<?xml version="1.0"?>
<div class="add">

<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="conmetr1.html#V5" title="CONMETR1:attr.5">satisfying_minor_indirect_Scherungssatz</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V1" title="CONMETR1:attr.1">satisfying_minor_Scherungssatz</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:9"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V5" title="CONMETR1:attr.5">satisfying_minor_indirect_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="conmetr1.html#V1" title="CONMETR1:attr.1">satisfying_minor_Scherungssatz</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="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">  for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">a4</font>, <font color="Olive" title="b5">b1</font>, <font color="Olive" title="b6">b2</font>, <font color="Olive" title="b7">b3</font>, <font color="Olive" title="b8">b4</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><br/>  for <font color="Olive" title="b9">M</font>, <font color="Olive" title="b10">N</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b9">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b10">N</font> &amp; <font color="Olive" title="b1">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">M</font> &amp; <font color="Olive" title="b3">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">M</font> &amp; <font color="Olive" title="b5">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">M</font> &amp; <font color="Olive" title="b7">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">M</font> &amp; <font color="Olive" title="b2">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">N</font> &amp; <font color="Olive" title="b4">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">N</font> &amp; <font color="Olive" title="b6">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">N</font> &amp; <font color="Olive" title="b8">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">N</font> &amp;  not <font color="Olive" title="b4">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">M</font> &amp;  not <font color="Olive" title="b2">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">M</font> &amp;  not <font color="Olive" title="b6">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">M</font> &amp;  not <font color="Olive" title="b8">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">M</font> &amp;  not <font color="Olive" title="b1">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">N</font> &amp;  not <font color="Olive" title="b3">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">N</font> &amp;  not <font color="Olive" title="b5">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">N</font> &amp;  not <font color="Olive" title="b7">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b10">N</font> &amp; <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b2">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">b3</font>,<font color="Olive" title="b6">b2</font> &amp; <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b1">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b2</font>,<font color="Olive" title="b5">b1</font> &amp; <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b4">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b1</font>,<font color="Olive" title="b8">b4</font> holds <br/><font color="Olive" title="b3">a3</font>,<font color="Olive" title="b4">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b7">b3</font>,<font color="Olive" title="b8">b4</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c5">a4</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c9">b4</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.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">M</font>, <font color="Olive" title="b2">N</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp;  not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp;  not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp;  not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp;  not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp;  not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> holds <br/><font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c11">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.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">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp;  not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp;  not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp;  not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp;  not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp;  not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp;  not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp;  not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp;  not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> implies <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:9_1"/><span class="lab"><font color="Green" title="E5">A2</font></span>: 
<font color="Maroon" title="c10">M</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E2:9_1"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E3:9_1"/><span class="lab"><font color="Green" title="E7">A4</font></span>: 
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E4:9_1"/><span class="lab"><font color="Green" title="E8">A5</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E5:9_1"/><span class="lab"><font color="Green" title="E9">A6</font></span>: 
<font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E6:9_1"/><span class="lab"><font color="Green" title="E10">A7</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E7:9_1"/><span class="lab"><font color="Green" title="E11">A8</font></span>: 
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E8:9_1"/><span class="lab"><font color="Green" title="E12">A9</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E9:9_1"/><span class="lab"><font color="Green" title="E13">A10</font></span>: 
<font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E10:9_1"/><span class="lab"><font color="Green" title="E14">A11</font></span>: 
 not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E11:9_1"/><span class="lab"><font color="Green" title="E15">A12</font></span>: 
 not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E12:9_1"/><span class="lab"><font color="Green" title="E16">A13</font></span>: 
 not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E13:9_1"/><span class="lab"><font color="Green" title="E17">A14</font></span>: 
 not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E14:9_1"/><span class="lab"><font color="Green" title="E18">A15</font></span>: 
 not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E15:9_1"/><span class="lab"><font color="Green" title="E19">A16</font></span>: 
 not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E16:9_1"/><span class="lab"><font color="Green" title="E20">A17</font></span>: 
 not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E17:9_1"/><span class="lab"><font color="Green" title="E21">A18</font></span>: 
 not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E18:9_1"/><span class="lab"><font color="Green" title="E22">A19</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">and </span><br/><a NAME="E19:9_1"/><span class="lab"><font color="Green" title="E23">A20</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E20:9_1"/><span class="lab"><font color="Green" title="E24">A21</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 ; <a class="txt" onmouseover="tooltip.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="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E21:9_1"/><span class="lab"><font color="Green" title="E25">A22</font></span>: 
<font color="Maroon" title="c11">N</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="ref" href="aff_1.html#T36" onmouseover="rs('aff_1/T36')" onmouseout="rh()">AFF_1:36</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c12">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="E23:9_1"/>
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">d1</font>
 <span class="kw">and </span><br/><a NAME="E24:9_1"/><span class="lab"><font color="Green" title="E26">A23</font></span>: 
<font color="Maroon" title="c12">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T20" onmouseover="rs('aff_1/T20')" onmouseout="rh()">AFF_1:20</a></span>;<br/><a NAME="E25:9_1"/><span class="lab"><font color="Green" title="E27">A24</font></span>: 
 not <font color="Maroon" title="c12">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E7:9_1"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E10:9_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E24:9_1"><span class="lab"><font color="Green" title="E26">A23</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="E26:9_1"/><span class="lab"><font color="Green" title="E28">A25</font></span>: 
<font color="Maroon" title="c10">M</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="ref" href="aff_1.html#T36" onmouseover="rs('aff_1/T36')" onmouseout="rh()">AFF_1:36</a></span>;<br/><a NAME="E27:9_1"/>
 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="c10">M</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">d2</font>,<font color="Maroon" title="c12">d1</font> )
 <div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="9_1_1"><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="E2:9_1_1"/><span class="lab"><font color="Green" title="E29">A26</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:9_1_1"/><span class="lab"><font color="Green" title="E30">A27</font></span>: 
<font color="Maroon" title="c13">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:9_1"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="ref" href="aff_1.html#T20" onmouseover="rs('aff_1/T20')" onmouseout="rh()">AFF_1:20</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="E5:9_1_1"/><span class="lab"><font color="Green" title="E31">A28</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c14">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:9_1_1"/><span class="lab"><font color="Green" title="E32">A29</font></span>: 
<font color="Maroon" title="c12">d1</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="E7:9_1_1"/>
 not <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</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="9_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:9_1_1_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</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="E2:9_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:9_1_1"><span class="lab"><font color="Green" title="E31">A28</font></span></a>, <a class="txt" href="#E6:9_1_1"><span class="lab"><font color="Green" title="E32">A29</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="E3:9_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c13">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E4:9_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="c2">a1</font>,<font color="Maroon" title="c13">e1</font>,<font color="Maroon" title="c3">a2</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="E5:9_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9_1"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E11:9_1"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="txt" href="#E26:9_1"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E2:9_1_1"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E3:9_1_1"><span class="lab"><font color="Green" title="E30">A27</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="E9:9_1_1"/><span class="lab"><font color="Green" title="E33">A30</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c13">e1</font>,<font color="Maroon" title="c15">d2</font>
 <span class="kw">and </span><br/><a NAME="E10:9_1_1"/><span class="lab"><font color="Green" title="E34">A31</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d1</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/>
<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="c15">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">d2</font>,<font color="Maroon" title="c12">d1</font> )</span><br/>

<a NAME="E11:9_1_1"/>
<font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c14">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c15">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:9_1_1"><span class="lab"><font color="Green" title="E34">A31</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="E12:9_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c15">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:9_1_1"><span class="lab"><font color="Green" title="E31">A28</font></span></a>, <a class="txt" href="#E6:9_1_1"><span class="lab"><font color="Green" title="E32">A29</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="E13:9_1_1"/>
( <font color="Maroon" title="c15">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">d2</font>,<font color="Maroon" title="c12">d1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9_1"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E26:9_1"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E2:9_1_1"><span class="lab"><font color="Green" title="E29">A26</font></span></a>, <a class="txt" href="#E3:9_1_1"><span class="lab"><font color="Green" title="E30">A27</font></span></a>, <a class="txt" href="#E9:9_1_1"><span class="lab"><font color="Green" title="E33">A30</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</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="E29:9_1"/><span class="lab"><font color="Green" title="E29">A32</font></span>: 
<font color="Maroon" title="c13">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E30:9_1"/><span class="lab"><font color="Green" title="E30">A33</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c12">d1</font>
 ;<br/><a NAME="E31:9_1"/><span class="lab"><font color="Green" title="E31">A34</font></span>: 
 not <font color="Maroon" title="c13">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E7:9_1"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E10:9_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E29:9_1"><span class="lab"><font color="Green" title="E29">A32</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="E32:9_1"/>
 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="c11">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">d3</font>,<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="9_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c14">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:9_1_2"/><span class="lab"><font color="Green" title="E32">A35</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:9_1_2"/><span class="lab"><font color="Green" title="E33">A36</font></span>: 
<font color="Maroon" title="c14">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:9_1"><span class="lab"><font color="Green" title="E25">A22</font></span></a>, <a class="ref" href="aff_1.html#T20" onmouseover="rs('aff_1/T20')" onmouseout="rh()">AFF_1:20</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:9_1_2"/><span class="lab"><font color="Green" title="E34">A37</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c15">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:9_1_2"/><span class="lab"><font color="Green" title="E35">A38</font></span>: 
<font color="Maroon" title="c13">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" onmouseover="rs('diraf/T40')" onmouseout="rh()">DIRAF:40</a></span>;<br/>
<a NAME="E7:9_1_2"/>
 not <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c15">e2</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="9_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:9_1_2_1"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c15">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="E2:9_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:9_1_2"><span class="lab"><font color="Green" title="E34">A37</font></span></a>, <a class="txt" href="#E6:9_1_2"><span class="lab"><font color="Green" title="E35">A38</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="E3:9_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c14">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</a></span>;<br/>
<a NAME="E4:9_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c14">e1</font>,<font color="Maroon" title="c4">a3</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="E5:9_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:9_1"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="txt" href="#E15:9_1"><span class="lab"><font color="Green" title="E19">A16</font></span></a>, <a class="txt" href="#E21:9_1"><span class="lab"><font color="Green" title="E25">A22</font></span></a>, <a class="txt" href="#E2:9_1_2"><span class="lab"><font color="Green" title="E32">A35</font></span></a>, <a class="txt" href="#E3:9_1_2"><span class="lab"><font color="Green" title="E33">A36</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="c16">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="E9:9_1_2"/><span class="lab"><font color="Green" title="E36">A39</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c14">e1</font>,<font color="Maroon" title="c16">d3</font>
 <span class="kw">and </span><br/><a NAME="E10:9_1_2"/><span class="lab"><font color="Green" title="E37">A40</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c15">e2</font>,<font color="Maroon" title="c16">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="c16">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="c16">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">d3</font>,<font color="Maroon" title="c13">d2</font> )</span><br/>

<a NAME="E11:9_1_2"/>
<font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c15">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c16">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:9_1_2"><span class="lab"><font color="Green" title="E37">A40</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="E12:9_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c16">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:9_1_2"><span class="lab"><font color="Green" title="E34">A37</font></span></a>, <a class="txt" href="#E6:9_1_2"><span class="lab"><font color="Green" title="E35">A38</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="E13:9_1_2"/>
( <font color="Maroon" title="c16">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">d3</font>,<font color="Maroon" title="c13">d2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:9_1"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="txt" href="#E21:9_1"><span class="lab"><font color="Green" title="E25">A22</font></span></a>, <a class="txt" href="#E2:9_1_2"><span class="lab"><font color="Green" title="E32">A35</font></span></a>, <a class="txt" href="#E3:9_1_2"><span class="lab"><font color="Green" title="E33">A36</font></span></a>, <a class="txt" href="#E9:9_1_2"><span class="lab"><font color="Green" title="E36">A39</font></span></a>, <a class="ref" href="aff_1.html#T4" onmouseover="rs('aff_1/T4')" onmouseout="rh()">AFF_1:4</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="c14">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="E34:9_1"/><span class="lab"><font color="Green" title="E32">A41</font></span>: 
<font color="Maroon" title="c14">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E35:9_1"/><span class="lab"><font color="Green" title="E33">A42</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d3</font>,<font color="Maroon" title="c13">d2</font>
 ;<br/><a NAME="E36:9_1"/><span class="lab"><font color="Green" title="E34">A43</font></span>: 
 not <font color="Maroon" title="c14">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E7:9_1"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E10:9_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E34:9_1"><span class="lab"><font color="Green" title="E32">A41</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="E37:9_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="c10">M</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">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="9_1_3"><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="E2:9_1_3"/><span class="lab"><font color="Green" title="E35">A44</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:9_1_3"/><span class="lab"><font color="Green" title="E36">A45</font></span>: 
<font color="Maroon" title="c15">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:9_1"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="ref" href="aff_1.html#T20" onmouseover="rs('aff_1/T20')" onmouseout="rh()">AFF_1:20</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="E5:9_1_3"/><span class="lab"><font color="Green" title="E37">A46</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c16">e2</font>
 <span class="kw">and </span><br/><a NAME="E6:9_1_3"/><span class="lab"><font color="Green" title="E38">A47</font></span>: 
<font color="Maroon" title="c12">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="E7:9_1_3"/>
 not <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">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="9_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:9_1_3_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">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="E2:9_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c15">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:9_1_3"><span class="lab"><font color="Green" title="E37">A46</font></span></a>, <a class="txt" href="#E6:9_1_3"><span class="lab"><font color="Green" title="E38">A47</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="E3:9_1_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c15">e1</font>,<font color="Maroon" title="c5">a4</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="E4:9_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9_1"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E10:9_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E26:9_1"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E2:9_1_3"><span class="lab"><font color="Green" title="E35">A44</font></span></a>, <a class="txt" href="#E3:9_1_3"><span class="lab"><font color="Green" title="E36">A45</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="c17">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="E9:9_1_3"/><span class="lab"><font color="Green" title="E39">A48</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c15">e1</font>,<font color="Maroon" title="c17">d4</font>
 <span class="kw">and </span><br/><a NAME="E10:9_1_3"/><span class="lab"><font color="Green" title="E40">A49</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c16">e2</font>,<font color="Maroon" title="c17">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="c17">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="c17">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c17">d4</font> )</span><br/>

<a NAME="E11:9_1_3"/>
<font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c16">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c17">d4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:9_1_3"><span class="lab"><font color="Green" title="E40">A49</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="E12:9_1_3"/>
( <font color="Maroon" title="c17">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c17">d4</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9_1"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E26:9_1"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="txt" href="#E2:9_1_3"><span class="lab"><font color="Green" title="E35">A44</font></span></a>, <a class="txt" href="#E3:9_1_3"><span class="lab"><font color="Green" title="E36">A45</font></span></a>, <a class="txt" href="#E5:9_1_3"><span class="lab"><font color="Green" title="E37">A46</font></span></a>, <a class="txt" href="#E6:9_1_3"><span class="lab"><font color="Green" title="E38">A47</font></span></a>, <a class="txt" href="#E9:9_1_3"><span class="lab"><font color="Green" title="E39">A48</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="c15">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="E39:9_1"/><span class="lab"><font color="Green" title="E35">A50</font></span>: 
<font color="Maroon" title="c15">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E40:9_1"/><span class="lab"><font color="Green" title="E36">A51</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c15">d4</font>
 ;<br/><a NAME="E41:9_1"/><span class="lab"><font color="Green" title="E37">A52</font></span>: 
 not <font color="Maroon" title="c15">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E7:9_1"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E10:9_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E39:9_1"><span class="lab"><font color="Green" title="E35">A50</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="E42:9_1"/><span class="lab"><font color="Green" title="E38">A53</font></span>: 
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d2</font>,<font color="Maroon" title="c12">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9_1"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E11:9_1"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="txt" href="#E19:9_1"><span class="lab"><font color="Green" title="E23">A20</font></span></a>, <a class="txt" href="#E30:9_1"><span class="lab"><font color="Green" title="E30">A33</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="E43:9_1"/><span class="lab"><font color="Green" title="E39">A54</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">d1</font>,<font color="Maroon" title="c15">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:9_1"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E10:9_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E20:9_1"><span class="lab"><font color="Green" title="E24">A21</font></span></a>, <a class="txt" href="#E40:9_1"><span class="lab"><font color="Green" title="E36">A51</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="E44:9_1"/>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d3</font>,<font color="Maroon" title="c13">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:9_1"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E11:9_1"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="txt" href="#E18:9_1"><span class="lab"><font color="Green" title="E22">A19</font></span></a>, <a class="txt" href="#E35:9_1"><span class="lab"><font color="Green" title="E33">A42</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="E45:9_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A55</font></span>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d3</font>,<font color="Maroon" title="c15">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E1:9_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E4:9_1"><span class="lab"><font color="Green" title="E8">A5</font></span></a>, <a class="txt" href="#E5:9_1"><span class="lab"><font color="Green" title="E9">A6</font></span></a>, <a class="txt" href="#E8:9_1"><span class="lab"><font color="Green" title="E12">A9</font></span></a>, <a class="txt" href="#E9:9_1"><span class="lab"><font color="Green" title="E13">A10</font></span></a>, <a class="txt" href="#E12:9_1"><span class="lab"><font color="Green" title="E16">A13</font></span></a>, <a class="txt" href="#E13:9_1"><span class="lab"><font color="Green" title="E17">A14</font></span></a>, <a class="txt" href="#E16:9_1"><span class="lab"><font color="Green" title="E20">A17</font></span></a>, <a class="txt" href="#E17:9_1"><span class="lab"><font color="Green" title="E21">A18</font></span></a>, <a class="txt" href="#E24:9_1"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="txt" href="#E29:9_1"><span class="lab"><font color="Green" title="E29">A32</font></span></a>, <a class="txt" href="#E34:9_1"><span class="lab"><font color="Green" title="E32">A41</font></span></a>, <a class="txt" href="#E39:9_1"><span class="lab"><font color="Green" title="E35">A50</font></span></a>, <a class="txt" href="#E25:9_1"><span class="lab"><font color="Green" title="E27">A24</font></span></a>, <a class="txt" href="#E36:9_1"><span class="lab"><font color="Green" title="E34">A43</font></span></a>, <a class="txt" href="#E31:9_1"><span class="lab"><font color="Green" title="E31">A34</font></span></a>, <a class="txt" href="#E41:9_1"><span class="lab"><font color="Green" title="E37">A52</font></span></a>, <a class="txt" href="#E42:9_1"><span class="lab"><font color="Green" title="E38">A53</font></span></a>, <a class="txt" href="#E43:9_1"><span class="lab"><font color="Green" title="E39">A54</font></span></a></span>;<br/><a NAME="E46:9_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">d3</font>,<font color="Maroon" title="c15">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:9"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="#E1:9_1"><span class="lab"><font color="Green" title="E5">A2</font></span></a>, <a class="txt" href="#E2:9_1"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E3:9_1"><span class="lab"><font color="Green" title="E7">A4</font></span></a>, <a class="txt" href="#E6:9_1"><span class="lab"><font color="Green" title="E10">A7</font></span></a>, <a class="txt" href="#E7:9_1"><span class="lab"><font color="Green" title="E11">A8</font></span></a>, <a class="txt" href="#E10:9_1"><span class="lab"><font color="Green" title="E14">A11</font></span></a>, <a class="txt" href="#E11:9_1"><span class="lab"><font color="Green" title="E15">A12</font></span></a>, <a class="txt" href="#E14:9_1"><span class="lab"><font color="Green" title="E18">A15</font></span></a>, <a class="txt" href="#E15:9_1"><span class="lab"><font color="Green" title="E19">A16</font></span></a>, <a class="txt" href="#E24:9_1"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="txt" href="#E29:9_1"><span class="lab"><font color="Green" title="E29">A32</font></span></a>, <a class="txt" href="#E30:9_1"><span class="lab"><font color="Green" title="E30">A33</font></span></a>, <a class="txt" href="#E34:9_1"><span class="lab"><font color="Green" title="E32">A41</font></span></a>, <a class="txt" href="#E35:9_1"><span class="lab"><font color="Green" title="E33">A42</font></span></a>, <a class="txt" href="#E39:9_1"><span class="lab"><font color="Green" title="E35">A50</font></span></a>, <a class="txt" href="#E40:9_1"><span class="lab"><font color="Green" title="E36">A51</font></span></a>, <a class="txt" href="#E25:9_1"><span class="lab"><font color="Green" title="E27">A24</font></span></a>, <a class="txt" href="#E36:9_1"><span class="lab"><font color="Green" title="E34">A43</font></span></a>, <a class="txt" href="#E31:9_1"><span class="lab"><font color="Green" title="E31">A34</font></span></a>, <a class="txt" href="#E41:9_1"><span class="lab"><font color="Green" title="E37">A52</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E47:9_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:9_1"><span class="lab"><font color="Green" title="E35">A50</font></span></a>, <a class="txt" href="#E36:9_1"><span class="lab"><font color="Green" title="E34">A43</font></span></a>, <a class="txt" href="#E45:9_1"><span class="lab"><font color="Green" title="E40">A55</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="E3:9"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr1.html#V1" title="CONMETR1:attr.1">satisfying_minor_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"> verum</span><br/>


</div>
