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

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

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c6">a4</font>, <font color="Maroon" title="c7">b1</font>, <font color="Maroon" title="c8">b2</font>, <font color="Maroon" title="c9">b3</font>, <font color="Maroon" title="c10">b4</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><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> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Olive" title="b2">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font> holds <br/><font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><b>let </b><font color="Maroon" title="c11">M</font>, <font color="Maroon" title="c12">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c11">M</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c12">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font> implies <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font> )</span><br/><b>assume </b><a NAME="E1:13_1"/><i><font color="Green" title="E14">A2</font></i>: 
( <font color="Maroon" title="c11">M</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c12">N</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c8">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c10">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">M</font> &amp; not <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c7">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; not <font color="Maroon" title="c9">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">N</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c8">b2</font> &amp; <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E2:13_1"/><b>then </b><i><font color="Green" title="E15">A3</font></i>: 
( <font color="Maroon" title="c11">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c12">N</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">N</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><div><i><font color="Green" title="E16">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_1"/><i><font color="Green" title="E17">A5</font></i>: 
( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font> or <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><div><i><font color="Green" title="E18">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_1_1"/><i><font color="Green" title="E19">A7</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E2:13_1_1_1"/><i><font color="Green" title="E20">A8</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:13_1_1_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E2:13_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:13_1_1_1"/><b>then </b><i><font color="Green" title="E21">A9</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E5:13_1_1_1"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E6:13_1_1_1"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</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="E7:13_1_1_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_1_1"><i><font color="Green" title="E19">A7</font></i></a>, <a class="txt" href="#E2:13_1_1_1"><i><font color="Green" title="E20">A8</font></i></a>, <a class="txt" href="#E4:13_1_1_1"><i><font color="Green" title="E21">A9</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_1_2"/><i><font color="Green" title="E19">A10</font></i>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E2:13_1_1_2"/><i><font color="Green" title="E20">A11</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:13_1_1_2"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E2:13_1"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:13_1_1_2"/><b>then </b><i><font color="Green" title="E21">A12</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E5:13_1_1_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E6:13_1_1_2"/><b>then </b>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_1_2"><i><font color="Green" title="E19">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="E7:13_1_1_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_1_2"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="#E2:13_1_1_2"><i><font color="Green" title="E20">A11</font></i></a>, <a class="txt" href="#E4:13_1_1_2"><i><font color="Green" title="E21">A12</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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="E4:13_1_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1_1"><i><font color="Green" title="E17">A5</font></i></a>, <a class="txt" href="#E2:13_1_1"><i><font color="Green" title="E18">A6</font></i></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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_2"/><i><font color="Green" title="E17">A13</font></i>: 
( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">a4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><div><i><font color="Green" title="E18">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_2_1"/>
 ex <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><b>then consider </b><font color="Maroon" title="c13">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:13_1_2_1"/><i><font color="Green" title="E19">A15</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font> )
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="translac.html#T2" title="TRANSLAC:th.2">TRANSLAC:2</a></i>;<br/><a NAME="E4:13_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c13">d</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><b>then consider </b><font color="Maroon" title="c14">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E6:13_1_2_1"/><i><font color="Green" title="E20">A16</font></i>: 
( <font color="Maroon" title="c14">Y</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> &amp; <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> &amp; <font color="Maroon" title="c13">d</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E7:13_1_2_1"/>
 ex <font color="Olive" title="b1">d1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Olive" title="b1">d1</font> &amp; <font color="Olive" title="b1">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:13_1_2_1_1"/>
not <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_1_1_1"/>
<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</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="E2:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<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="E3:13_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E21">A17</font></i>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:13_1_2_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E3:13_1_2_1_1_1"><i><font color="Green" title="E21">A17</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E7:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">o</font>
 
<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="E8:13_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:13_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E10:13_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E22">A18</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:13_1_2_1_1_1"/><i><font color="Green" title="E23">A19</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_1_1_1_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_2_1_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:13_1_2_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</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>
<a NAME="E12:13_1_2_1_1_1"/><b>then </b><i><font color="Green" title="E24">A20</font></i>: 
<font color="Maroon" title="c14">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">N</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E6:13_1_2_1"><i><font color="Green" title="E20">A16</font></i></a>, <a class="txt" href="#E10:13_1_2_1_1_1"><i><font color="Green" title="E22">A18</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E13:13_1_2_1_1_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</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="E14:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 
<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="E15:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E3:13_1_2_1_1_1"><i><font color="Green" title="E21">A17</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E16:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">a1</font>
 
<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="E17:13_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E18:13_1_2_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E19:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E20:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c14">Y</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c11">M</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E6:13_1_2_1"><i><font color="Green" title="E20">A16</font></i></a>, <a class="txt" href="#E11:13_1_2_1_1_1"><i><font color="Green" title="E23">A19</font></i></a>, <a class="ref" href="aff_1.html#T52" title="AFF_1:th.52">AFF_1:52</a></i>;<br/>
<a NAME="E21:13_1_2_1_1_1"/><b>then </b>
<font color="Maroon" title="c11">M</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c12">N</font>
 
<b>by </b><i><a class="txt" href="#E12:13_1_2_1_1_1"><i><font color="Green" title="E24">A20</font></i></a>, <a class="ref" href="aff_1.html#T58" title="AFF_1:th.58">AFF_1:58</a></i>;<br/>
<b>hence </b><a NAME="E22:13_1_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</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">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="E3:13_1_2_1_1"/><i><font color="Green" title="E21">A21</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c15">d1</font> )
 <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">d1</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font> &amp; <font color="Maroon" title="c15">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )</span><br/>

<a NAME="E4:13_1_2_1_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_1_1_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_2_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:13_1_2_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</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>hence </b><a NAME="E5:13_1_2_1_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font> &amp; <font color="Maroon" title="c15">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 <b>by </b><i><a class="txt" href="#E6:13_1_2_1"><i><font color="Green" title="E20">A16</font></i></a>, <a class="txt" href="#E3:13_1_2_1_1"><i><font color="Green" title="E21">A21</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">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="E9:13_1_2_1"/><i><font color="Green" title="E21">A22</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font> &amp; <font color="Maroon" title="c15">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c14">Y</font> )
 ;<br/><a NAME="E10:13_1_2_1"/><i><font color="Green" title="E22">A23</font></i>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">d</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_1_2"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">d</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:13_1_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</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><a NAME="E11:13_1_2_1"/><i><font color="Green" title="E23">A24</font></i>: 
( <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">M</font> &amp; <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> &amp; <font color="Maroon" title="c11">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_1_3"/><i><font color="Green" title="E24">A25</font></i>: 
(  not <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">M</font> or  not <font color="Maroon" title="c12">N</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> or  not <font color="Maroon" title="c11">M</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">Y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_2_1_3_1"/><i><font color="Green" title="E25">A26</font></i>: 
( <font color="Maroon" title="c12">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y</font> or <font color="Maroon" title="c11">M</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">Y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_2_1_3_1"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c4">a2</font> )
 <b>by </b><i><a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E3:13_1_2_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="txt" href="#E6:13_1_2_1"><i><font color="Green" title="E20">A16</font></i></a>, <a class="txt" href="#E1:13_1_2_1_3_1"><i><font color="Green" title="E25">A26</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>hence </b><a NAME="E3:13_1_2_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2_1_3"><i><font color="Green" title="E24">A25</font></i></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><a NAME="E12:13_1_2_1"/><i><font color="Green" title="E24">A27</font></i>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_4"><b>proof </b></a><div class="add">

<a NAME="E1:13_1_2_1_4"/>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font> )
 
<b>by </b><i><a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="txt" href="#E9:13_1_2_1"><i><font color="Green" title="E21">A22</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E2:13_1_2_1_4"/><b>then </b><i><font color="Green" title="E25">A28</font></i>: 
( <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font> )
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E3:13_1_2_1_4"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</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="E4:13_1_2_1_4"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c15">d1</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E2:13_1_2_1_4"><i><font color="Green" title="E25">A28</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><a NAME="E13:13_1_2_1"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E14:13_1_2_1"/><b>then </b><i><font color="Green" title="E25">A29</font></i>: 
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">d1</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E6:13_1_2_1"><i><font color="Green" title="E20">A16</font></i></a>, <a class="txt" href="#E9:13_1_2_1"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E10:13_1_2_1"><i><font color="Green" title="E22">A23</font></i></a>, <a class="txt" href="#E11:13_1_2_1"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E12:13_1_2_1"><i><font color="Green" title="E24">A27</font></i></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></i>;<br/><a NAME="E15:13_1_2_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_1_5"><b>proof </b></a><div class="add">

<a NAME="E1:13_1_2_1_5"/>
( <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c8">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font> )
 
<b>by </b><i><a class="txt" href="#E3:13_1_2_1"><i><font color="Green" title="E19">A15</font></i></a>, <a class="txt" href="#E9:13_1_2_1"><i><font color="Green" title="E21">A22</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="E2:13_1_2_1_5"/><b>then </b><i><font color="Green" title="E26">A30</font></i>: 
( <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> &amp; <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font> )
 
<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="E3:13_1_2_1_5"/><b>then </b>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</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="E4:13_1_2_1_5"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c13">d</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b1</font>,<font color="Maroon" title="c15">d1</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E2:13_1_2_1_5"><i><font color="Green" title="E26">A30</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><a NAME="E16:13_1_2_1"/><b>then </b>
<font color="Maroon" title="c13">d</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">d1</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E6:13_1_2_1"><i><font color="Green" title="E20">A16</font></i></a>, <a class="txt" href="#E9:13_1_2_1"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E10:13_1_2_1"><i><font color="Green" title="E22">A23</font></i></a>, <a class="txt" href="#E11:13_1_2_1"><i><font color="Green" title="E23">A24</font></i></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</a></i>;<br/><b>hence </b><a NAME="E17:13_1_2_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E6:13_1_2_1"><i><font color="Green" title="E20">A16</font></i></a>, <a class="txt" href="#E9:13_1_2_1"><i><font color="Green" title="E21">A22</font></i></a>, <a class="txt" href="#E10:13_1_2_1"><i><font color="Green" title="E22">A23</font></i></a>, <a class="txt" href="#E11:13_1_2_1"><i><font color="Green" title="E23">A24</font></i></a>, <a class="txt" href="#E14:13_1_2_1"><i><font color="Green" title="E25">A29</font></i></a>, <a class="ref" href="aff_2.html#D4" title="AFF_2:def.4">AFF_2:def 4</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_2_2"/><i><font color="Green" title="E19">A31</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  holds <br/>(  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b3">z</font> or  not <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">y</font> or  not <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> or  not <font color="Olive" title="b2">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">z</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E2:13_1_2_2"/><i><font color="Green" title="E20">A32</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b1</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><div><i><font color="Green" title="E21">A33</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_2_2_1"/><i><font color="Green" title="E22">A34</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E2:13_1_2_2_1"/><i><font color="Green" title="E23">A35</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E3:13_1_2_2_1"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_2_1_1"/><i><font color="Green" title="E24">A36</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_2_2_1_1"/><i><font color="Green" title="E25">A37</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:13_1_2_2_1_1"/><i><font color="Green" title="E26">A38</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/>
<a NAME="E4:13_1_2_2_1_1"/>
<font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2_2_1"><i><font color="Green" title="E22">A34</font></i></a>, <a class="txt" href="#E1:13_1_2_2_1_1"><i><font color="Green" title="E24">A36</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:13_1_2_2_1_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</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="E6:13_1_2_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="#E2:13_1_2_2_1_1"><i><font color="Green" title="E25">A37</font></i></a>, <a class="txt" href="#E3:13_1_2_2_1_1"><i><font color="Green" title="E26">A38</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</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><a NAME="E4:13_1_2_2_1"/><b>then </b><i><font color="Green" title="E24">A39</font></i>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="#E1:13_1_2_2"><i><font color="Green" title="E19">A31</font></i></a>, <a class="txt" href="#E2:13_1_2_2_1"><i><font color="Green" title="E23">A35</font></i></a></i>;<br/><a NAME="E5:13_1_2_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E6:13_1_2_2_1"/><b>then </b><i><font color="Green" title="E25">A40</font></i>: 
( <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font> or <font color="Maroon" title="c6">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font> )
 <b>by </b><i><a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="#E1:13_1_2_2"><i><font color="Green" title="E19">A31</font></i></a></i>;<br/><a NAME="E7:13_1_2_2_1"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_2_1_2"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_2_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2_2_1"><i><font color="Green" title="E22">A34</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="E3:13_1_2_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:13_1_2_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">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>hence </b><a NAME="E8:13_1_2_2_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E4:13_1_2_2_1"><i><font color="Green" title="E24">A39</font></i></a>, <a class="txt" href="#E6:13_1_2_2_1"><i><font color="Green" title="E25">A40</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</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><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_2_2_2"/><i><font color="Green" title="E22">A41</font></i>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font></span><br/><a NAME="E2:13_1_2_2_2"/><i><font color="Green" title="E23">A42</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E3:13_1_2_2_2"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_2_2_1"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2_2_2"><i><font color="Green" title="E22">A41</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E3:13_1_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/>
<a NAME="E4:13_1_2_2_2_1"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<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="E5:13_1_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E6:13_1_2_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E7:13_1_2_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">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><a NAME="E4:13_1_2_2_2"/><b>then </b><i><font color="Green" title="E24">A43</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="#E1:13_1_2_2"><i><font color="Green" title="E19">A31</font></i></a>, <a class="txt" href="#E2:13_1_2_2_2"><i><font color="Green" title="E23">A42</font></i></a></i>;<br/><a NAME="E5:13_1_2_2_2"/><i><font color="Green" title="E25">A44</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c8">b2</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E6:13_1_2_2_2"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_2_2_2"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_2_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2_2_2"><i><font color="Green" title="E22">A41</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="E3:13_1_2_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:13_1_2_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">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><a NAME="E7:13_1_2_2_2"/><b>then </b><i><font color="Green" title="E26">A45</font></i>: 
<font color="Maroon" title="c6">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b2</font>
 <b>by </b><i><a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="#E1:13_1_2_2"><i><font color="Green" title="E19">A31</font></i></a>, <a class="txt" href="#E5:13_1_2_2_2"><i><font color="Green" title="E25">A44</font></i></a></i>;<br/><a NAME="E8:13_1_2_2_2"/><i><font color="Green" title="E27">A46</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><a NAME="E9:13_1_2_2_2"/>
<font color="Maroon" title="c6">a4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">b4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2_2_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1_2_2_2_3"/>
<font color="Maroon" title="c6">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_1_2_2_2_3"/><b>then </b>
<font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2_2_2"><i><font color="Green" title="E22">A41</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E3:13_1_2_2_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a4</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:13_1_2_2_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E5:13_1_2_2_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">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><a NAME="E10:13_1_2_2_2"/><b>then </b><i><font color="Green" title="E28">A47</font></i>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="#E1:13_1_2_2"><i><font color="Green" title="E19">A31</font></i></a>, <a class="txt" href="#E8:13_1_2_2_2"><i><font color="Green" title="E27">A46</font></i></a></i>;<br/><a NAME="E11:13_1_2_2_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b2</font>,<font color="Maroon" title="c7">b1</font>
 <b>by </b><i><a class="txt" href="#E1:13_1_2_2_2"><i><font color="Green" title="E22">A41</font></i></a>, <a class="txt" href="#E7:13_1_2_2_2"><i><font color="Green" title="E26">A45</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/><a NAME="E12:13_1_2_2_2"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b4</font>,<font color="Maroon" title="c9">b3</font>
 <b>by </b><i><a class="txt" href="#E1:13_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="txt" href="#E4:13_1_2_2_2"><i><font color="Green" title="E24">A43</font></i></a>, <a class="txt" href="#E10:13_1_2_2_2"><i><font color="Green" title="E28">A47</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="E13:13_1_2_2_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</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="E5:13_1_2_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E17">A13</font></i></a>, <a class="txt" href="#E1:13_1_2_2"><i><font color="Green" title="E19">A31</font></i></a>, <a class="txt" href="#E2:13_1_2_2"><i><font color="Green" title="E20">A32</font></i></a>, <a class="txt" href="#E3:13_1_2_2"><i><font color="Green" title="E21">A33</font></i></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="E4:13_1_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E2:13_1_2"><i><font color="Green" title="E18">A14</font></i></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="E5:13_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">b3</font>,<font color="Maroon" title="c10">b4</font>
 <b>by </b><i><a class="txt" href="#E3:13_1"><i><font color="Green" title="E16">A4</font></i></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="E3:13"/>
<font color="Maroon" title="c1">X</font> is <a href="conmetr1.html#V2" title="CONMETR1:attr.2">satisfying_major_Scherungssatz</a>
 <b>by </b><i><a class="ref" href="conmetr1.html#D2" target="_self" title="CONMETR1:def.2">Def2</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>
