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

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR5" title="CONMETR1:NR.5">satisfies_minor_SCH*</a>  implies <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR1" title="CONMETR1:NR.1">satisfies_minor_SCH</a>  )</span><br/>

<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E10">A1</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR5" title="CONMETR1:NR.5">satisfies_minor_SCH*</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR1" title="CONMETR1:NR.1">satisfies_minor_SCH</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c5">a4</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c9">b4</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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#R4" title="AFF_1:pred.4">//</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/><b>let </b><font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c11">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</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/><b>assume </b><a NAME="E1:15_1"/><i><font color="Green" title="E11">A2</font></i>: 
( <font color="Maroon" title="c10">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:15_1"/><b>then </b><i><font color="Green" title="E12">A3</font></i>: 
( <font color="Maroon" title="c10">M</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c11">N</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  )
 <b>by </b><i><a class="ref" href="aff_1.html#T50" title="AFF_1:th.50">AFF_1:50</a></i>;<br/><b>then consider </b><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><b> such that </b><br/><a NAME="E4:15_1"/><i><font color="Green" title="E13">A4</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></i>;<br/><a NAME="E5:15_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" onclick="hs2(this)" href="javascript:()" title="15_1_1"><b>proof </b></a><div class="add">

<b>consider </b><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><b> such that </b><br/><a NAME="E2:15_1_1"/><i><font color="Green" title="E14">A5</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E4:15_1_1"/><i><font color="Green" title="E15">A6</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:15_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" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:15_1_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:15_1_1"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:15_1_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:15_1_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1_1"><i><font color="Green" title="E14">A5</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="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><b> such that </b><br/><a NAME="E7:15_1_1"/><i><font color="Green" title="E16">A7</font></i>: 
(  <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> &amp;  <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> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c15">d2</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="E8:15_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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:15_1_1"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:15_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:15_1_1"><i><font color="Green" title="E15">A6</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E10:15_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> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1_1"><i><font color="Green" title="E14">A5</font></i></a>, <a class="txt" href="conmetr1.html#E7:15_1_1"><i><font color="Green" title="E16">A7</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="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><b> such that </b><br/><a NAME="E7:15_1"/><i><font color="Green" title="E14">A8</font></i>: 
( <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> &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="c13">d2</font>,<font color="Maroon" title="c12">d1</font> )
 ;<br/><a NAME="E8:15_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" onclick="hs2(this)" href="javascript:()" title="15_1_2"><b>proof </b></a><div class="add">

<b>consider </b><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><b> such that </b><br/><a NAME="E2:15_1_2"/><i><font color="Green" title="E15">A9</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E4:15_1_2"/><i><font color="Green" title="E16">A10</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:15_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" onclick="hs2(this)" href="javascript:()" title="15_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:15_1_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:15_1_2"><i><font color="Green" title="E16">A10</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:15_1_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:15_1_2_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:15_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1_2"><i><font color="Green" title="E15">A9</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="c16">d3</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E7:15_1_2"/><i><font color="Green" title="E17">A11</font></i>: 
(  <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> &amp;  <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> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c16">d3</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="E8:15_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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:15_1_2"><i><font color="Green" title="E17">A11</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:15_1_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:15_1_2"><i><font color="Green" title="E16">A10</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<b>hence </b><a NAME="E10:15_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> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1_2"><i><font color="Green" title="E15">A9</font></i></a>, <a class="txt" href="conmetr1.html#E7:15_1_2"><i><font color="Green" title="E17">A11</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="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><b> such that </b><br/><a NAME="E10:15_1"/><i><font color="Green" title="E15">A12</font></i>: 
( <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> &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="c14">d3</font>,<font color="Maroon" title="c13">d2</font> )
 ;<br/><a NAME="E11:15_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" onclick="hs2(this)" href="javascript:()" title="15_1_3"><b>proof </b></a><div class="add">

<b>consider </b><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><b> such that </b><br/><a NAME="E2:15_1_3"/><i><font color="Green" title="E16">A13</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E4:15_1_3"/><i><font color="Green" title="E17">A14</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E5:15_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" onclick="hs2(this)" href="javascript:()" title="15_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_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" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:15_1_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E4:15_1_3"><i><font color="Green" title="E17">A14</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E3:15_1_3_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:15_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1_3"><i><font color="Green" title="E16">A13</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>then consider </b><font color="Maroon" title="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><b> such that </b><br/><a NAME="E7:15_1_3"/><i><font color="Green" title="E18">A15</font></i>: 
(  <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> &amp;  <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> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c17">d4</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="E8:15_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>
 
<b>by </b><i><a class="txt" href="conmetr1.html#E7:15_1_3"><i><font color="Green" title="E18">A15</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E9:15_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> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1"><i><font color="Green" title="E12">A3</font></i></a>, <a class="txt" href="conmetr1.html#E2:15_1_3"><i><font color="Green" title="E16">A13</font></i></a>, <a class="txt" href="conmetr1.html#E4:15_1_3"><i><font color="Green" title="E17">A14</font></i></a>, <a class="txt" href="conmetr1.html#E7:15_1_3"><i><font color="Green" title="E18">A15</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="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><b> such that </b><br/><a NAME="E13:15_1"/><i><font color="Green" title="E16">A16</font></i>: 
( <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> &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="c15">d4</font> )
 ;<br/><a NAME="E14:15_1"/><i><font color="Green" title="E17">A17</font></i>: 
( 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> &amp; 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> &amp; 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> &amp; 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> )
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E4:15_1"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="conmetr1.html#E7:15_1"><i><font color="Green" title="E14">A8</font></i></a>, <a class="txt" href="conmetr1.html#E10:15_1"><i><font color="Green" title="E15">A12</font></i></a>, <a class="txt" href="conmetr1.html#E13:15_1"><i><font color="Green" title="E16">A16</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></i>;<br/><a NAME="E15:15_1"/><b>then </b><i><font color="Green" title="E18">A18</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E4:15_1"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="conmetr1.html#E7:15_1"><i><font color="Green" title="E14">A8</font></i></a>, <a class="txt" href="conmetr1.html#E10:15_1"><i><font color="Green" title="E15">A12</font></i></a>, <a class="txt" href="conmetr1.html#E13:15_1"><i><font color="Green" title="E16">A16</font></i></a>, <a class="ref" href="conmetr1.html#D5" target="_self" title="CONMETR1:def.5">Def5</a></i>;<br/><a NAME="E16:15_1"/><i><font color="Green" title="E19">A19</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E7:15_1"><i><font color="Green" title="E14">A8</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E17:15_1"/><i><font color="Green" title="E20">A20</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E10:15_1"><i><font color="Green" title="E15">A12</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E18:15_1"/>
<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>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E13:15_1"><i><font color="Green" title="E16">A16</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E19:15_1"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conmetr1.html#E1:15"><i><font color="Green" title="E10">A1</font></i></a>, <a class="txt" href="conmetr1.html#E1:15_1"><i><font color="Green" title="E11">A2</font></i></a>, <a class="txt" href="conmetr1.html#E4:15_1"><i><font color="Green" title="E13">A4</font></i></a>, <a class="txt" href="conmetr1.html#E7:15_1"><i><font color="Green" title="E14">A8</font></i></a>, <a class="txt" href="conmetr1.html#E10:15_1"><i><font color="Green" title="E15">A12</font></i></a>, <a class="txt" href="conmetr1.html#E13:15_1"><i><font color="Green" title="E16">A16</font></i></a>, <a class="txt" href="conmetr1.html#E14:15_1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="conmetr1.html#E16:15_1"><i><font color="Green" title="E19">A19</font></i></a>, <a class="txt" href="conmetr1.html#E17:15_1"><i><font color="Green" title="E20">A20</font></i></a>, <a class="ref" href="conmetr1.html#D5" target="_self" title="CONMETR1:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E20:15_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>
 <b>by </b><i><a class="txt" href="conmetr1.html#E13:15_1"><i><font color="Green" title="E16">A16</font></i></a>, <a class="txt" href="conmetr1.html#E14:15_1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="conmetr1.html#E15:15_1"><i><font color="Green" title="E18">A18</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:15"/>
<font color="Maroon" title="c1">X</font> <a href="conmetr1.html#NR1" title="CONMETR1:NR.1">satisfies_minor_SCH</a> 
 <b>by </b><i><a class="ref" href="conmetr1.html#D1" target="_self" title="CONMETR1:def.1">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
