span class="kw">hence </span><a NAME="E5:14_1_1_1_1_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E61">A82</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_1_1"><span class="lab"><font color="Green" title="E60">A77</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E60">A83</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A84</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><a NAME="E3:14_1_1_1_1_2_1_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_1_2"><span class="lab"><font color="Green" title="E61">A84</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:14_1_1_1_1_2_1_1"/>
(  not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font> or  not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1_1"><span class="lab"><font color="Green" title="E60">A83</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_1"><span class="lab"><font color="Green" title="E59">A76</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:14_1_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" onmouseover="rs('aff_1/T7')" onmouseout="rh()">AFF_1:7</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">C</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="E5:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E59">A85</font></span>: 
<font color="Maroon" title="c23">C</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E60">A86</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 <span class="kw">and </span><br/><a NAME="E7:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 <span class="kw">and </span><br/><a NAME="E8:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E61">A87</font></span>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T21" onmouseover="rs('aff_1/T21')" onmouseout="rh()">AFF_1:21</a></span>;<br/><a NAME="E9:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E62">A88</font></span>: 
 ex <font color="Olive" title="b1">d2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Olive" title="b1">d2</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c24">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:14_1_1_1_1_2_1_2"/><span class="lab"><font color="Green" title="E63">A89</font></span>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1_1_1_2_1_2"/><span class="lab"><font color="Green" title="E64">A90</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c25">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:14_1_1_1_1_2_1_2"/><span class="lab"><font color="Green" title="E65">A91</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_1_1_2_1_2"/><span class="lab"><font color="Green" title="E66">A92</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c25">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E65">A91</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A93</font></span>: 
<font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_2"/>
 not <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E65">A91</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E66">A92</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E63">A89</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E64">A90</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_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="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A94</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:14_1_1_1_1_2_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E7:14_1_1_1_1_2_1_2_1"><span class="lab"><font color="Green" title="E68">A94</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">d2</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="E11:14_1_1_1_1_2_1_2"/><span class="lab"><font color="Green" title="E68">A95</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c26">d2</font>
 <span class="kw">and </span><br/><a NAME="E12:14_1_1_1_1_2_1_2"/><span class="lab"><font color="Green" title="E69">A96</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>,<font color="Maroon" title="c26">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c26">d2</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c26">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d2</font> )</span><br/>

<a NAME="E13:14_1_1_1_1_2_1_2"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E69">A96</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:14_1_1_1_1_2_1_2"/>
( <font color="Maroon" title="c26">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp; <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E66">A92</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E63">A89</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E64">A90</font></span></a>, <a class="txt" href="#E11:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E68">A95</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_2"><span class="lab"><font color="Green" title="E67">A93</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E10:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E63">A97</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/>( <font color="Olive" title="b1">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp; <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Olive" title="b1">d1</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c24">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:14_1_1_1_1_2_1_3"/><span class="lab"><font color="Green" title="E64">A98</font></span>: 
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1_1_1_2_1_3"/><span class="lab"><font color="Green" title="E65">A99</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c25">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:14_1_1_1_1_2_1_3"/><span class="lab"><font color="Green" title="E66">A100</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_1_1_2_1_3"/><span class="lab"><font color="Green" title="E67">A101</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c25">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E66">A100</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A102</font></span>: 
<font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_3"/>
 not <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_3_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E66">A100</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E67">A101</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A103</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E64">A98</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E65">A99</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_3_1"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_3_1"><span class="lab"><font color="Green" title="E69">A103</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A104</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_3_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E10:14_1_1_1_1_2_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_3_1"><span class="lab"><font color="Green" title="E70">A104</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">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="E11:14_1_1_1_1_2_1_3"/><span class="lab"><font color="Green" title="E69">A105</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c26">d1</font>
 <span class="kw">and </span><br/><a NAME="E12:14_1_1_1_1_2_1_3"/><span class="lab"><font color="Green" title="E70">A106</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font>,<font color="Maroon" title="c26">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c26">d1</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp; <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font> )</span><br/>

<a NAME="E13:14_1_1_1_1_2_1_3"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E70">A106</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:14_1_1_1_1_2_1_3"/>
( <font color="Maroon" title="c26">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp; <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c26">d1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E67">A101</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E64">A98</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E65">A99</font></span></a>, <a class="txt" href="#E11:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E69">A105</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_3"><span class="lab"><font color="Green" title="E68">A102</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">consider </span><font color="Maroon" title="c24">d2</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="E12:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E64">A107</font></span>: 
<font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 <span class="kw">and </span><br/><a NAME="E13:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E65">A108</font></span>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E62">A88</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c25">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="E15:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E66">A109</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 <span class="kw">and </span><br/><a NAME="E16:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E67">A110</font></span>: 
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E63">A97</font></span></a></span>;<br/><a NAME="E17:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E18:14_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A111</font></span>: 
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E16:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E67">A110</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E19:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E20:14_1_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="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E21:14_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A112</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><a NAME="E22:14_1_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" onmouseover="rs('aff_1/T7')" onmouseout="rh()">AFF_1:7</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">A</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="E24:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E70">A113</font></span>: 
<font color="Maroon" title="c26">A</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E25:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E71">A114</font></span>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 <span class="kw">and </span><br/><a NAME="E26:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 <span class="kw">and </span><br/><a NAME="E27:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E72">A115</font></span>: 
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T21" onmouseover="rs('aff_1/T21')" onmouseout="rh()">AFF_1:21</a></span>;<br/><a NAME="E28:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E73">A116</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1_1_1"><span class="lab"><font color="Green" title="E50">A44</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2"><span class="lab"><font color="Green" title="E55">A72</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><a NAME="E29:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E74">A117</font></span>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="ref" href="aff_1.html#T3" onmouseover="rs('aff_1/T3')" onmouseout="rh()">AFF_1:3</a></span>;<br/><a NAME="E30:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E75">A118</font></span>: 
 ex <font color="Olive" title="b1">d3</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Olive" title="b1">d3</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c27">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:14_1_1_1_1_2_1_4"/><span class="lab"><font color="Green" title="E76">A119</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c27">e2</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1_1_1_2_1_4"/><span class="lab"><font color="Green" title="E77">A120</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c28">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:14_1_1_1_1_2_1_4"/><span class="lab"><font color="Green" title="E78">A121</font></span>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c28">e1</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_1_1_2_1_4"/><span class="lab"><font color="Green" title="E79">A122</font></span>: 
<font color="Maroon" title="c17">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c28">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E78">A121</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A123</font></span>: 
<font color="Maroon" title="c28">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E74">A117</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_4"/>
 not <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c27">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_4_1"/>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c27">e2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c27">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E78">A121</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E79">A122</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A124</font></span>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E76">A119</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E77">A120</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A125</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_4_1"/><span class="lab"><font color="Green" title="E83">A126</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_4_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E7:14_1_1_1_1_2_1_4_1"><span class="lab"><font color="Green" title="E82">A125</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_4_1"><span class="lab"><font color="Green" title="E83">A126</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E14:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E15:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E16:14_1_1_1_1_2_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_4_1"><span class="lab"><font color="Green" title="E83">A126</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:14_1_1_1_1_2_1_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_4_1"><span class="lab"><font color="Green" title="E81">A124</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c29">d3</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="E11:14_1_1_1_1_2_1_4"/><span class="lab"><font color="Green" title="E81">A127</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c28">e1</font>,<font color="Maroon" title="c29">d3</font>
 <span class="kw">and </span><br/><a NAME="E12:14_1_1_1_1_2_1_4"/><span class="lab"><font color="Green" title="E82">A128</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c27">e2</font>,<font color="Maroon" title="c29">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c29">d3</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c29">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">d3</font> )</span><br/>

<a NAME="E13:14_1_1_1_1_2_1_4"/>
<font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c27">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E82">A128</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:14_1_1_1_1_2_1_4"/>
( <font color="Maroon" title="c29">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> &amp; <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">d3</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E79">A122</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E76">A119</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E77">A120</font></span></a>, <a class="txt" href="#E11:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E81">A127</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_4"><span class="lab"><font color="Green" title="E80">A123</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E31:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E76">A129</font></span>: 
(  not <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> &amp;  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> &amp;  not <font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> &amp;  not <font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E77">A130</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_2_1_5_1"/><span class="lab"><font color="Green" title="E78">A131</font></span>: 
<font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_5_1_1"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_5_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A132</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_5_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_5_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_5_1_1"><span class="lab"><font color="Green" title="E79">A132</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_1_1_2_1_5_1"/><span class="lab"><font color="Green" title="E79">A133</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">b1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_5_1_2"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">b1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_5_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A134</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_5_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_5_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_5_1_2"><span class="lab"><font color="Green" title="E80">A134</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E3:14_1_1_1_1_2_1_5_1"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A135</font></span>: 
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_5_1"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_5_1_3"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">c</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_5_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A136</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_5_1_3"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_5_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_5_1_3"><span class="lab"><font color="Green" title="E81">A136</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_5_1"><span class="lab"><font color="Green" title="E80">A135</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E7:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_5_1"><span class="lab"><font color="Green" title="E78">A131</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E8:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E9:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E10:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E11:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A137</font></span>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E12:14_1_1_1_1_2_1_5_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1_1_2_1_5_1"><span class="lab"><font color="Green" title="E80">A135</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E13:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E14:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E15:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E16:14_1_1_1_1_2_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_5_1"><span class="lab"><font color="Green" title="E78">A131</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><span class="kw">hence </span><a NAME="E17:14_1_1_1_1_2_1_5_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E11:14_1_1_1_1_2_1_5_1"><span class="lab"><font color="Green" title="E81">A137</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_5_1"><span class="lab"><font color="Green" title="E79">A133</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E78">A138</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_2_1_5_2"/><span class="lab"><font color="Green" title="E79">A139</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">d2</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_5_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_1_1_2_1_5_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_5_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A140</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:14_1_1_1_1_2_1_5_2_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">d2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:14_1_1_1_1_2_1_5_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="txt" href="#E12:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E64">A107</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_5_2_1"><span class="lab"><font color="Green" title="E80">A140</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_5_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_5_2"/><span class="lab"><font color="Green" title="E80">A141</font></span>: 
<font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_1_2_1_5_2"/><span class="lab"><font color="Green" title="E81">A142</font></span>: 
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E65">A108</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_5_2"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1_1_1"><span class="lab"><font color="Green" title="E50">A44</font></span></a>, <a class="txt" href="#E29:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E74">A117</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><span class="kw">hence </span><a NAME="E5:14_1_1_1_1_2_1_5_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_5"><span class="lab"><font color="Green" title="E77">A130</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_5_2"><span class="lab"><font color="Green" title="E80">A141</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_5_2"><span class="lab"><font color="Green" title="E79">A139</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_5_2"><span class="lab"><font color="Green" title="E81">A142</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E79">A143</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_5_3"/>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A144</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_1_1_2_1_5_3"/><span class="lab"><font color="Green" title="E81">A145</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_5_3"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_5_3"><span class="lab"><font color="Green" title="E80">A144</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E6:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_5_3"><span class="lab"><font color="Green" title="E81">A145</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E7:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E8:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E9:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E10:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E11:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_5_3"><span class="lab"><font color="Green" title="E81">A145</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E12:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A146</font></span>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E13:14_1_1_1_1_2_1_5_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1_5_3"><span class="lab"><font color="Green" title="E80">A144</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E14:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E15:14_1_1_1_1_2_1_5_3"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E16:14_1_1_1_1_2_1_5_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E12:14_1_1_1_1_2_1_5_3"><span class="lab"><font color="Green" title="E82">A146</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E80">A147</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_2_1_5_4"/><span class="lab"><font color="Green" title="E81">A148</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">d1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_5_4_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_5_4_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_1_1_2_1_5_4_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_5_4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A149</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:14_1_1_1_1_2_1_5_4_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">d1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:14_1_1_1_1_2_1_5_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_5_4_1"><span class="lab"><font color="Green" title="E82">A149</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_5_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_5_4"/><span class="lab"><font color="Green" title="E82">A150</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_1_2_1_5_4"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_5_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A151</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_5_4"/><span class="lab"><font color="Green" title="E84">A152</font></span>: 
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E67">A110</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E6:14_1_1_1_1_2_1_5_4"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1_1_1"><span class="lab"><font color="Green" title="E50">A44</font></span></a>, <a class="txt" href="#E29:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E74">A117</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><a NAME="E7:14_1_1_1_1_2_1_5_4"/><span class="kw">then </span>
<font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_5_4"><span class="lab"><font color="Green" title="E82">A150</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_5_4"><span class="lab"><font color="Green" title="E81">A148</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1_5_4"><span class="lab"><font color="Green" title="E84">A152</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>;<br/><span class="kw">hence </span><a NAME="E8:14_1_1_1_1_2_1_5_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_5"><span class="lab"><font color="Green" title="E79">A143</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_5_4"><span class="lab"><font color="Green" title="E83">A151</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E5:14_1_1_1_1_2_1_5"/>
( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> or <font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> or <font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> or <font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1_2_1_5"><span class="lab"><font color="Green" title="E79">A143</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_5"><span class="lab"><font color="Green" title="E77">A130</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_5"><span class="lab"><font color="Green" title="E80">A147</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_5"><span class="lab"><font color="Green" title="E78">A138</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E32:14_1_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" onmouseover="rs('aff_1/T7')" onmouseout="rh()">AFF_1:7</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c27">K</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="E34:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E77">A153</font></span>: 
<font color="Maroon" title="c27">K</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E35:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E78">A154</font></span>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 <span class="kw">and </span><br/><a NAME="E36:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 <span class="kw">and </span><br/><a NAME="E37:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E79">A155</font></span>: 
<font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T21" onmouseover="rs('aff_1/T21')" onmouseout="rh()">AFF_1:21</a></span>;<br/><a NAME="E38:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="ref" href="aff_1.html#T3" onmouseover="rs('aff_1/T3')" onmouseout="rh()">AFF_1:3</a></span>;<br/><a NAME="E39:14_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A156</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1_1_1"><span class="lab"><font color="Green" title="E51">A45</font></span></a>, <a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c28">d3</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="E41:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E81">A157</font></span>: 
<font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 <span class="kw">and </span><br/><a NAME="E42:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E82">A158</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E75">A118</font></span></a></span>;<br/><a NAME="E43:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E83">A159</font></span>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="ref" href="aff_1.html#T3" onmouseover="rs('aff_1/T3')" onmouseout="rh()">AFF_1:3</a></span>;<br/><a NAME="E44:14_1_1_1_1_2_1"/>
 ex <font color="Olive" title="b1">d4</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> &amp; <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Olive" title="b1">d4</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c29">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:14_1_1_1_1_2_1_6"/><span class="lab"><font color="Green" title="E84">A160</font></span>: 
<font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">e2</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1_1_1_2_1_6"/><span class="lab"><font color="Green" title="E85">A161</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c30">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:14_1_1_1_1_2_1_6"/><span class="lab"><font color="Green" title="E86">A162</font></span>: 
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c30">e1</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_1_1_2_1_6"/><span class="lab"><font color="Green" title="E87">A163</font></span>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_6"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E86">A162</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A164</font></span>: 
<font color="Maroon" title="c30">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E83">A159</font></span></a>, <a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_6"/>
 not <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c30">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_6_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_6_1"/><span class="lab"><font color="Green" title="E89">A165</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_6_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_6_1_1"/><span class="lab"><font color="Green" title="E90">A166</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_6_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_6_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_6_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_6_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_6_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A167</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_6_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_6_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_6_1_1_1"><span class="lab"><font color="Green" title="E91">A167</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_6_1_1"/><span class="lab"><font color="Green" title="E91">A168</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_1_1_2_1_6_1_1"/>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E58">A75</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_6_1_1"><span class="lab"><font color="Green" title="E91">A168</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A169</font></span>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_6_1_1"/>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E7:14_1_1_1_1_2_1_6_1_1"><span class="lab"><font color="Green" title="E92">A169</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A170</font></span>: 
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:14_1_1_1_1_2_1_6_1_1"/>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E14:14_1_1_1_1_2_1_6_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_1_1_2_1_6_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E58">A75</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_6_1_1"><span class="lab"><font color="Green" title="E91">A168</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_6_1_1"><span class="lab"><font color="Green" title="E90">A166</font></span></a>, <a class="txt" href="#E12:14_1_1_1_1_2_1_6_1_1"><span class="lab"><font color="Green" title="E93">A170</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:14_1_1_1_1_2_1_6_1"/><span class="lab"><font color="Green" title="E90">A171</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">d3</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_6_1_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_6_1_2"/><span class="lab"><font color="Green" title="E91">A172</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">d1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_6_1_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_6_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_1_1_2_1_6_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="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_6_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A173</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:14_1_1_1_1_2_1_6_1_2_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">d1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:14_1_1_1_1_2_1_6_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_6_1_2_1"><span class="lab"><font color="Green" title="E92">A173</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_6_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_6_1_2"/><span class="lab"><font color="Green" title="E92">A174</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">d3</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_1_1_2_1_6_1_2"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E16:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E67">A110</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A175</font></span>: 
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_6_1_2"/><span class="lab"><font color="Green" title="E94">A176</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_6_1_2"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1_1_1"><span class="lab"><font color="Green" title="E50">A44</font></span></a>, <a class="txt" href="#E29:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E74">A117</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="txt" href="#E41:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E81">A157</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_6_1_2"><span class="lab"><font color="Green" title="E92">A174</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_6_1_2"><span class="lab"><font color="Green" title="E91">A172</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1_6_1_2"><span class="lab"><font color="Green" title="E93">A175</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A177</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_6_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E9:14_1_1_1_1_2_1_6_1_2"><span class="lab"><font color="Green" title="E95">A177</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_6_1_2"><span class="lab"><font color="Green" title="E94">A176</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E13:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E14:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E15:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E16:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E17:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A178</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_6_1_2"><span class="lab"><font color="Green" title="E94">A176</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E18:14_1_1_1_1_2_1_6_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1_1_1_2_1_6_1_2"><span class="lab"><font color="Green" title="E95">A177</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E20:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E21:14_1_1_1_1_2_1_6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:14_1_1_1_1_2_1_6_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E17:14_1_1_1_1_2_1_6_1_2"><span class="lab"><font color="Green" title="E96">A178</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:14_1_1_1_1_2_1_6_1"/>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c30">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">e2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E86">A162</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E87">A163</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A179</font></span>: 
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E84">A160</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E85">A161</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_6_1"/><span class="lab"><font color="Green" title="E92">A180</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E42:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E82">A158</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A181</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1_6_1"><span class="lab"><font color="Green" title="E91">A179</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_6_1"><span class="lab"><font color="Green" title="E90">A171</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A182</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_6_1"><span class="lab"><font color="Green" title="E92">A180</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E14:14_1_1_1_1_2_1_6_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E15:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14_1_1_1_1_2_1_6_1"><span class="lab"><font color="Green" title="E94">A182</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_6_1"><span class="lab"><font color="Green" title="E89">A165</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E16:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E17:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E18:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E20:14_1_1_1_1_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_6_1"><span class="lab"><font color="Green" title="E92">A180</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E21:14_1_1_1_1_2_1_6_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_6_1"><span class="lab"><font color="Green" title="E93">A181</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c31">d4</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="E11:14_1_1_1_1_2_1_6"/><span class="lab"><font color="Green" title="E89">A183</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c30">e1</font>,<font color="Maroon" title="c31">d4</font>
 <span class="kw">and </span><br/><a NAME="E12:14_1_1_1_1_2_1_6"/><span class="lab"><font color="Green" title="E90">A184</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">e2</font>,<font color="Maroon" title="c31">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c31">d4</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c31">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> &amp; <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c31">d4</font> )</span><br/>

<a NAME="E13:14_1_1_1_1_2_1_6"/>
<font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c31">d4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E90">A184</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:14_1_1_1_1_2_1_6"/>
( <font color="Maroon" title="c31">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> &amp; <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c31">d4</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E87">A163</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E84">A160</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E85">A161</font></span></a>, <a class="txt" href="#E11:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E89">A183</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_6"><span class="lab"><font color="Green" title="E88">A164</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c29">d4</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="E46:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E84">A185</font></span>: 
<font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 <span class="kw">and </span><br/><a NAME="E47:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E85">A186</font></span>: 
<font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">d4</font>
 ;<br/><a NAME="E48:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E86">A187</font></span>: 
(  not <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp;  not <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp;  not <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp;  not <font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_7"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E87">A188</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_7_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_7_1"/>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_7_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_1_1_2_1_7_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_7_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_7_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A189</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><a NAME="E6:14_1_1_1_1_2_1_7_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><span class="kw">hence </span><a NAME="E7:14_1_1_1_1_2_1_7_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1_7_1"><span class="lab"><font color="Green" title="E88">A189</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E88">A190</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_7_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_2_1_7_2"/><span class="lab"><font color="Green" title="E89">A191</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">d3</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_7_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_7_2_1"/><span class="lab"><font color="Green" title="E90">A192</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">d1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_7_2_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_7_2_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_1_1_2_1_7_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="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_7_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A193</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:14_1_1_1_1_2_1_7_2_1_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">d1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:14_1_1_1_1_2_1_7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_7_2_1_1"><span class="lab"><font color="Green" title="E91">A193</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_7_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_7_2_1"/><span class="lab"><font color="Green" title="E91">A194</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">d3</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_1_1_2_1_7_2_1"/><span class="lab"><font color="Green" title="E92">A195</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_7_2_1"/><span class="lab"><font color="Green" title="E93">A196</font></span>: 
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E67">A110</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_7_2_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1_1_1"><span class="lab"><font color="Green" title="E50">A44</font></span></a>, <a class="txt" href="#E29:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E74">A117</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="txt" href="#E41:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E81">A157</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E91">A194</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E90">A192</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E93">A196</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A197</font></span>: 
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_7_2_1"/><span class="lab"><font color="Green" title="E95">A198</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_7_2_1"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E7:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E94">A197</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A199</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E13:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E14:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E95">A198</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E15:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E92">A195</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E16:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E17:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E18:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E20:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A200</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E95">A198</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E21:14_1_1_1_1_2_1_7_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E96">A199</font></span></a>, <a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E22:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E23:14_1_1_1_1_2_1_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E24:14_1_1_1_1_2_1_7_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E20:14_1_1_1_1_2_1_7_2_1"><span class="lab"><font color="Green" title="E97">A200</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_7_2"/><span class="lab"><font color="Green" title="E90">A201</font></span>: 
<font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_1_2_1_7_2"/>
<font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E82">A158</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_7_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_7"><span class="lab"><font color="Green" title="E87">A188</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_7_2"><span class="lab"><font color="Green" title="E90">A201</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_7_2"><span class="lab"><font color="Green" title="E89">A191</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E89">A202</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_7_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_7_3"/>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_7_3"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_1_1_2_1_7_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_7_3"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_7_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A203</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><a NAME="E6:14_1_1_1_1_2_1_7_3"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><span class="kw">hence </span><a NAME="E7:14_1_1_1_1_2_1_7_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1_7_3"><span class="lab"><font color="Green" title="E90">A203</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E90">A204</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_7_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_7_4"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_7_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A205</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_1_1_2_1_7_4"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_7_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_7_4"><span class="lab"><font color="Green" title="E91">A205</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><span class="kw">hence </span><a NAME="E5:14_1_1_1_1_2_1_7_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E5:14_1_1_1_1_2_1_7"/>
( <font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> or <font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> or <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> or <font color="Maroon" title="c28">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1_2_1_7"><span class="lab"><font color="Green" title="E89">A202</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_7"><span class="lab"><font color="Green" title="E87">A188</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_7"><span class="lab"><font color="Green" title="E90">A204</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_7"><span class="lab"><font color="Green" title="E88">A190</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E49:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E87">A206</font></span>: 
<font color="Maroon" title="c29">d4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">d3</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_8"/><span class="lab"><font color="Green" title="E88">A207</font></span>: 
<font color="Maroon" title="c29">d4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">d3</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_8"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">d3</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_8_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_8_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c26">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14_1_1_1"><span class="lab"><font color="Green" title="E50">A44</font></span></a>, <a class="txt" href="#E29:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E74">A117</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E2:14_1_1_1_1_2_1_8_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A208</font></span>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="txt" href="#E41:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E81">A157</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_8_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1_1_1"><span class="lab"><font color="Green" title="E51">A45</font></span></a>, <a class="txt" href="#E43:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E83">A159</font></span></a>, <a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_8_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A209</font></span>: 
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c28">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="txt" href="#E46:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E84">A185</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_8"><span class="lab"><font color="Green" title="E88">A207</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:14_1_1_1_1_2_1_8_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">d3</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_8_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_8_1"><span class="lab"><font color="Green" title="E90">A209</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_8_1"><span class="lab"><font color="Green" title="E89">A208</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:14_1_1_1_1_2_1_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A210</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E82">A158</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_8"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E16:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E67">A110</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A211</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E48:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E86">A187</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_8"><span class="lab"><font color="Green" title="E89">A210</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_8"/><span class="lab"><font color="Green" title="E91">A212</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_8"/><span class="lab"><font color="Green" title="E92">A213</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_8"><span class="lab"><font color="Green" title="E90">A211</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E7:14_1_1_1_1_2_1_8"><span class="lab"><font color="Green" title="E91">A212</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E13:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E14:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E15:14_1_1_1_1_2_1_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A214</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1_8"><span class="lab"><font color="Green" title="E92">A213</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E16:14_1_1_1_1_2_1_8"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1_1_2_1_8"><span class="lab"><font color="Green" title="E90">A211</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E17:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E18:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:14_1_1_1_1_2_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E20:14_1_1_1_1_2_1_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1_8"><span class="lab"><font color="Green" title="E93">A214</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E50:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E88">A215</font></span>: 
( <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> &amp; <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_9"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E89">A216</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_9_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">c</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_9_1"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">c</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_9_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A217</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><a NAME="E3:14_1_1_1_1_2_1_9_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_9_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_9_1"><span class="lab"><font color="Green" title="E90">A217</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E90">A218</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_9_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_9_2"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_9_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A219</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><a NAME="E3:14_1_1_1_1_2_1_9_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_9_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_9_2"><span class="lab"><font color="Green" title="E91">A219</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:14_1_1_1_1_2_1_9"/>
(  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b</font> or  not <font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1_9"><span class="lab"><font color="Green" title="E90">A218</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_9"><span class="lab"><font color="Green" title="E89">A216</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E51:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E89">A220</font></span>: 
(  not <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> &amp;  not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> &amp;  not <font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> &amp;  not <font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E90">A221</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_2_1_10_1"/><span class="lab"><font color="Green" title="E91">A222</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_10_1_1"/><span class="lab"><font color="Green" title="E92">A223</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_1_10_1_1_1"/><span class="lab"><font color="Green" title="E93">A224</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_10_1_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_10_1_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_10_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_10_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A225</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_10_1_1_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_10_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_10_1_1_1_1"><span class="lab"><font color="Green" title="E94">A225</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:14_1_1_1_1_2_1_10_1_1_1"/><span class="lab"><font color="Green" title="E94">A226</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_1_1_2_1_10_1_1_1"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:14_1_1_1_1_2_1_10_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10_1_1_1"><span class="lab"><font color="Green" title="E94">A226</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_10_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_10_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_10_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_10_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_10_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10_1_1_1"><span class="lab"><font color="Green" title="E94">A226</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_10_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_10_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A227</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_10_1_1_1"/>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c20">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:14_1_1_1_1_2_1_10_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_10_1_1_1"><span class="lab"><font color="Green" title="E93">A224</font></span></a>, <a class="txt" href="#E11:14_1_1_1_1_2_1_10_1_1_1"><span class="lab"><font color="Green" title="E95">A227</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:14_1_1_1_1_2_1_10_1_1"/><span class="lab"><font color="Green" title="E93">A228</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_10_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_10_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_10_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_10_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A229</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_10_1_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_10_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_10_1_1_2"><span class="lab"><font color="Green" title="E94">A229</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:14_1_1_1_1_2_1_10_1_1"/><span class="lab"><font color="Green" title="E94">A230</font></span>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:14_1_1_1_1_2_1_10_1_1"/>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_10_1_1"><span class="lab"><font color="Green" title="E92">A223</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_10_1_1"><span class="lab"><font color="Green" title="E94">A230</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_10_1_1"><span class="lab"><font color="Green" title="E94">A230</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E11:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E12:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:14_1_1_1_1_2_1_10_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A231</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E14:14_1_1_1_1_2_1_10_1_1"/>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_1_1_2_1_10_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1_10_1_1"><span class="lab"><font color="Green" title="E92">A223</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10_1_1"><span class="lab"><font color="Green" title="E93">A228</font></span></a>, <a class="txt" href="#E13:14_1_1_1_1_2_1_10_1_1"><span class="lab"><font color="Green" title="E95">A231</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_1_1_2_1_10_1"/><span class="lab"><font color="Green" title="E92">A232</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><span class="kw">assume </span><a NAME="E3:14_1_1_1_1_2_1_10_1"/>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A233</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_10_1"/><span class="lab"><font color="Green" title="E94">A234</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E6:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_10_1"><span class="lab"><font color="Green" title="E93">A233</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E7:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1_10_1"><span class="lab"><font color="Green" title="E91">A222</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10_1"><span class="lab"><font color="Green" title="E92">A232</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E8:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E9:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E10:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E11:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E12:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1_10_1"><span class="lab"><font color="Green" title="E94">A234</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E13:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A235</font></span>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E14:14_1_1_1_1_2_1_10_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1_1_2_1_10_1"><span class="lab"><font color="Green" title="E93">A233</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E15:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E16:14_1_1_1_1_2_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E17:14_1_1_1_1_2_1_10_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E13:14_1_1_1_1_2_1_10_1"><span class="lab"><font color="Green" title="E95">A235</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E91">A236</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_2_1_10_2"/><span class="lab"><font color="Green" title="E92">A237</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">d1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_10_2_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">d1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A238</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_10_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_10_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10_2_1"><span class="lab"><font color="Green" title="E93">A238</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_2_1_10_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_10_2"/><span class="lab"><font color="Green" title="E93">A239</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_1_2_1_10_2"/>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A240</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_10_2"/><span class="lab"><font color="Green" title="E95">A241</font></span>: 
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E67">A110</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E6:14_1_1_1_1_2_1_10_2"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1_1_1"><span class="lab"><font color="Green" title="E51">A45</font></span></a>, <a class="txt" href="#E43:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E83">A159</font></span></a>, <a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><a NAME="E7:14_1_1_1_1_2_1_10_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10_2"><span class="lab"><font color="Green" title="E93">A239</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_10_2"><span class="lab"><font color="Green" title="E92">A237</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1_10_2"><span class="lab"><font color="Green" title="E95">A241</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>;<br/><span class="kw">hence </span><a NAME="E8:14_1_1_1_1_2_1_10_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_10"><span class="lab"><font color="Green" title="E90">A221</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_10_2"><span class="lab"><font color="Green" title="E94">A240</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E92">A242</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_10_3"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E93">A243</font></span>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E58">A75</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E58">A75</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E6:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E7:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E8:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E9:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A244</font></span>: 
<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E50:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E88">A215</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E10:14_1_1_1_1_2_1_10_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1_10_3"><span class="lab"><font color="Green" title="E93">A243</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E11:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E12:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E13:14_1_1_1_1_2_1_10_3"/><span class="kw">then </span>
<font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><span class="kw">hence </span><a NAME="E14:14_1_1_1_1_2_1_10_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E58">A75</font></span></a>, <a class="txt" href="#E9:14_1_1_1_1_2_1_10_3"><span class="lab"><font color="Green" title="E94">A244</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E93">A245</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_4"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font></span></a><div class="add"><a NAME="E1:14_1_1_1_1_2_1_10_4"/><span class="lab"><font color="Green" title="E94">A246</font></span>: 
<font color="Maroon" title="c22">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">d2</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_10_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_10_4_1"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">d2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_10_4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A247</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="txt" href="#E12:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E64">A107</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_10_4_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_10_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c22">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10_4_1"><span class="lab"><font color="Green" title="E95">A247</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_2_1_10_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1"><span class="lab"><font color="Green" title="E52">A46</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_1_10_4"/><span class="lab"><font color="Green" title="E95">A248</font></span>: 
<font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_1_2_1_10_4"/>
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E50:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E88">A215</font></span></a>, <a class="txt" href="#E13:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E65">A108</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E4:14_1_1_1_1_2_1_10_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A249</font></span>: 
<font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c19">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E5:14_1_1_1_1_2_1_10_4"/>
<font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1_1_1"><span class="lab"><font color="Green" title="E51">A45</font></span></a>, <a class="txt" href="#E43:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E83">A159</font></span></a>, <a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_10_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_10"><span class="lab"><font color="Green" title="E92">A242</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10_4"><span class="lab"><font color="Green" title="E95">A248</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_10_4"><span class="lab"><font color="Green" title="E94">A246</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_10_4"><span class="lab"><font color="Green" title="E96">A249</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E5:14_1_1_1_1_2_1_10"/>
( <font color="Maroon" title="c15">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> or <font color="Maroon" title="c19">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> or <font color="Maroon" title="c25">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> or <font color="Maroon" title="c24">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">K</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_1_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1_10"><span class="lab"><font color="Green" title="E90">A221</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_10"><span class="lab"><font color="Green" title="E92">A242</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_10"><span class="lab"><font color="Green" title="E91">A236</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_1_10"><span class="lab"><font color="Green" title="E93">A245</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E52:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E90">A250</font></span>: 
(  not <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp;  not <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp;  not <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> &amp;  not <font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_11"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E91">A251</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_11_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_11_1"/><span class="lab"><font color="Green" title="E92">A252</font></span>: 
<font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_11_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c18">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><span class="kw">hence </span><a NAME="E3:14_1_1_1_1_2_1_11_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E48:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E86">A187</font></span></a>, <a class="txt" href="#E51:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E89">A220</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_11_1"><span class="lab"><font color="Green" title="E92">A252</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E92">A253</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_11_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_11_2"/><span class="lab"><font color="Green" title="E93">A254</font></span>: 
<font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_11_2"/>
<font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">d4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E85">A186</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><span class="kw">hence </span><a NAME="E3:14_1_1_1_1_2_1_11_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E46:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E84">A185</font></span></a>, <a class="txt" href="#E48:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E86">A187</font></span></a>, <a class="txt" href="#E51:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E89">A220</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_11_2"><span class="lab"><font color="Green" title="E93">A254</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E93">A255</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_11_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_11_3"/><span class="lab"><font color="Green" title="E94">A256</font></span>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_1_11_3"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><span class="kw">hence </span><a NAME="E3:14_1_1_1_1_2_1_11_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E57">A74</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E48:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E86">A187</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_11_3"><span class="lab"><font color="Green" title="E94">A256</font></span></a>, <a class="ref" href="aff_1.html#T48" onmouseover="rs('aff_1/T48')" onmouseout="rh()">AFF_1:48</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E4:14_1_1_1_1_2_1_11"/>
( <font color="Maroon" title="c21">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> or <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> or <font color="Maroon" title="c22">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> or <font color="Maroon" title="c29">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">C</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_2_1_11"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E86">A187</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_1_11"><span class="lab"><font color="Green" title="E91">A251</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_1_11"><span class="lab"><font color="Green" title="E93">A255</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_11"><span class="lab"><font color="Green" title="E92">A253</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E53:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c18">c</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_12"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_12"/>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">c</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_12"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A257</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_12"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_1_12"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_1_12"><span class="lab"><font color="Green" title="E91">A257</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E54:14_1_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c24">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E13:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E65">A108</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E55:14_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E91">A258</font></span>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c22">d</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E56:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E57:14_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A259</font></span>: 
<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d</font>,<font color="Maroon" title="c25">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="txt" href="#E16:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E67">A110</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E58:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E93">A260</font></span>: 
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">d2</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_13"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_13"/>
<font color="Maroon" title="c25">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">d2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E16:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E67">A110</font></span></a>, <a class="txt" href="#E13:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E65">A108</font></span></a>, <a class="txt" href="#E48:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E86">A187</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_1_13"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c21">c1</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1"><span class="lab"><font color="Green" title="E54">A48</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_1_13"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A261</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E7:14_1_1_1_1_2_1_13"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:14_1_1_1_1_2_1_13"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1_13"><span class="lab"><font color="Green" title="E94">A261</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E59:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E94">A262</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c25">d1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_1_14"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_1_14"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c25">d1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_1_14"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c29">d4</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_1_1_2_1_14"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E12:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E64">A107</font></span></a>, <a class="txt" href="#E52:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E90">A250</font></span></a>, <a class="txt" href="#E58:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E93">A260</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E60:14_1_1_1_1_2_1"/><span class="lab"><font color="Green" title="E95">A263</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E11:14_1_1_1"><span class="lab"><font color="Green" title="E40">A34</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T51" onmouseover="rs('aff_1/T51')" onmouseout="rh()">AFF_1:51</a></span>;<br/><a NAME="E61:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c22">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E65">A108</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E62:14_1_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c28">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1"><span class="lab"><font color="Green" title="E30">A24</font></span></a>, <a class="txt" href="#E24:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E70">A113</font></span></a>, <a class="txt" href="#E25:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E71">A114</font></span></a>, <a class="txt" href="#E27:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E72">A115</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E8:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E61">A87</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E12:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E64">A107</font></span></a>, <a class="txt" href="#E41:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E81">A157</font></span></a>, <a class="txt" href="#E42:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E82">A158</font></span></a>, <a class="txt" href="#E28:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E73">A116</font></span></a>, <a class="txt" href="#E31:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E76">A129</font></span></a>, <a class="txt" href="#E48:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E86">A187</font></span></a>, <a class="txt" href="#E18:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E68">A111</font></span></a></span>;<br/><a NAME="E63:14_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A264</font></span>: 
<font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E50:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E88">A215</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E64:14_1_1_1_1_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E42:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E82">A158</font></span></a>, <a class="txt" href="#E47:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E85">A186</font></span></a>, <a class="txt" href="#E48:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E86">A187</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E65:14_1_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c29">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E60:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E95">A263</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E66:14_1_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c20">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c29">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_1"><span class="lab"><font color="Green" title="E30">A24</font></span></a>, <a class="txt" href="#E34:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E77">A153</font></span></a>, <a class="txt" href="#E35:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E78">A154</font></span></a>, <a class="txt" href="#E37:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E79">A155</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E59">A85</font></span></a>, <a class="txt" href="#E6:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E60">A86</font></span></a>, <a class="txt" href="#E15:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E66">A109</font></span></a>, <a class="txt" href="#E12:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E64">A107</font></span></a>, <a class="txt" href="#E46:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E84">A185</font></span></a>, <a class="txt" href="#E21:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E69">A112</font></span></a>, <a class="txt" href="#E39:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E80">A156</font></span></a>, <a class="txt" href="#E51:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E89">A220</font></span></a>, <a class="txt" href="#E52:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E90">A250</font></span></a>, <a class="txt" href="#E55:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E91">A258</font></span></a>, <a class="txt" href="#E57:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E92">A259</font></span></a></span>;<br/><a NAME="E67:14_1_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">d2</font>,<font color="Maroon" title="c29">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E58">A75</font></span></a>, <a class="txt" href="#E63:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E96">A264</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E68:14_1_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="c24">d2</font>,<font color="Maroon" title="c28">d3</font>,<font color="Maroon" title="c29">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E69:14_1_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="c29">d4</font>,<font color="Maroon" title="c28">d3</font>,<font color="Maroon" title="c24">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E70:14_1_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A265</font></span>: 
<font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c24">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E71:14_1_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">d1</font>,<font color="Maroon" title="c28">d3</font>,<font color="Maroon" title="c29">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E85">A186</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E72:14_1_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="c29">d4</font>,<font color="Maroon" title="c28">d3</font>,<font color="Maroon" title="c25">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E73:14_1_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c28">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c25">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E74:14_1_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c24">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">d4</font>,<font color="Maroon" title="c25">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E87">A206</font></span></a>, <a class="txt" href="#E70:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E97">A265</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><span class="kw">hence </span><a NAME="E75:14_1_1_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:14_1_1_1_1_2_1"><span class="lab"><font color="Green" title="E94">A262</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c20">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">o</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_2"/><span class="lab"><font color="Green" title="E57">A266</font></span>: 
<font color="Maroon" title="c20">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_1_1_2_2"/><span class="lab"><font color="Green" title="E58">A267</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">a1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_2_1"/><span class="lab"><font color="Green" title="E59">A268</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_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="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A269</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_2_1_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_2_1_1"><span class="lab"><font color="Green" title="E60">A269</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:14_1_1_1_1_2_2_1"/><span class="lab"><font color="Green" title="E60">A270</font></span>: 
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">a</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_2_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_2_1_2"/>
<font color="Maroon" title="c19">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">a</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_2_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E57">A266</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_2_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A271</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E6:14_1_1_1_1_2_2_1_2"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c17">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c13">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E10:14_1_1_1"><span class="lab"><font color="Green" title="E39">A33</font></span></a>, <a class="txt" href="#E15:14_1_1_1"><span class="lab"><font color="Green" title="E44">A38</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_1_1_2_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E32">A26</font></span></a>, <a class="txt" href="#E6:14_1_1_1"><span class="lab"><font color="Green" title="E35">A29</font></span></a>, <a class="txt" href="#E17:14_1_1_1"><span class="lab"><font color="Green" title="E46">A40</font></span></a>, <a class="txt" href="#E5:14_1_1_1_1_2_2_1_2"><span class="lab"><font color="Green" title="E61">A271</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:14_1_1_1_1_2_2_1"/><span class="lab"><font color="Green" title="E61">A272</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:14_1_1_1_1_2_2_1"/>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T51" onmouseover="rs('aff_1/T51')" onmouseout="rh()">AFF_1:51</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_1"><span class="lab"><font color="Green" title="E48">A42</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E57">A266</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_2_1"><span class="lab"><font color="Green" title="E61">A272</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_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="c16">a</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:14_1_1_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="c19">a1</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A273</font></span>: 
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_2_1"/>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T51" onmouseover="rs('aff_1/T51')" onmouseout="rh()">AFF_1:51</a></span>;<br/>
<a NAME="E10:14_1_1_1_1_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c17">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1_1_1_1_2_2_1"><span class="lab"><font color="Green" title="E62">A273</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_2_1"><span class="lab"><font color="Green" title="E60">A270</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E11:14_1_1_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="c19">a1</font>,<font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c15">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_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="c17">b</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c19">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:14_1_1_1_1_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E9:14_1_1_1"><span class="lab"><font color="Green" title="E38">A32</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_2_1"><span class="lab"><font color="Green" title="E61">A272</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_2_1"><span class="lab"><font color="Green" title="E59">A268</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a>, <a class="ref" href="aff_1.html#T51" onmouseover="rs('aff_1/T51')" onmouseout="rh()">AFF_1:51</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:14_1_1_1_1_2_2"/>
<font color="Maroon" title="c15">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_2_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_2_2_2"/><span class="lab"><font color="Green" title="E59">A274</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_2_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_1_2_2_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_1_2_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="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E3:14_1_1_1_1_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E5:14_1_1_1"><span class="lab"><font color="Green" title="E34">A28</font></span></a>, <a class="txt" href="#E8:14_1_1_1"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A275</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c12">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E14:14_1_1_1"><span class="lab"><font color="Green" title="E43">A37</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_2_2_1"/>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c14">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_1_1_2_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E31">A25</font></span></a>, <a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E18:14_1_1_1"><span class="lab"><font color="Green" title="E47">A41</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1_2_2_2_1"><span class="lab"><font color="Green" title="E60">A275</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_1_1_2_2_2"/><span class="lab"><font color="Green" title="E60">A276</font></span>: 
<font color="Maroon" title="c15">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_1_1_2_2_2"/><span class="lab"><font color="Green" title="E61">A277</font></span>: 
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="ref" href="aff_1.html#T51" onmouseover="rs('aff_1/T51')" onmouseout="rh()">AFF_1:51</a></span>;<br/>
<a NAME="E4:14_1_1_1_1_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_1"><span class="lab"><font color="Green" title="E49">A43</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E58">A267</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E60">A276</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_1_1_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c15">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">c</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E6:14_1_1_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="c18">c</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:14_1_1_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="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E8:14_1_1_1_1_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c18">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_1_1_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c16">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a>, <a class="txt" href="#E3:14_1_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E61">A277</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E10:14_1_1_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="c15">o</font>,<font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_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="c16">a</font>,<font color="Maroon" title="c15">o</font>,<font color="Maroon" title="c21">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:14_1_1_1_1_2_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_1"><span class="lab"><font color="Green" title="E33">A27</font></span></a>, <a class="txt" href="#E12:14_1_1_1"><span class="lab"><font color="Green" title="E41">A35</font></span></a>, <a class="txt" href="#E13:14_1_1_1"><span class="lab"><font color="Green" title="E42">A36</font></span></a>, <a class="txt" href="#E16:14_1_1_1"><span class="lab"><font color="Green" title="E45">A39</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E60">A276</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_2_2"><span class="lab"><font color="Green" title="E59">A274</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a>, <a class="ref" href="aff_1.html#T51" onmouseover="rs('aff_1/T51')" onmouseout="rh()">AFF_1:51</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1_2_2"><span class="lab"><font color="Green" title="E57">A266</font></span></a>, <a class="ref" href="aff_1.html#T3" onmouseover="rs('aff_1/T3')" onmouseout="rh()">AFF_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_1_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1_2"><span class="lab"><font color="Green" title="E56">A73</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_1_1"><span class="lab"><font color="Green" title="E53">A47</font></span></a>, <a class="ref" href="aff_1.html#T3" onmouseover="rs('aff_1/T3')" onmouseout="rh()">AFF_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E24:14_1_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a</font>,<font color="Maroon" title="c19">a1</font>,<font color="Maroon" title="c22">d</font> or <font color="Maroon" title="c17">b</font>,<font color="Maroon" title="c18">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">b1</font>,<font color="Maroon" title="c21">c1</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E30">A278</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">Z</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c4">M</font></span></a><div class="add"><a NAME="E1:14_1_1_2"/><span class="lab"><font color="Green" title="E31">A279</font></span>: 
<font color="Maroon" title="c4">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c12">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:14_1_1_2"/><span class="lab"><font color="Green" title="E32">A280</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">and </span><br/><a NAME="E4:14_1_1_2"/><span class="lab"><font color="Green" title="E33">A281</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/><a NAME="E5:14_1_1_2"/><span class="lab"><font color="Green" title="E34">A282</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E16:14_1_1"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E17:14_1_1"><span class="lab"><font color="Green" title="E25">A19</font></span></a>, <a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E21:14_1_1"><span class="lab"><font color="Green" title="E29">A23</font></span></a>, <a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="txt" href="#E4:14_1_1_2"><span class="lab"><font color="Green" title="E33">A281</font></span></a></span>;<br/><a NAME="E6:14_1_1_2"/><span class="lab"><font color="Green" title="E35">A283</font></span>: 
(  not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> &amp;  not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E36">A284</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_2_1_1"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A285</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><a NAME="E3:14_1_1_2_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><span class="kw">hence </span><a NAME="E4:14_1_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="txt" href="#E17:14_1_1"><span class="lab"><font color="Green" title="E25">A19</font></span></a>, <a class="txt" href="#E2:14_1_1_2_1_1"><span class="lab"><font color="Green" title="E37">A285</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E37">A286</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_1_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_2_1_2"/>
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A287</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><a NAME="E3:14_1_1_2_1_2"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/><span class="kw">hence </span><a NAME="E4:14_1_1_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="txt" href="#E16:14_1_1"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E2:14_1_1_2_1_2"><span class="lab"><font color="Green" title="E38">A287</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:14_1_1_2_1"/>
( <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font> or <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_1"><span class="lab"><font color="Green" title="E37">A286</font></span></a>, <a class="txt" href="#E1:14_1_1_2_1"><span class="lab"><font color="Green" title="E36">A284</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E7:14_1_1_2"/><span class="lab"><font color="Green" title="E36">A288</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/>( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</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="c3">Z</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c13">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:14_1_1_2_2"/><span class="lab"><font color="Green" title="E37">A289</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1_2_2"/><span class="lab"><font color="Green" title="E38">A290</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:14_1_1_2_2"/><span class="lab"><font color="Green" title="E39">A291</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_2_2"/><span class="lab"><font color="Green" title="E40">A292</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<a NAME="E7:14_1_1_2_2"/>
 not <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_2_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_2"><span class="lab"><font color="Green" title="E37">A289</font></span></a>, <a class="txt" href="#E3:14_1_1_2_2"><span class="lab"><font color="Green" title="E38">A290</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_2_2"><span class="lab"><font color="Green" title="E39">A291</font></span></a>, <a class="txt" href="#E6:14_1_1_2_2"><span class="lab"><font color="Green" title="E40">A292</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E4:14_1_1_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E5:14_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="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="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="E9:14_1_1_2_2"/><span class="lab"><font color="Green" title="E41">A293</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">and </span><br/><a NAME="E10:14_1_1_2_2"/><span class="lab"><font color="Green" title="E42">A294</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>,<font color="Maroon" title="c15">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/>
<a NAME="E11:14_1_1_2_2"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c15">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1_2_2"><span class="lab"><font color="Green" title="E41">A293</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c15">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_2"><span class="lab"><font color="Green" title="E37">A289</font></span></a>, <a class="txt" href="#E3:14_1_1_2_2"><span class="lab"><font color="Green" title="E38">A290</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E13:14_1_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A295</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c15">d1</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</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="c3">Z</font> )</span><br/>

<a NAME="E14:14_1_1_2_2"/>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14_1_1_2_2"><span class="lab"><font color="Green" title="E42">A294</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_2_2"/>
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</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="c3">Z</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E5:14_1_1_2_2"><span class="lab"><font color="Green" title="E39">A291</font></span></a>, <a class="txt" href="#E6:14_1_1_2_2"><span class="lab"><font color="Green" title="E40">A292</font></span></a>, <a class="txt" href="#E13:14_1_1_2_2"><span class="lab"><font color="Green" title="E43">A295</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E8:14_1_1_2"/><span class="lab"><font color="Green" title="E37">A296</font></span>: 
<font color="Maroon" title="c3">Z</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c3">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E9:14_1_1_2"/><span class="lab"><font color="Green" title="E38">A297</font></span>: 
( <font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a1</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_3"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E39">A298</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_3_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a1</font></span></a><div class="add"><a NAME="E1:14_1_1_2_3_1"/><span class="lab"><font color="Green" title="E40">A299</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_3_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_3_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_3_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_2_3_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_2_3_1"/><span class="lab"><font color="Green" title="E41">A300</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_3_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_3_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_3_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_2_3_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E3:14_1_1_2_3_1"/><span class="lab"><font color="Green" title="E42">A301</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:14_1_1_2_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E5:14_1_1_2_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A302</font></span>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E1:14_1_1_2"><span class="lab"><font color="Green" title="E31">A279</font></span></a>, <a class="txt" href="#E2:14_1_1_2_3_1"><span class="lab"><font color="Green" title="E41">A300</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a></span>;<br/><a NAME="E6:14_1_1_2_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E3:14_1_1_2_3_1"><span class="lab"><font color="Green" title="E42">A301</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E7:14_1_1_2_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E8:14_1_1_2"><span class="lab"><font color="Green" title="E37">A296</font></span></a>, <a class="txt" href="#E1:14_1_1_2_3_1"><span class="lab"><font color="Green" title="E40">A299</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a></span>;<br/><span class="kw">hence </span><a NAME="E8:14_1_1_2_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E5:14_1_1_2_3_1"><span class="lab"><font color="Green" title="E43">A302</font></span></a>, <a class="ref" href="aff_1.html#T2" onmouseover="rs('aff_1/T2')" onmouseout="rh()">AFF_1:2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E40">A303</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_3_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_2_3_2"/>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_2_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E3:14_1_1_2_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A304</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E4:14_1_1_2_3_2"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><span class="kw">hence </span><a NAME="E5:14_1_1_2_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E1:14_1_1_2_3"><span class="lab"><font color="Green" title="E39">A298</font></span></a>, <a class="txt" href="#E3:14_1_1_2_3_2"><span class="lab"><font color="Green" title="E41">A304</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E41">A305</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_3_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_2_3_3"/>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_2_3_3"/><span class="kw">then </span>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E3:14_1_1_2_3_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A306</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E4:14_1_1_2_3_3"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><span class="kw">hence </span><a NAME="E5:14_1_1_2_3_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E1:14_1_1_2_3"><span class="lab"><font color="Green" title="E39">A298</font></span></a>, <a class="txt" href="#E3:14_1_1_2_3_3"><span class="lab"><font color="Green" title="E42">A306</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E4:14_1_1_2_3"/>
(  not <font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a1</font> or  not <font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font> or  not <font color="Maroon" title="c8">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E5:14_1_1_2_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_2_3"><span class="lab"><font color="Green" title="E39">A298</font></span></a>, <a class="txt" href="#E2:14_1_1_2_3"><span class="lab"><font color="Green" title="E40">A303</font></span></a>, <a class="txt" href="#E3:14_1_1_2_3"><span class="lab"><font color="Green" title="E41">A305</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E10:14_1_1_2"/><span class="lab"><font color="Green" title="E39">A307</font></span>: 
( <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> &amp; <font color="Maroon" title="c10">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> &amp; <font color="Maroon" title="c11">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E40">A308</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_2_4_1"/><span class="lab"><font color="Green" title="E41">A309</font></span>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_2_4_1"/><span class="lab"><font color="Green" title="E42">A310</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_4_1_1"/><span class="lab"><font color="Green" title="E43">A311</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_4_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_4_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_2_4_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_4_1_1"/><span class="lab"><font color="Green" title="E44">A312</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_4_1_1"/><span class="lab"><font color="Green" title="E45">A313</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_2_4_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E1:14_1_1_2_4_1"><span class="lab"><font color="Green" title="E41">A309</font></span></a>, <a class="txt" href="#E2:14_1_1_2_4_1_1"><span class="lab"><font color="Green" title="E44">A312</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_2_4_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E6:14_1_1_2_4_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:14_1_1_2_4_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E8:14_1_1_2_4_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_2_4_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E3:14_1_1_2_4_1_1"><span class="lab"><font color="Green" title="E45">A313</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E10:14_1_1_2_4_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_2_4_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E12:14_1_1_2_4_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A314</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:14_1_1_2_4_1_1"/>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E14:14_1_1_2_4_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_2_4_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_4_1_1"><span class="lab"><font color="Green" title="E44">A312</font></span></a>, <a class="txt" href="#E1:14_1_1_2_4_1_1"><span class="lab"><font color="Green" title="E43">A311</font></span></a>, <a class="txt" href="#E12:14_1_1_2_4_1_1"><span class="lab"><font color="Green" title="E46">A314</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:14_1_1_2_4_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_1_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_4_1_2"/><span class="lab"><font color="Green" title="E43">A315</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_4_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_4_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="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_2_4_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_4_1_2"/><span class="lab"><font color="Green" title="E44">A316</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_4_1_2"/><span class="lab"><font color="Green" title="E45">A317</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_2_4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E1:14_1_1_2_4_1"><span class="lab"><font color="Green" title="E41">A309</font></span></a>, <a class="txt" href="#E2:14_1_1_2_4_1_2"><span class="lab"><font color="Green" title="E44">A316</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_2_4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E6:14_1_1_2_4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:14_1_1_2_4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E8:14_1_1_2_4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_2_4_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E3:14_1_1_2_4_1_2"><span class="lab"><font color="Green" title="E45">A317</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E10:14_1_1_2_4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_2_4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E12:14_1_1_2_4_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A318</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:14_1_1_2_4_1_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E14:14_1_1_2_4_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_2_4_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_4_1_2"><span class="lab"><font color="Green" title="E44">A316</font></span></a>, <a class="txt" href="#E1:14_1_1_2_4_1_2"><span class="lab"><font color="Green" title="E43">A315</font></span></a>, <a class="txt" href="#E12:14_1_1_2_4_1_2"><span class="lab"><font color="Green" title="E46">A318</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:14_1_1_2_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E2:14_1_1_2_4_1"><span class="lab"><font color="Green" title="E42">A310</font></span></a>, <a class="ref" href="aff_1.html#T3" onmouseover="rs('aff_1/T3')" onmouseout="rh()">AFF_1:3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E41">A319</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c10">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font></span></a><div class="add"><a NAME="E1:14_1_1_2_4_2"/><span class="lab"><font color="Green" title="E42">A320</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_4_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_4_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_2_4_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_2_4_2"/><span class="lab"><font color="Green" title="E43">A321</font></span>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><span class="kw">assume </span><a NAME="E3:14_1_1_2_4_2"/>
<font color="Maroon" title="c10">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:14_1_1_2_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E1:14_1_1_2_4"><span class="lab"><font color="Green" title="E40">A308</font></span></a>, <a class="txt" href="#E2:14_1_1_2_4_2"><span class="lab"><font color="Green" title="E43">A321</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E5:14_1_1_2_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E6:14_1_1_2_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E7:14_1_1_2_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E8:14_1_1_2_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E9:14_1_1_2_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1_2"><span class="lab"><font color="Green" title="E38">A297</font></span></a>, <a class="txt" href="#E2:14_1_1_2_4_2"><span class="lab"><font color="Green" title="E43">A321</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E10:14_1_1_2_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E11:14_1_1_2_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E12:14_1_1_2_4_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A322</font></span>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E13:14_1_1_2_4_2"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E14:14_1_1_2_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E15:14_1_1_2_4_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_2_4"><span class="lab"><font color="Green" title="E40">A308</font></span></a>, <a class="txt" href="#E1:14_1_1_2_4_2"><span class="lab"><font color="Green" title="E42">A320</font></span></a>, <a class="txt" href="#E12:14_1_1_2_4_2"><span class="lab"><font color="Green" title="E44">A322</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E42">A323</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c11">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font></span></a><div class="add"><a NAME="E1:14_1_1_2_4_3"/><span class="lab"><font color="Green" title="E43">A324</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_4_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_4_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_2_4_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_2_4_3"/><span class="lab"><font color="Green" title="E44">A325</font></span>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><span class="kw">assume </span><a NAME="E3:14_1_1_2_4_3"/>
<font color="Maroon" title="c11">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:14_1_1_2_4_3"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E1:14_1_1_2_4"><span class="lab"><font color="Green" title="E40">A308</font></span></a>, <a class="txt" href="#E2:14_1_1_2_4_3"><span class="lab"><font color="Green" title="E44">A325</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E5:14_1_1_2_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E6:14_1_1_2_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E7:14_1_1_2_4_3"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E8:14_1_1_2_4_3"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E9:14_1_1_2_4_3"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1_2"><span class="lab"><font color="Green" title="E38">A297</font></span></a>, <a class="txt" href="#E2:14_1_1_2_4_3"><span class="lab"><font color="Green" title="E44">A325</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E10:14_1_1_2_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E11:14_1_1_2_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E12:14_1_1_2_4_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A326</font></span>: 
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E13:14_1_1_2_4_3"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/><a NAME="E14:14_1_1_2_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E15:14_1_1_2_4_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_2_4"><span class="lab"><font color="Green" title="E40">A308</font></span></a>, <a class="txt" href="#E1:14_1_1_2_4_3"><span class="lab"><font color="Green" title="E43">A324</font></span></a>, <a class="txt" href="#E12:14_1_1_2_4_3"><span class="lab"><font color="Green" title="E45">A326</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E4:14_1_1_2_4"/>
(  not <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> or  not <font color="Maroon" title="c10">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> or  not <font color="Maroon" title="c11">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E5:14_1_1_2_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_2_4"><span class="lab"><font color="Green" title="E40">A308</font></span></a>, <a class="txt" href="#E2:14_1_1_2_4"><span class="lab"><font color="Green" title="E41">A319</font></span></a>, <a class="txt" href="#E3:14_1_1_2_4"><span class="lab"><font color="Green" title="E42">A323</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E11:14_1_1_2"/>
 ex <font color="Olive" title="b1">d2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Olive" title="b1">d2</font> &amp; <font color="Olive" title="b1">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c13">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:14_1_1_2_5"/><span class="lab"><font color="Green" title="E40">A327</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1_2_5"/><span class="lab"><font color="Green" title="E41">A328</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:14_1_1_2_5"/><span class="lab"><font color="Green" title="E42">A329</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_2_5"/><span class="lab"><font color="Green" title="E43">A330</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<a NAME="E7:14_1_1_2_5"/>
 not <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_5_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_5_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_5"><span class="lab"><font color="Green" title="E40">A327</font></span></a>, <a class="txt" href="#E3:14_1_1_2_5"><span class="lab"><font color="Green" title="E41">A328</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_2_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_2_5"><span class="lab"><font color="Green" title="E42">A329</font></span></a>, <a class="txt" href="#E6:14_1_1_2_5"><span class="lab"><font color="Green" title="E43">A330</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E4:14_1_1_2_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E5:14_1_1_2_5_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_2_5_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">d2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E9:14_1_1_2_5"/><span class="lab"><font color="Green" title="E44">A331</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font>,<font color="Maroon" title="c15">d2</font>
 <span class="kw">and </span><br/><a NAME="E10:14_1_1_2_5"/><span class="lab"><font color="Green" title="E45">A332</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font>,<font color="Maroon" title="c15">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/>
<a NAME="E11:14_1_1_2_5"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c15">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1_2_5"><span class="lab"><font color="Green" title="E44">A331</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c15">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_5"><span class="lab"><font color="Green" title="E40">A327</font></span></a>, <a class="txt" href="#E3:14_1_1_2_5"><span class="lab"><font color="Green" title="E41">A328</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E13:14_1_1_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A333</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c15">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c15">d2</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d2</font> &amp; <font color="Maroon" title="c15">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )</span><br/>

<a NAME="E14:14_1_1_2_5"/>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14_1_1_2_5"><span class="lab"><font color="Green" title="E45">A332</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_2_5"/>
( <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d2</font> &amp; <font color="Maroon" title="c15">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E5:14_1_1_2_5"><span class="lab"><font color="Green" title="E42">A329</font></span></a>, <a class="txt" href="#E6:14_1_1_2_5"><span class="lab"><font color="Green" title="E43">A330</font></span></a>, <a class="txt" href="#E13:14_1_1_2_5"><span class="lab"><font color="Green" title="E46">A333</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">d2</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="E13:14_1_1_2"/><span class="lab"><font color="Green" title="E40">A334</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">and </span><br/><a NAME="E14:14_1_1_2"/><span class="lab"><font color="Green" title="E41">A335</font></span>: 
<font color="Maroon" title="c13">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c14">d1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E16:14_1_1_2"/><span class="lab"><font color="Green" title="E42">A336</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d1</font>
 <span class="kw">and </span><br/><a NAME="E17:14_1_1_2"/><span class="lab"><font color="Green" title="E43">A337</font></span>: 
<font color="Maroon" title="c14">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_2"><span class="lab"><font color="Green" title="E36">A288</font></span></a></span>;<br/><span class="kw">assume </span><a NAME="E18:14_1_1_2"/><span class="lab"><font color="Green" title="E44">A338</font></span>: 
 not <font color="Maroon" title="c3">Z</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c4">M</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E19:14_1_1_2"/><span class="lab"><font color="Green" title="E45">A339</font></span>: 
<font color="Maroon" title="c14">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d2</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_6"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_6"/><span class="lab"><font color="Green" title="E46">A340</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_6_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_6_1"/><span class="lab"><font color="Green" title="E47">A341</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_6_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_6_1_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_6_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E3:14_1_1_2_6_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_2_6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A342</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E5:14_1_1_2_6_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:14_1_1_2_6_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E18:14_1_1_2"><span class="lab"><font color="Green" title="E44">A338</font></span></a>, <a class="txt" href="#E4:14_1_1_2_6_1_1"><span class="lab"><font color="Green" title="E48">A342</font></span></a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:14_1_1_2_6_1"/><span class="lab"><font color="Green" title="E48">A343</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_2"><span class="lab"><font color="Green" title="E34">A282</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E3:14_1_1_2_6_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_2_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1_2"><span class="lab"><font color="Green" title="E38">A297</font></span></a>, <a class="txt" href="#E2:14_1_1_2_6_1"><span class="lab"><font color="Green" title="E48">A343</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_2_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E6:14_1_1_2_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E7:14_1_1_2_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_2_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A344</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<span class="kw">assume </span><a NAME="E9:14_1_1_2_6_1"/>
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">d1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E10:14_1_1_2_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:14_1_1_2"><span class="lab"><font color="Green" title="E42">A336</font></span></a>, <a class="txt" href="#E1:14_1_1_2_6_1"><span class="lab"><font color="Green" title="E47">A341</font></span></a>, <a class="txt" href="#E8:14_1_1_2_6_1"><span class="lab"><font color="Green" title="E49">A344</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E11:14_1_1_2_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_2_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E13:14_1_1_2_6_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_6"/>
<font color="Maroon" title="c14">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A345</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c14">d1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E14:14_1_1_2"><span class="lab"><font color="Green" title="E41">A335</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E4:14_1_1_2_6"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c14">d1</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E17:14_1_1_2"><span class="lab"><font color="Green" title="E43">A337</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_2_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1_1_2"><span class="lab"><font color="Green" title="E44">A338</font></span></a>, <a class="txt" href="#E3:14_1_1_2_6"><span class="lab"><font color="Green" title="E47">A345</font></span></a>, <a class="txt" href="#E1:14_1_1_2_6"><span class="lab"><font color="Green" title="E46">A340</font></span></a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E46">A346</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_2_7"/><span class="lab"><font color="Green" title="E47">A347</font></span>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_2_7"/>
 ex <font color="Olive" title="b1">d5</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">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Olive" title="b1">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>,<font color="Olive" title="b1">d5</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c15">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:14_1_1_2_7_1"/><span class="lab"><font color="Green" title="E48">A348</font></span>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1_2_7_1"/><span class="lab"><font color="Green" title="E49">A349</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c16">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:14_1_1_2_7_1"/><span class="lab"><font color="Green" title="E50">A350</font></span>: 
<font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c16">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:14_1_1_2_7_1"/><span class="lab"><font color="Green" title="E51">A351</font></span>: 
<font color="Maroon" title="c14">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<a NAME="E7:14_1_1_2_7_1"/>
 not <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c16">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_7_1_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c16">e2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_7_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E50">A350</font></span></a>, <a class="txt" href="#E6:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E51">A351</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_2_7_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E48">A348</font></span></a>, <a class="txt" href="#E3:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E49">A349</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_2_7_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E45">A339</font></span></a>, <a class="txt" href="#E1:14_1_1_2_7"><span class="lab"><font color="Green" title="E47">A347</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c17">d5</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E9:14_1_1_2_7_1"/><span class="lab"><font color="Green" title="E52">A352</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font>,<font color="Maroon" title="c17">d5</font>
 <span class="kw">and </span><br/><a NAME="E10:14_1_1_2_7_1"/><span class="lab"><font color="Green" title="E53">A353</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c16">e2</font>,<font color="Maroon" title="c17">d5</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/>
<a NAME="E11:14_1_1_2_7_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c17">d5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E52">A352</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_2_7_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A354</font></span>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c17">d5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E48">A348</font></span></a>, <a class="txt" href="#E3:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E49">A349</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c17">d5</font>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  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">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c17">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c17">d5</font> )</span><br/>

<a NAME="E13:14_1_1_2_7_1"/>
<font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c16">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c17">d5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E53">A353</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E14:14_1_1_2_7_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c17">d5</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E50">A350</font></span></a>, <a class="txt" href="#E6:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E51">A351</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_2_7_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c17">d5</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c17">d5</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E54">A354</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">d5</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="E4:14_1_1_2_7"/><span class="lab"><font color="Green" title="E48">A355</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c15">d5</font>
 <span class="kw">and </span><br/><a NAME="E5:14_1_1_2_7"/><span class="lab"><font color="Green" title="E49">A356</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c15">d5</font>
 ;<br/><a NAME="E6:14_1_1_2_7"/><span class="lab"><font color="Green" title="E50">A357</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E9:14_1_1_2"><span class="lab"><font color="Green" title="E38">A297</font></span></a>, <a class="txt" href="#E5:14_1_1_2"><span class="lab"><font color="Green" title="E34">A282</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><div><span class="lab"><font color="Green" title="E51">A358</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_2"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d5</font></span></a><div class="add"><a NAME="E1:14_1_1_2_7_2"/><span class="lab"><font color="Green" title="E52">A359</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_7_2_1"/><span class="lab"><font color="Green" title="E53">A360</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_2_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_7_2_1_1"/><span class="lab"><font color="Green" title="E54">A361</font></span>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_2_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_7_2_1_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_2_7_2_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A362</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_2_7_2_1_1_1"/>
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_2_7_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E39">A307</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7_2_1_1_1"><span class="lab"><font color="Green" title="E55">A362</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_7_2_1_1"/><span class="lab"><font color="Green" title="E55">A363</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_7_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="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E4:14_1_1_2_7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:14_1_1_2_7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_2_7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E7:14_1_1_2_7_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="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_2_7_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="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c9">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E9:14_1_1_2_7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c9">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:14_1_1_2_7_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A364</font></span>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E11:14_1_1_2_7_2_1_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7_2_1_1"><span class="lab"><font color="Green" title="E55">A363</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_2_7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E13:14_1_1_2_7_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:14_1_1_2_7_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E10:14_1_1_2_7_2_1_1"><span class="lab"><font color="Green" title="E56">A364</font></span></a>, <a class="txt" href="#E1:14_1_1_2_7_2_1_1"><span class="lab"><font color="Green" title="E54">A361</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_7_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_7_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E4:14_1_1_2_7_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E6:14_1_1_2_7"><span class="lab"><font color="Green" title="E50">A357</font></span></a>, <a class="txt" href="#E1:14_1_1_2_7_2_1"><span class="lab"><font color="Green" title="E53">A360</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E5:14_1_1_2_7_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A365</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E6:14_1_1_2_7_2_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_2_7_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E16:14_1_1"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E5:14_1_1_2_7_2_1"><span class="lab"><font color="Green" title="E54">A365</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_2_7_2"/><span class="lab"><font color="Green" title="E53">A366</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d5</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_2_7_2"/><span class="lab"><font color="Green" title="E54">A367</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_2_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_7_2_2"/><span class="lab"><font color="Green" title="E55">A368</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_7_2_2"/><span class="lab"><font color="Green" title="E56">A369</font></span>: 
<font color="Maroon" title="c5">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_7_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E4:14_1_1_2_7_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:14_1_1_2_7_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A370</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E1:14_1_1_2_7_2_2"><span class="lab"><font color="Green" title="E55">A368</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_2_7_2_2"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E7:14_1_1_2_7_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E5:14_1_1_2_7_2_2"><span class="lab"><font color="Green" title="E57">A370</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E8:14_1_1_2_7_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_2_7_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E10:14_1_1_2_7_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_2_7_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A371</font></span>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E12:14_1_1_2_7_2_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7_2_2"><span class="lab"><font color="Green" title="E56">A369</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:14_1_1_2_7_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E14:14_1_1_2_7_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E1:14_1_1_2_7_2_2"><span class="lab"><font color="Green" title="E55">A368</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_2_7_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E39">A307</font></span></a>, <a class="txt" href="#E11:14_1_1_2_7_2_2"><span class="lab"><font color="Green" title="E58">A371</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E4:14_1_1_2_7_2"/><span class="lab"><font color="Green" title="E55">A372</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_2_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_7_2_3"/>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">d1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_7_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A373</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c3">Z</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E17:14_1_1_2"><span class="lab"><font color="Green" title="E43">A337</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E3:14_1_1_2_7_2_3"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E6:14_1_1_2_7"><span class="lab"><font color="Green" title="E50">A357</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_2_7_2_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E16:14_1_1"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E3:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E54">A367</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7_2_3"><span class="lab"><font color="Green" title="E56">A373</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:14_1_1_2_7_2"/><span class="lab"><font color="Green" title="E56">A374</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d2</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_2_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_7_2_4"/>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_7_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A375</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E14:14_1_1_2"><span class="lab"><font color="Green" title="E41">A335</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<a NAME="E3:14_1_1_2_7_2_4"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E6:14_1_1_2_7"><span class="lab"><font color="Green" title="E50">A357</font></span></a>, <a class="ref" href="aff_1.html#T52" onmouseover="rs('aff_1/T52')" onmouseout="rh()">AFF_1:52</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_2_7_2_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E17:14_1_1"><span class="lab"><font color="Green" title="E25">A19</font></span></a>, <a class="txt" href="#E3:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E54">A367</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7_2_4"><span class="lab"><font color="Green" title="E57">A375</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a>, <a class="ref" href="aff_1.html#T53" onmouseover="rs('aff_1/T53')" onmouseout="rh()">AFF_1:53</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:14_1_1_2_7_2"/><span class="lab"><font color="Green" title="E57">A376</font></span>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">d5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_2_7"><span class="lab"><font color="Green" title="E48">A355</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E7:14_1_1_2_7_2"/><span class="lab"><font color="Green" title="E58">A377</font></span>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E8:14_1_1_2_7_2"/>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="ref" href="aff_1.html#T3" onmouseover="rs('aff_1/T3')" onmouseout="rh()">AFF_1:3</a></span>;<br/><a NAME="E9:14_1_1_2_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c15">d5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E58">A377</font></span></a>, <a class="txt" href="#E6:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E57">A376</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E10:14_1_1_2_7_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1_2_7"><span class="lab"><font color="Green" title="E49">A356</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E53">A366</font></span></a>, <a class="txt" href="#E1:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E52">A359</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>;<br/><a NAME="E11:14_1_1_2_7_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E12:14_1_1_2_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E13:14_1_1_2_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:14_1_1_2"><span class="lab"><font color="Green" title="E42">A336</font></span></a>, <a class="txt" href="#E4:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E55">A372</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E14:14_1_1_2_7_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A378</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14_1_1_2"><span class="lab"><font color="Green" title="E40">A334</font></span></a>, <a class="txt" href="#E5:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E56">A374</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E15:14_1_1_2_7_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E16:14_1_1_2_7_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E17:14_1_1_2_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E18:14_1_1_2_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E19:14_1_1_2_7_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A379</font></span>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E20:14_1_1_2_7_2"/>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E14:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E59">A378</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E21:14_1_1_2_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E22:14_1_1_2_7_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E23:14_1_1_2_7_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E24:14_1_1_2_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E25:14_1_1_2_7_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A380</font></span>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E26:14_1_1_2_7_2"/>
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_2_5"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_7_2_5"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_2_7_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A381</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_2_7_2_5"/>
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_2_7_2_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E39">A307</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7_2_5"><span class="lab"><font color="Green" title="E62">A381</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E27:14_1_1_2_7_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E25:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E61">A380</font></span></a>, <a class="txt" href="#E19:14_1_1_2_7_2"><span class="lab"><font color="Green" title="E60">A379</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E8:14_1_1_2_7"/>
 not <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E45">A339</font></span></a>, <a class="txt" href="#E1:14_1_1_2_7"><span class="lab"><font color="Green" title="E47">A347</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><span class="kw">hence </span><a NAME="E9:14_1_1_2_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E16:14_1_1"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E17:14_1_1"><span class="lab"><font color="Green" title="E25">A19</font></span></a>, <a class="txt" href="#E21:14_1_1"><span class="lab"><font color="Green" title="E29">A23</font></span></a>, <a class="txt" href="#E16:14_1_1_2"><span class="lab"><font color="Green" title="E42">A336</font></span></a>, <a class="txt" href="#E17:14_1_1_2"><span class="lab"><font color="Green" title="E43">A337</font></span></a>, <a class="txt" href="#E13:14_1_1_2"><span class="lab"><font color="Green" title="E40">A334</font></span></a>, <a class="txt" href="#E14:14_1_1_2"><span class="lab"><font color="Green" title="E41">A335</font></span></a>, <a class="txt" href="#E4:14_1_1_2_7"><span class="lab"><font color="Green" title="E48">A355</font></span></a>, <a class="txt" href="#E5:14_1_1_2_7"><span class="lab"><font color="Green" title="E49">A356</font></span></a>, <a class="txt" href="#E6:14_1_1_2_7"><span class="lab"><font color="Green" title="E50">A357</font></span></a>, <a class="txt" href="#E7:14_1_1_2_7"><span class="lab"><font color="Green" title="E51">A358</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font></span></a><div class="add"><a NAME="E1:14_1_1_2_8"/><span class="lab"><font color="Green" title="E47">A382</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E9:14_1_1_2"><span class="lab"><font color="Green" title="E38">A297</font></span></a>, <a class="txt" href="#E5:14_1_1_2"><span class="lab"><font color="Green" title="E34">A282</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/><a NAME="E2:14_1_1_2_8"/><span class="lab"><font color="Green" title="E48">A383</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_8_1"/><span class="lab"><font color="Green" title="E49">A384</font></span>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_8_1_1"/><span class="lab"><font color="Green" title="E50">A385</font></span>: 
( <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font> &amp; <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font> )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_8_1_1_1"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_2_8_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A386</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_2_8_1_1_1"/>
(  not <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font> or  not <font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font> )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_2_8_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E39">A307</font></span></a>, <a class="txt" href="#E2:14_1_1_2_8_1_1_1"><span class="lab"><font color="Green" title="E51">A386</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_8_1_1"/><span class="lab"><font color="Green" title="E51">A387</font></span>: 
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">d</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_8_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_2"><span class="lab"><font color="Green" title="E33">A281</font></span></a>, <a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E4:14_1_1_2_8_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:14_1_1_2_8_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8_1_1"><span class="lab"><font color="Green" title="E50">A385</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_2_8_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8_1_1"><span class="lab"><font color="Green" title="E50">A385</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E7:14_1_1_2_8_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:14_1_1_2_8_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E9:14_1_1_2_8_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:14_1_1_2_8_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A388</font></span>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E11:14_1_1_2_8_1_1"/>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c9">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_2"><span class="lab"><font color="Green" title="E33">A281</font></span></a>, <a class="txt" href="#E2:14_1_1_2_8_1_1"><span class="lab"><font color="Green" title="E51">A387</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:14_1_1_2_8_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E13:14_1_1_2_8_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8_1_1"><span class="lab"><font color="Green" title="E50">A385</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:14_1_1_2_8_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E10:14_1_1_2_8_1_1"><span class="lab"><font color="Green" title="E52">A388</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_8_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_8_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E4:14_1_1_2_8_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8"><span class="lab"><font color="Green" title="E47">A382</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8_1"><span class="lab"><font color="Green" title="E49">A384</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>;<br/>
<a NAME="E5:14_1_1_2_8_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E6:14_1_1_2_8_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_2_8_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E39">A307</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:14_1_1_2_8"/><span class="lab"><font color="Green" title="E49">A389</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">o</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_8_2"/><span class="lab"><font color="Green" title="E50">A390</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_8_2"/><span class="lab"><font color="Green" title="E51">A391</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">o</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_8_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E4:14_1_1_2_8_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:14_1_1_2_8_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A392</font></span>: 
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8_2"><span class="lab"><font color="Green" title="E50">A390</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E6:14_1_1_2_8_2"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E7:14_1_1_2_8_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14_1_1"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="txt" href="#E5:14_1_1_2_8_2"><span class="lab"><font color="Green" title="E52">A392</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<a NAME="E8:14_1_1_2_8_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_2_8_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/>
<a NAME="E10:14_1_1_2_8_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:14_1_1_2_8_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A393</font></span>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E12:14_1_1_2_8_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c5">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2"><span class="lab"><font color="Green" title="E32">A280</font></span></a>, <a class="txt" href="#E2:14_1_1_2_8_2"><span class="lab"><font color="Green" title="E51">A391</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:14_1_1_2_8_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E14:14_1_1_2_8_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c10">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8_2"><span class="lab"><font color="Green" title="E50">A390</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:14_1_1_2_8_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E39">A307</font></span></a>, <a class="txt" href="#E11:14_1_1_2_8_2"><span class="lab"><font color="Green" title="E53">A393</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E4:14_1_1_2_8"/><span class="lab"><font color="Green" title="E50">A394</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">d1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8_3"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_8_3"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8"><span class="lab"><font color="Green" title="E47">A382</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_2_8_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A395</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_2_8_3"/>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">d1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_2_8_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E17:14_1_1_2"><span class="lab"><font color="Green" title="E43">A337</font></span></a>, <a class="txt" href="#E3:14_1_1_2_8"><span class="lab"><font color="Green" title="E49">A389</font></span></a>, <a class="txt" href="#E2:14_1_1_2_8_3"><span class="lab"><font color="Green" title="E51">A395</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:14_1_1_2_8"/><span class="lab"><font color="Green" title="E51">A396</font></span>: 
<font color="Maroon" title="c12">d</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d2</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8_4"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_8_4"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8"><span class="lab"><font color="Green" title="E47">A382</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_2_8_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A397</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_2_8_4"/>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_2_8_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E14:14_1_1_2"><span class="lab"><font color="Green" title="E41">A335</font></span></a>, <a class="txt" href="#E3:14_1_1_2_8"><span class="lab"><font color="Green" title="E49">A389</font></span></a>, <a class="txt" href="#E2:14_1_1_2_8_4"><span class="lab"><font color="Green" title="E52">A397</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:14_1_1_2_8"/><span class="lab"><font color="Green" title="E52">A398</font></span>: 
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E13:14_1_1_2"><span class="lab"><font color="Green" title="E40">A334</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E7:14_1_1_2_8"/><span class="lab"><font color="Green" title="E53">A399</font></span>: 
<font color="Maroon" title="c10">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="ref" href="aff_1.html#T3" onmouseover="rs('aff_1/T3')" onmouseout="rh()">AFF_1:3</a></span>;<br/><a NAME="E8:14_1_1_2_8"/><span class="lab"><font color="Green" title="E54">A400</font></span>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_2"><span class="lab"><font color="Green" title="E33">A281</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E9:14_1_1_2_8"/><span class="lab"><font color="Green" title="E55">A401</font></span>: 
 not <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c15">d5</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="E11:14_1_1_2_8"/><span class="lab"><font color="Green" title="E56">A402</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c15">d5</font>
 <span class="kw">and </span><br/><a NAME="E12:14_1_1_2_8"/><span class="lab"><font color="Green" title="E57">A403</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c15">d5</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T60" onmouseover="rs('aff_1/T60')" onmouseout="rh()">AFF_1:60</a></span>;<br/><a NAME="E13:14_1_1_2_8"/>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c15">d5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1_2_8"><span class="lab"><font color="Green" title="E56">A402</font></span></a>, <a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E14:14_1_1_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A404</font></span>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c12">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c15">d5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14_1_1_2_8"><span class="lab"><font color="Green" title="E53">A399</font></span></a>, <a class="txt" href="#E8:14_1_1_2_8"><span class="lab"><font color="Green" title="E54">A400</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E15:14_1_1_2_8"/>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E16:14_1_1_2"><span class="lab"><font color="Green" title="E42">A336</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E16:14_1_1_2_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c15">d5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E8">A2</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E16:14_1_1"><span class="lab"><font color="Green" title="E24">A18</font></span></a>, <a class="txt" href="#E17:14_1_1"><span class="lab"><font color="Green" title="E25">A19</font></span></a>, <a class="txt" href="#E21:14_1_1"><span class="lab"><font color="Green" title="E29">A23</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E39">A307</font></span></a>, <a class="txt" href="#E17:14_1_1_2"><span class="lab"><font color="Green" title="E43">A337</font></span></a>, <a class="txt" href="#E14:14_1_1_2"><span class="lab"><font color="Green" title="E41">A335</font></span></a>, <a class="txt" href="#E9:14_1_1_2_8"><span class="lab"><font color="Green" title="E55">A401</font></span></a>, <a class="txt" href="#E11:14_1_1_2_8"><span class="lab"><font color="Green" title="E56">A402</font></span></a>, <a class="txt" href="#E12:14_1_1_2_8"><span class="lab"><font color="Green" title="E57">A403</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8"><span class="lab"><font color="Green" title="E47">A382</font></span></a>, <a class="txt" href="#E6:14_1_1_2_8"><span class="lab"><font color="Green" title="E52">A398</font></span></a></span>;<br/><a NAME="E17:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c12">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">d5</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1_2_8"><span class="lab"><font color="Green" title="E48">A383</font></span></a>, <a class="txt" href="#E14:14_1_1_2_8"><span class="lab"><font color="Green" title="E58">A404</font></span></a>, <a class="ref" href="aff_1.html#T14" onmouseover="rs('aff_1/T14')" onmouseout="rh()">AFF_1:14</a></span>;<br/><a NAME="E18:14_1_1_2_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d1</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:14_1_1_2_8"><span class="lab"><font color="Green" title="E57">A403</font></span></a>, <a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E19:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c14">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E20:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:14_1_1_2"><span class="lab"><font color="Green" title="E42">A336</font></span></a>, <a class="txt" href="#E4:14_1_1_2_8"><span class="lab"><font color="Green" title="E50">A394</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E21:14_1_1_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A405</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:14_1_1_2"><span class="lab"><font color="Green" title="E40">A334</font></span></a>, <a class="txt" href="#E5:14_1_1_2_8"><span class="lab"><font color="Green" title="E51">A396</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E22:14_1_1_2_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E23:14_1_1_2_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E24:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E25:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E26:14_1_1_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A406</font></span>: 
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E27:14_1_1_2_8"/>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E18:14_1_1"><span class="lab"><font color="Green" title="E26">A20</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E21:14_1_1_2_8"><span class="lab"><font color="Green" title="E59">A405</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E28:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c11">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E19:14_1_1"><span class="lab"><font color="Green" title="E27">A21</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>;<br/><a NAME="E29:14_1_1_2_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E30:14_1_1_2_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" onmouseover="rs('aff_1/T6')" onmouseout="rh()">AFF_1:6</a></span>;<br/><a NAME="E31:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c9">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/><a NAME="E32:14_1_1_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A407</font></span>: 
<font color="Maroon" title="c10">b1</font>,<font color="Maroon" title="c11">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c10">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/><a NAME="E33:14_1_1_2_8"/>
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b1</font>
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8_5"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_8_5"/>
<font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E9">A3</font></span></a>, <a class="txt" href="#E7:14_1_1"><span class="lab"><font color="Green" title="E15">A9</font></span></a>, <a class="txt" href="#E8:14_1_1"><span class="lab"><font color="Green" title="E16">A10</font></span></a>, <a class="txt" href="#E13:14_1_1"><span class="lab"><font color="Green" title="E21">A15</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_2_8_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A408</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">o</font>,<font color="Maroon" title="c9">a1</font>,<font color="Maroon" title="c6">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" onmouseover="rs('aff_1/D1')" onmouseout="rh()">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_2_8_5"/>
<font color="Maroon" title="c9">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b1</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_2_8_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="txt" href="#E14:14_1_1"><span class="lab"><font color="Green" title="E22">A16</font></span></a>, <a class="txt" href="#E6:14_1_1_2"><span class="lab"><font color="Green" title="E35">A283</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E39">A307</font></span></a>, <a class="txt" href="#E2:14_1_1_2_8_5"><span class="lab"><font color="Green" title="E62">A408</font></span></a>, <a class="ref" href="aff_1.html#T25" onmouseover="rs('aff_1/T25')" onmouseout="rh()">AFF_1:25</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E34:14_1_1_2_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E32:14_1_1_2_8"><span class="lab"><font color="Green" title="E61">A407</font></span></a>, <a class="txt" href="#E26:14_1_1_2_8"><span class="lab"><font color="Green" title="E60">A406</font></span></a>, <a class="ref" href="aff_1.html#T5" onmouseover="rs('aff_1/T5')" onmouseout="rh()">AFF_1:5</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E22:14_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E46">A346</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_1_3"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c3">Z</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c4">M</font></span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_3"/><span class="lab"><font color="Green" title="E31">A409</font></span>: 
<font color="Maroon" title="c3">Z</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c4">M</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A410</font></span>: 
<font color="Maroon" title="c10">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E10:14_1_1"><span class="lab"><font color="Green" title="E18">A12</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a></span>;<br/><a NAME="E3:14_1_1_3"/>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E9:14_1_1"><span class="lab"><font color="Green" title="E17">A11</font></span></a>, <a class="txt" href="#E1:14_1_1_3"><span class="lab"><font color="Green" title="E31">A409</font></span></a>, <a class="ref" href="aff_1.html#T45" onmouseover="rs('aff_1/T45')" onmouseout="rh()">AFF_1:45</a></span>;<br/><span class="kw">hence </span><a NAME="E4:14_1_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1"><span class="lab"><font color="Green" title="E19">A13</font></span></a>, <a class="txt" href="#E12:14_1_1"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E15:14_1_1"><span class="lab"><font color="Green" title="E23">A17</font></span></a>, <a class="txt" href="#E20:14_1_1"><span class="lab"><font color="Green" title="E28">A22</font></span></a>, <a class="txt" href="#E2:14_1_1_3"><span class="lab"><font color="Green" title="E32">A410</font></span></a>, <a class="ref" href="aff_1.html#T39" onmouseover="rs('aff_1/T39')" onmouseout="rh()">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" onmouseover="rs('aff_1/T41')" onmouseout="rh()">AFF_1:41</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E24:14_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1_1"><span class="lab"><font color="Green" title="E30">A278</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:14_1"/>
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_2.html#D4" onmouseover="rs('aff_2/D4')" onmouseout="rh()">AFF_2:def 4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:14"/>
( <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#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a>  )
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_2"/><span class="lab"><font color="Green" title="E8">A411</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a> </span><br/>

<a NAME="E2:14_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V8" title="AFF_2:attr.8">satisfying_TDES_1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_2.html#T3" onmouseover="rs('aff_2/T3')" onmouseout="rh()">AFF_2:3</a>, <a class="ref" href="aff_2.html#T12" onmouseover="rs('aff_2/T12')" onmouseout="rh()">AFF_2:12</a></span>;<br/>
<a NAME="E3:14_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V12" title="AFF_2:attr.12">satisfying_des_1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_2.html#T13" onmouseover="rs('aff_2/T13')" onmouseout="rh()">AFF_2:13</a></span>;<br/>
<a NAME="E4:14_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_2.html#T7" onmouseover="rs('aff_2/T7')" onmouseout="rh()">AFF_2:7</a></span>;<br/>
<a NAME="E5:14_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A412</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V1" title="CONMETR1:attr.1">satisfying_minor_Scherungssatz</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr1.html#T6" target="_self" onmouseover="rs('conmetr1/T6')" onmouseout="rh()">Th6</a></span>;<br/>
<a NAME="E6:14_2"/>
<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="txt" href="#E1:14_2"><span class="lab"><font color="Green" title="E8">A411</font></span></a>, <a class="ref" href="conmetr1.html#T7" target="_self" onmouseover="rs('conmetr1/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_2"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_2"><span class="lab"><font color="Green" title="E9">A412</font></span></a>, <a class="ref" href="conmetr1.html#T2" target="_self" onmouseover="rs('conmetr1/T2')" onmouseout="rh()">Th2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:14"/>
( <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V4" title="AFF_2:attr.4">Desarguesian</a>  iff <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V3" title="CONMETR1:attr.3">satisfying_Scherungssatz</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E7">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
