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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</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="conmetr.html#V3" title="CONMETR:attr.3">satisfying_MH1</a> &amp; <font color="Maroon" title="c1">X</font> is <a href="conmetr.html#V4" title="CONMETR:attr.4">satisfying_MH2</a> implies <font color="Maroon" title="c1">X</font> is <a href="conmetr.html#V1" title="CONMETR:attr.1">satisfying_OPAP</a> )</span><br/>

<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="conmetr.html#V3" title="CONMETR:attr.3">satisfying_MH1</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c1">X</font> is <a href="conmetr.html#V4" title="CONMETR:attr.4">satisfying_MH2</a> or <font color="Maroon" title="c1">X</font> is <a href="conmetr.html#V1" title="CONMETR:attr.1">satisfying_OPAP</a> )</span><br/>

<b>assume </b><a NAME="E2:15"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="conmetr.html#V4" title="CONMETR:attr.4">satisfying_MH2</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="conmetr.html#V1" title="CONMETR:attr.1">satisfying_OPAP</a></span><br/>

<b>let </b><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="conmetr.html#D1" target="_self" title="CONMETR:def.1">CONMETR:def 1</a> <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">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b7">M</font>, <font color="Olive" title="b8">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="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; <font color="Olive" title="b1">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; <font color="Olive" title="b2">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; <font color="Olive" title="b3">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">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="b8">N</font> &amp; <font color="Olive" title="b4">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; <font color="Olive" title="b5">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; <font color="Olive" title="b6">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; not <font color="Olive" title="b5">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; not <font color="Olive" title="b3">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; <font color="Olive" title="b7">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b8">N</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">a3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">b3</font> &amp; <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b6">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b4">b1</font> holds <br/><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b6">b3</font></span><br/><b>let </b><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">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</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="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="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="c4">a2</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="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="c6">b1</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="c8">b3</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">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="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b1">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</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="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> holds <br/><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><b>let </b><font color="Maroon" title="c9">M</font>, <font color="Maroon" title="c10">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="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">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="c9">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="c9">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="c10">N</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">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="c10">N</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">N</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="c9">M</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="c10">N</font> &amp; <font color="Maroon" title="c9">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</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="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> implies <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font> )</span><br/>

















<b>assume </b><a NAME="E3:15"/><i><font color="Green" title="E17">A3</font></i>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">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="c9">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="c9">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="c10">N</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">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="c10">N</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">N</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="c9">M</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="c10">N</font> &amp; <font color="Maroon" title="c9">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</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="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">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="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c11">o'</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c12">a1'</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c13">a2'</font> = <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c14">a3'</font> = <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c15">b1'</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c16">b2'</font> = <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c17">b3'</font> = <font color="Maroon" title="c8">b3</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c18">M'</font> = <font color="Maroon" title="c9">M</font>, <font color="Maroon" title="c19">N'</font> = <font color="Maroon" title="c10">N</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/>
<a NAME="E6:15"/>
( <font color="Maroon" title="c9">M</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> &amp; <font color="Maroon" title="c10">N</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> )
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></i>;<br/>
<a NAME="E7:15"/><b>then </b><i><font color="Green" title="E18">A4</font></i>: 
( <font color="Maroon" title="c18">M'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c19">N'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></i>;<br/>
<a NAME="E8:15"/><b>then </b><i><font color="Green" title="E19">A5</font></i>: 
( <font color="Maroon" title="c18">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font> &amp; <font color="Maroon" title="c19">N'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c19">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="E20">A6</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1"/><i><font color="Green" title="E21">A7</font></i>: 
( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> or <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font> or <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="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><div><i><font color="Green" title="E22">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_1"/><i><font color="Green" title="E23">A9</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E2:15_1_1"/><i><font color="Green" title="E24">A10</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E3:15_1_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:15_1_1"/><b>then </b><i><font color="Green" title="E25">A11</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">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="E5:15_1_1"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_1_1_1"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_1_1_1_1"/><i><font color="Green" title="E26">A12</font></i>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</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_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:15_1_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">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="E4:15_1_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E1:15_1_1_1_1"><i><font color="Green" title="E26">A12</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="E2:15_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:15_1_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_1_1"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</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="E6:15_1_1"/><b>then </b>
<font color="Maroon" title="c16">b2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="txt" href="#E2:15_1_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="txt" href="#E4:15_1_1"><i><font color="Green" title="E25">A11</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E7:15_1_1"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="txt" href="#E1:15_1_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E8:15_1_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</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><i><font color="Green" title="E23">A13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_2"/><i><font color="Green" title="E24">A14</font></i>: 
<font color="Maroon" title="c4">a2</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="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E2:15_1_2"/><i><font color="Green" title="E25">A15</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">b1'</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"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">b1'</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>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c14">a3'</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="E3:15_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:15"><i><font color="Green" title="E18">A4</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="E3:15_1_2"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:15_1_2"/><b>then </b><i><font color="Green" title="E26">A16</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c16">b2'</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="E5:15_1_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:15_1_2"><i><font color="Green" title="E24">A14</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E6:15_1_2"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E7:15_1_2"/><b>then </b>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:15_1_2"><i><font color="Green" title="E24">A14</font></i></a>, <a class="txt" href="#E2:15_1_2"><i><font color="Green" title="E25">A15</font></i></a>, <a class="txt" href="#E4:15_1_2"><i><font color="Green" title="E26">A16</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E8:15_1_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</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="15_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_1_3"/><i><font color="Green" title="E24">A17</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="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E2:15_1_3"/><i><font color="Green" title="E25">A18</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">b1'</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"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">b1'</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>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c14">a3'</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="E3:15_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:15"><i><font color="Green" title="E18">A4</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="E3:15_1_3"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E4:15_1_3"/><b>then </b><i><font color="Green" title="E26">A19</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c17">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="E5:15_1_3"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:15_1_3"><i><font color="Green" title="E24">A17</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E6:15_1_3"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><b>hence </b><a NAME="E7:15_1_3"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:15_1_3"><i><font color="Green" title="E24">A17</font></i></a>, <a class="txt" href="#E2:15_1_3"><i><font color="Green" title="E25">A18</font></i></a>, <a class="txt" href="#E4:15_1_3"><i><font color="Green" title="E26">A19</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="E5:15_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="#E1:15_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="txt" href="#E2:15_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="#E3:15_1"><i><font color="Green" title="E23">A13</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="15_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:15_2"/><i><font color="Green" title="E21">A20</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="c4">a2</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="c5">a3</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="c5">a3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  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 <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E2:15_2"/><i><font color="Green" title="E22">A21</font></i>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_1"/><i><font color="Green" title="E23">A22</font></i>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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="E2:15_2_1"/><i><font color="Green" title="E24">A23</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c13">a2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c13">a2'</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_2_1_1"/><b>then </b><i><font color="Green" title="E25">A24</font></i>: 
<font color="Maroon" title="c13">a2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N'</font>
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E3:15_2_1_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c14">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_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E2:15_2_1_1"><i><font color="Green" title="E25">A24</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="E3:15_2_1"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E8:15"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_2_1"/><b>then </b><i><font color="Green" title="E25">A25</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c12">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="E5:15_2_1"/>
<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c13">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_2_1_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:15_2_1"><i><font color="Green" title="E23">A22</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E2:15_2_1_2"/><b>then </b>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E3:15_2_1_2"/>
<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c13">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c12">a1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</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="E6:15_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:15_2"><i><font color="Green" title="E21">A20</font></i></a>, <a class="txt" href="#E2:15_2_1"><i><font color="Green" title="E24">A23</font></i></a>, <a class="txt" href="#E4:15_2_1"><i><font color="Green" title="E25">A25</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="E3:15_2"/><i><font color="Green" title="E23">A26</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</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="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:15_2_2"/>
( <font color="Maroon" title="c9">M</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> &amp; <font color="Maroon" title="c10">N</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> )
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></i>;<br/>
<a NAME="E2:15_2_2"/><b>then </b><i><font color="Green" title="E24">A27</font></i>: 
( <font color="Maroon" title="c18">M'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c19">N'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></i>;<br/>
<a NAME="E3:15_2_2"/><b>then </b>
( <font color="Maroon" title="c18">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c18">M'</font> &amp; <font color="Maroon" title="c19">N'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c19">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/>
<a NAME="E4:15_2_2"/><b>then </b>
( <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> &amp; <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c13">a2'</font> &amp; <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> &amp; <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c15">b1'</font> )
 
<b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">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="E5:15_2_2"/><b>then </b><i><font color="Green" title="E25">A28</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</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> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</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> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:15_2_2"/><i><font color="Green" title="E26">A29</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">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="E2:15_2_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:15_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E1:15_2"><i><font color="Green" title="E21">A20</font></i></a>, <a class="txt" href="#E2:15_2_2"><i><font color="Green" title="E24">A27</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="E7:15_2_2"/>
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_2_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">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="E2:15_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</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="E4:15_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E2:15_2"><i><font color="Green" title="E22">A21</font></i></a>, <a class="txt" href="#E2:15_2_2"><i><font color="Green" title="E24">A27</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="E8:15_2_2"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</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="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> )
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E5:15_2_2"><i><font color="Green" title="E25">A28</font></i></a>, <a class="txt" href="#E6:15_2_2"><i><font color="Green" title="E26">A29</font></i></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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><b>consider </b><font color="Maroon" title="c20">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="E5:15_2"/><i><font color="Green" title="E24">A30</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">d1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><a NAME="E6:15_2"/><i><font color="Green" title="E25">A31</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c20">d1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">d1</font> )
 <b>by </b><i><a class="txt" href="#E5:15_2"><i><font color="Green" title="E24">A30</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c21">d1'</font> = <font color="Maroon" title="c20">d1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon" title="c22">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="E9:15_2"/><i><font color="Green" title="E26">A32</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c22">e1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon" title="c23">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="E11:15_2"/><i><font color="Green" title="E27">A33</font></i>: 
( <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c23">e2</font> &amp; <font color="Maroon" title="c20">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><a NAME="E12:15_2"/><i><font color="Green" title="E28">A34</font></i>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c22">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c23">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_3"/><i><font color="Green" title="E29">A35</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c22">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c23">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>reconsider </b><font color="Maroon" title="c24">e1'</font> = <font color="Maroon" title="c22">e1</font>, <font color="Maroon" title="c25">e2'</font> = <font color="Maroon" title="c23">e2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_2_3"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c24">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c25">e2'</font>
 
<b>by </b><i><a class="txt" href="#E1:15_2_3"><i><font color="Green" title="E29">A35</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:15_2_3"/><b>then </b>
<font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c25">e2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c24">e1'</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="E5:15_2_3"/><b>then </b>
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c23">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c22">e1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:15_2_3"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c22">e1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E11:15_2"><i><font color="Green" title="E27">A33</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:15_2_3"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E9:15_2"><i><font color="Green" title="E26">A32</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:15_2_3"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:15_2_3"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:15_2_3"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">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="E11:15_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">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="E12:15_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">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="E13:15_2_3"/><b>then </b><i><font color="Green" title="E30">A36</font></i>: 
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">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="E14:15_2_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:15_2_3"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">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="E16:15_2_3"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E17:15_2_3"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E13:15_2_3"><i><font color="Green" title="E30">A36</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E18:15_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E19:15_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E20:15_2_3"/><b>then </b><i><font color="Green" title="E31">A37</font></i>: 
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E21:15_2_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E22:15_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E23:15_2_3"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">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="E24:15_2_3"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E20:15_2_3"><i><font color="Green" title="E31">A37</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E25:15_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">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="E26:15_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E27:15_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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>reconsider </b><font color="Maroon" title="c24">e1'</font> = <font color="Maroon" title="c22">e1</font>, <font color="Maroon" title="c25">e2'</font> = <font color="Maroon" title="c23">e2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E14:15_2"/>
not <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c24">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c25">e2'</font>
 <b>by </b><i><a class="txt" href="#E12:15_2"><i><font color="Green" title="E28">A34</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon" title="c26">d2'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E16:15_2"/><i><font color="Green" title="E29">A38</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c24">e1'</font>,<font color="Maroon" title="c26">d2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c25">e2'</font>,<font color="Maroon" title="c26">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>reconsider </b><font color="Maroon" title="c27">d2</font> = <font color="Maroon" title="c26">d2'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E18:15_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c23">e2</font>,<font color="Maroon" title="c27">d2</font>
 <b>by </b><i><a class="txt" href="#E16:15_2"><i><font color="Green" title="E29">A38</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E19:15_2"/><b>then </b><i><font color="Green" title="E30">A39</font></i>: 
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c23">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E20:15_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c22">e1</font>,<font color="Maroon" title="c27">d2</font>
 <b>by </b><i><a class="txt" href="#E16:15_2"><i><font color="Green" title="E29">A38</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E21:15_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c22">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E22:15_2"/><b>then </b><i><font color="Green" title="E31">A40</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font>
 <b>by </b><i><a class="txt" href="#E9:15_2"><i><font color="Green" title="E26">A32</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E23:15_2"/><i><font color="Green" title="E32">A41</font></i>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_4"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</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_2_4"/><b>then </b><i><font color="Green" title="E33">A42</font></i>: 
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E11:15_2"><i><font color="Green" title="E27">A33</font></i></a>, <a class="txt" href="#E19:15_2"><i><font color="Green" title="E30">A39</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:15_2_4"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">d1</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E5:15_2"><i><font color="Green" title="E24">A30</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:15_2_4"/><b>then </b>
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:15_2_4"/><b>then </b><i><font color="Green" title="E34">A43</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E5:15_2"><i><font color="Green" title="E24">A30</font></i></a>, <a class="txt" href="#E2:15_2_4"><i><font color="Green" title="E33">A42</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:15_2_4"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</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="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:15_2_4"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</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="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E5:15_2_4"><i><font color="Green" title="E34">A43</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:15_2_4"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:15_2_4"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">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="E10:15_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">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="E11:15_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">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="E12:15_2_4"/><b>then </b><i><font color="Green" title="E35">A44</font></i>: 
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">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="E13:15_2_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:15_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</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="E15:15_2_4"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E16:15_2_4"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E12:15_2_4"><i><font color="Green" title="E35">A44</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E17:15_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E18:15_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E19:15_2_4"/><b>then </b><i><font color="Green" title="E36">A45</font></i>: 
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E20:15_2_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E21:15_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E22:15_2_4"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">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="E23:15_2_4"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E19:15_2_4"><i><font color="Green" title="E36">A45</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E24:15_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">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="E25:15_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E26:15_2_4"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E24:15_2"/><b>then </b><i><font color="Green" title="E33">A46</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c27">d2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font> &amp; <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font> )
 <b>by </b><i><a class="txt" href="#E11:15_2"><i><font color="Green" title="E27">A33</font></i></a>, <a class="txt" href="#E19:15_2"><i><font color="Green" title="E30">A39</font></i></a>, <a class="txt" href="#E22:15_2"><i><font color="Green" title="E31">A40</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><b>consider </b><font color="Maroon" title="c28">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E26:15_2"/><i><font color="Green" title="E34">A47</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon" title="c29">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E28:15_2"/><i><font color="Green" title="E35">A48</font></i>: 
( <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font> &amp; <font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><a NAME="E29:15_2"/><i><font color="Green" title="E36">A49</font></i>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_5"/><i><font color="Green" title="E37">A50</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>reconsider </b><font color="Maroon" title="c30">e1'</font> = <font color="Maroon" title="c28">e1</font>, <font color="Maroon" title="c31">e2'</font> = <font color="Maroon" title="c29">e2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_2_5"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c30">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c31">e2'</font>
 
<b>by </b><i><a class="txt" href="#E1:15_2_5"><i><font color="Green" title="E37">A50</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:15_2_5"/><b>then </b>
<font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c31">e2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c30">e1'</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="E5:15_2_5"/><b>then </b>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:15_2_5"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E28:15_2"><i><font color="Green" title="E35">A48</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:15_2_5"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E26:15_2"><i><font color="Green" title="E34">A47</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:15_2_5"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:15_2_5"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:15_2_5"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">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="E11:15_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">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="E12:15_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E13:15_2_5"/><b>then </b><i><font color="Green" title="E38">A51</font></i>: 
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E14:15_2_5"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E15:15_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E16:15_2_5"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</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="E17:15_2_5"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E13:15_2_5"><i><font color="Green" title="E38">A51</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E18:15_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</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="E19:15_2_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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="E20:15_2_5"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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>reconsider </b><font color="Maroon" title="c30">e1'</font> = <font color="Maroon" title="c28">e1</font>, <font color="Maroon" title="c31">e2'</font> = <font color="Maroon" title="c29">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E31:15_2"/>
not <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c30">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c31">e2'</font>
 <b>by </b><i><a class="txt" href="#E29:15_2"><i><font color="Green" title="E36">A49</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon" title="c32">d3'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E33:15_2"/><i><font color="Green" title="E37">A52</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c30">e1'</font>,<font color="Maroon" title="c32">d3'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c31">e2'</font>,<font color="Maroon" title="c32">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>reconsider </b><font color="Maroon" title="c33">d3</font> = <font color="Maroon" title="c32">d3'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E35:15_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font>,<font color="Maroon" title="c33">d3</font>
 <b>by </b><i><a class="txt" href="#E33:15_2"><i><font color="Green" title="E37">A52</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E36:15_2"/><b>then </b><i><font color="Green" title="E38">A53</font></i>: 
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E37:15_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font>,<font color="Maroon" title="c33">d3</font>
 <b>by </b><i><a class="txt" href="#E33:15_2"><i><font color="Green" title="E37">A52</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E38:15_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c33">d3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E39:15_2"/><b>then </b><i><font color="Green" title="E39">A54</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c33">d3</font>
 <b>by </b><i><a class="txt" href="#E26:15_2"><i><font color="Green" title="E34">A47</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E40:15_2"/><i><font color="Green" title="E40">A55</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="c33">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_6"/>
<font color="Maroon" title="c33">d3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</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_2_6"/><b>then </b><i><font color="Green" title="E41">A56</font></i>: 
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E28:15_2"><i><font color="Green" title="E35">A48</font></i></a>, <a class="txt" href="#E36:15_2"><i><font color="Green" title="E38">A53</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:15_2_6"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E22:15_2"><i><font color="Green" title="E31">A40</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:15_2_6"/><b>then </b>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:15_2_6"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E23:15_2"><i><font color="Green" title="E32">A41</font></i></a>, <a class="txt" href="#E2:15_2_6"><i><font color="Green" title="E41">A56</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:15_2_6"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:15_2_6"/><b>then </b><i><font color="Green" title="E42">A57</font></i>: 
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E8:15_2_6"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:15_2_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E10:15_2_6"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</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="E11:15_2_6"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E7:15_2_6"><i><font color="Green" title="E42">A57</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E12:15_2_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</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="E13:15_2_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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="E14:15_2_6"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E41:15_2"/><b>then </b><i><font color="Green" title="E41">A58</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c33">d3</font> &amp; <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</font> )
 <b>by </b><i><a class="txt" href="#E28:15_2"><i><font color="Green" title="E35">A48</font></i></a>, <a class="txt" href="#E36:15_2"><i><font color="Green" title="E38">A53</font></i></a>, <a class="txt" href="#E39:15_2"><i><font color="Green" title="E39">A54</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><b>consider </b><font color="Maroon" title="c34">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="E43:15_2"/><i><font color="Green" title="E42">A59</font></i>: 
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c34">e1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c34">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon" title="c35">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="E45:15_2"/><i><font color="Green" title="E43">A60</font></i>: 
( <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c35">e2</font> &amp; <font color="Maroon" title="c33">d3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c35">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><a NAME="E46:15_2"/><i><font color="Green" title="E44">A61</font></i>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c34">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c35">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_7"/><i><font color="Green" title="E45">A62</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c34">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c35">e2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>reconsider </b><font color="Maroon" title="c36">e1'</font> = <font color="Maroon" title="c34">e1</font>, <font color="Maroon" title="c37">e2'</font> = <font color="Maroon" title="c35">e2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E3:15_2_7"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c36">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c37">e2'</font>
 
<b>by </b><i><a class="txt" href="#E1:15_2_7"><i><font color="Green" title="E45">A62</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:15_2_7"/><b>then </b>
<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c37">e2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c36">e1'</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="E5:15_2_7"/><b>then </b>
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c35">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c34">e1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:15_2_7"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c34">e1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="#E45:15_2"><i><font color="Green" title="E43">A60</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:15_2_7"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="#E43:15_2"><i><font color="Green" title="E42">A59</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:15_2_7"/><b>then </b><i><font color="Green" title="E46">A63</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E9:15_2_7"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:15_2_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</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="E11:15_2_7"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:15_2_7"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E13:15_2_7"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E8:15_2_7"><i><font color="Green" title="E46">A63</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E14:15_2_7"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:15_2_7"/><b>then </b><i><font color="Green" title="E47">A64</font></i>: 
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">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="E16:15_2_7"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:15_2_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</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="E18:15_2_7"/><b>then </b>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">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="E19:15_2_7"/><b>then </b>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E15:15_2_7"><i><font color="Green" title="E47">A64</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E20:15_2_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">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/>
<b>hence </b><a NAME="E21:15_2_7"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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>reconsider </b><font color="Maroon" title="c36">e1'</font> = <font color="Maroon" title="c34">e1</font>, <font color="Maroon" title="c37">e2'</font> = <font color="Maroon" title="c35">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E48:15_2"/>
not <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c36">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c37">e2'</font>
 <b>by </b><i><a class="txt" href="#E46:15_2"><i><font color="Green" title="E44">A61</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><b>then consider </b><font color="Maroon" title="c38">d4'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E50:15_2"/><i><font color="Green" title="E45">A65</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c36">e1'</font>,<font color="Maroon" title="c38">d4'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c37">e2'</font>,<font color="Maroon" title="c38">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>reconsider </b><font color="Maroon" title="c39">d4</font> = <font color="Maroon" title="c38">d4'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E52:15_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c35">e2</font>,<font color="Maroon" title="c39">d4</font>
 <b>by </b><i><a class="txt" href="#E50:15_2"><i><font color="Green" title="E45">A65</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E53:15_2"/><b>then </b><i><font color="Green" title="E46">A66</font></i>: 
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c35">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c39">d4</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E54:15_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c34">e1</font>,<font color="Maroon" title="c39">d4</font>
 <b>by </b><i><a class="txt" href="#E50:15_2"><i><font color="Green" title="E45">A65</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E55:15_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c34">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c39">d4</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E56:15_2"/><b>then </b><i><font color="Green" title="E47">A67</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c39">d4</font>
 <b>by </b><i><a class="txt" href="#E43:15_2"><i><font color="Green" title="E42">A59</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><b>take </b><font color="Maroon" title="c40">d4</font> = <font color="Maroon" title="c39">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="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E57:15_2"/><i><font color="Green" title="E48">A68</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="c40">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_8"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_8"/>
<font color="Maroon" title="c40">d4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</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_2_8"/><b>then </b><i><font color="Green" title="E49">A69</font></i>: 
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="#E45:15_2"><i><font color="Green" title="E43">A60</font></i></a>, <a class="txt" href="#E53:15_2"><i><font color="Green" title="E46">A66</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E3:15_2_8"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c33">d3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E39:15_2"><i><font color="Green" title="E39">A54</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:15_2_8"/><b>then </b>
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:15_2_8"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="txt" href="#E40:15_2"><i><font color="Green" title="E40">A55</font></i></a>, <a class="txt" href="#E2:15_2_8"><i><font color="Green" title="E49">A69</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:15_2_8"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:15_2_8"/><b>then </b><i><font color="Green" title="E50">A70</font></i>: 
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</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="E8:15_2_8"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:15_2_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">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="E10:15_2_8"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">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="E11:15_2_8"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E7:15_2_8"><i><font color="Green" title="E50">A70</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E12:15_2_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c12">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="E13:15_2_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E14:15_2_8"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E58:15_2"/><b>then </b><i><font color="Green" title="E49">A71</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c40">d4</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c40">d4</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c40">d4</font> )
 <b>by </b><i><a class="txt" href="#E45:15_2"><i><font color="Green" title="E43">A60</font></i></a>, <a class="txt" href="#E53:15_2"><i><font color="Green" title="E46">A66</font></i></a>, <a class="txt" href="#E56:15_2"><i><font color="Green" title="E47">A67</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E59:15_2"/><i><font color="Green" title="E50">A72</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_9"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_9"/><i><font color="Green" title="E51">A73</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</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_2_9"/><i><font color="Green" title="E52">A74</font></i>: 
( <font color="Maroon" title="c20">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font> &amp; <font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</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="c5">a3</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_9_1"><b>proof </b></a><div class="add">

<a NAME="E1:15_2_9_1"/><i><font color="Green" title="E53">A75</font></i>: 
<font color="Maroon" title="c20">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_9_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_9_1_1"/>
<font color="Maroon" title="c20">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">d2</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_2_9_1_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">d1'</font>
 
<b>by </b><i><a class="txt" href="#E22:15_2"><i><font color="Green" title="E31">A40</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:15_2_9_1_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">d1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">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_2_9_1_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:15_2_9_1_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E5:15_2"><i><font color="Green" title="E24">A30</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:15_2_9_1_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:15_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E8:15_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E9:15_2_9_1_1"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E10:15_2_9_1_1"/><b>then </b><i><font color="Green" title="E54">A76</font></i>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:15_2_9_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:15_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E13:15_2_9_1_1"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</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="E14:15_2_9_1_1"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:15_2_9_1_1"/><b>then </b>
<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="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E10:15_2_9_1_1"><i><font color="Green" title="E54">A76</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:15_2_9_1_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:15_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:15_2_9_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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="E19:15_2_9_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E2:15_2_9_1"/><i><font color="Green" title="E54">A77</font></i>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_9_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_9_1_2"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">d3</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_2_9_1_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c26">d2'</font>
 
<b>by </b><i><a class="txt" href="#E39:15_2"><i><font color="Green" title="E39">A54</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:15_2_9_1_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c26">d2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</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_2_9_1_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:15_2_9_1_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E22:15_2"><i><font color="Green" title="E31">A40</font></i></a>, <a class="txt" href="#E23:15_2"><i><font color="Green" title="E32">A41</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:15_2_9_1_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:15_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E8:15_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E9:15_2_9_1_2"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E10:15_2_9_1_2"/><b>then </b><i><font color="Green" title="E55">A78</font></i>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:15_2_9_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:15_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E13:15_2_9_1_2"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</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="E14:15_2_9_1_2"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:15_2_9_1_2"/><b>then </b>
<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="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E10:15_2_9_1_2"><i><font color="Green" title="E55">A78</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:15_2_9_1_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:15_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:15_2_9_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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="E19:15_2_9_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E3:15_2_9_1"/>
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_9_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_9_1_3"/>
<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"> contradiction</span><br/>

<a NAME="E2:15_2_9_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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>hence </b><a NAME="E3:15_2_9_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E4:15_2_9_1"/>
( <font color="Maroon" title="c20">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font> &amp; <font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</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="c5">a3</font> )
 <b>by </b><i><a class="txt" href="#E1:15_2_9_1"><i><font color="Green" title="E53">A75</font></i></a>, <a class="txt" href="#E2:15_2_9_1"><i><font color="Green" title="E54">A77</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="E3:15_2_9"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c32">d3'</font>
 
<b>by </b><i><a class="txt" href="#E1:15_2_9"><i><font color="Green" title="E51">A73</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</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="E5:15_2_9"/><b>then </b>
<font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c21">d1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c32">d3'</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="E6:15_2_9"/><b>then </b>
<font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c26">d2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c32">d3'</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="E7:15_2_9"/><b>then </b>
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:15_2_9"/><b>then </b>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E24:15_2"><i><font color="Green" title="E33">A46</font></i></a>, <a class="txt" href="#E2:15_2_9"><i><font color="Green" title="E52">A74</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E9:15_2_9"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E41:15_2"><i><font color="Green" title="E41">A58</font></i></a>, <a class="txt" href="#E2:15_2_9"><i><font color="Green" title="E52">A74</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E10:15_2_9"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:15_2_9"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E12:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">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="E13:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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="E14:15_2_9"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">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="E15:15_2_9"/><b>then </b><i><font color="Green" title="E53">A79</font></i>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:15_2_9"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">o'</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="E18:15_2_9"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">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="E19:15_2_9"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E20:15_2_9"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E2:15_2_9"><i><font color="Green" title="E52">A74</font></i></a>, <a class="txt" href="#E15:15_2_9"><i><font color="Green" title="E53">A79</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:15_2_9"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E22:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E23:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">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="E24:15_2_9"/><b>then </b><i><font color="Green" title="E54">A80</font></i>: 
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">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="E25:15_2_9"/>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> )
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E26:15_2_9"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E27:15_2_9"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E28:15_2_9"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E24:15_2_9"><i><font color="Green" title="E54">A80</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E29:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E30:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E31:15_2_9"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E32:15_2_9"/><b>then </b><i><font color="Green" title="E55">A81</font></i>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E33:15_2_9"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E34:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E35:15_2_9"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">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="E36:15_2_9"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E37:15_2_9"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E32:15_2_9"><i><font color="Green" title="E55">A81</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E38:15_2_9"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E39:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E40:15_2_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E41:15_2_9"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E60:15_2"/><i><font color="Green" title="E51">A82</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c8">b3</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c7">b2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c5">a3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:15_2_10"/><i><font color="Green" title="E52">A83</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c21">d1'</font>
 
<b>by </b><i><a class="txt" href="#E6:15_2"><i><font color="Green" title="E25">A31</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:15_2_10"/><i><font color="Green" title="E53">A84</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c32">d3'</font>
 
<b>by </b><i><a class="txt" href="#E41:15_2"><i><font color="Green" title="E41">A58</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:15_2_10"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<a NAME="E4:15_2_10"/><b>then </b><i><font color="Green" title="E54">A85</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E1:15_2_10"><i><font color="Green" title="E52">A83</font></i></a>, <a class="txt" href="#E2:15_2_10"><i><font color="Green" title="E53">A84</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<a NAME="E5:15_2_10"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:15_2_10"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</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="E7:15_2_10"/><b>then </b><i><font color="Green" title="E55">A86</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E1:15_2_10"><i><font color="Green" title="E52">A83</font></i></a>, <a class="txt" href="#E2:15_2_10"><i><font color="Green" title="E53">A84</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<a NAME="E8:15_2_10"/><i><font color="Green" title="E56">A87</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c26">d2'</font>
 
<b>by </b><i><a class="txt" href="#E24:15_2"><i><font color="Green" title="E33">A46</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:15_2_10"/><i><font color="Green" title="E57">A88</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c38">d4'</font>
 
<b>by </b><i><a class="txt" href="#E58:15_2"><i><font color="Green" title="E49">A71</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:15_2_10"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<a NAME="E11:15_2_10"/><b>then </b><i><font color="Green" title="E58">A89</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c38">d4'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E8:15_2_10"><i><font color="Green" title="E56">A87</font></i></a>, <a class="txt" href="#E9:15_2_10"><i><font color="Green" title="E57">A88</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<a NAME="E12:15_2_10"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:15_2_10"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c38">d4'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E8:15_2_10"><i><font color="Green" title="E56">A87</font></i></a>, <a class="txt" href="#E9:15_2_10"><i><font color="Green" title="E57">A88</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<b>hence </b><a NAME="E14:15_2_10"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c8">b3</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c7">b2</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c5">a3</font> )
 <b>by </b><i><a class="txt" href="#E4:15_2_10"><i><font color="Green" title="E54">A85</font></i></a>, <a class="txt" href="#E7:15_2_10"><i><font color="Green" title="E55">A86</font></i></a>, <a class="txt" href="#E11:15_2_10"><i><font color="Green" title="E58">A89</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E61:15_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c21">d1'</font>
 <b>by </b><i><a class="txt" href="#E6:15_2"><i><font color="Green" title="E25">A31</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E62:15_2"/><b>then </b><i><font color="Green" title="E52">A90</font></i>: 
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">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="E63:15_2"/><b>then </b><i><font color="Green" title="E53">A91</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">d1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E64:15_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c32">d3'</font>
 <b>by </b><i><a class="txt" href="#E41:15_2"><i><font color="Green" title="E41">A58</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E65:15_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c32">d3'</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="E66:15_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">d1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c32">d3'</font>
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E62:15_2"><i><font color="Green" title="E52">A90</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E67:15_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</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="E68:15_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c32">d3'</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="E69:15_2"/><b>then </b>
<font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</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="E70:15_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">d1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</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="E71:15_2"/><b>then </b><i><font color="Green" title="E54">A92</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E72:15_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c26">d2'</font>
 <b>by </b><i><a class="txt" href="#E24:15_2"><i><font color="Green" title="E33">A46</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E73:15_2"/><b>then </b><i><font color="Green" title="E55">A93</font></i>: 
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c26">d2'</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="E74:15_2"/><b>then </b><i><font color="Green" title="E56">A94</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E75:15_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c38">d4'</font>
 <b>by </b><i><a class="txt" href="#E58:15_2"><i><font color="Green" title="E49">A71</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E76:15_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c38">d4'</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="E77:15_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c26">d2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c38">d4'</font>
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E73:15_2"><i><font color="Green" title="E55">A93</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E78:15_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c38">d4'</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="E79:15_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c38">d4'</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="E80:15_2"/><b>then </b>
<font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c38">d4'</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="E81:15_2"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c26">d2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c38">d4'</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="E82:15_2"/><b>then </b><i><font color="Green" title="E57">A95</font></i>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E83:15_2"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">d1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E63:15_2"><i><font color="Green" title="E53">A91</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E84:15_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>
 <b>by </b><i><a class="txt" href="#E5:15_2"><i><font color="Green" title="E24">A30</font></i></a>, <a class="txt" href="#E71:15_2"><i><font color="Green" title="E54">A92</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E85:15_2"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E74:15_2"><i><font color="Green" title="E56">A94</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E86:15_2"/><b>then </b><i><font color="Green" title="E58">A96</font></i>: 
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>
 <b>by </b><i><a class="txt" href="#E23:15_2"><i><font color="Green" title="E32">A41</font></i></a>, <a class="txt" href="#E82:15_2"><i><font color="Green" title="E57">A95</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E87:15_2"/><i><font color="Green" title="E59">A97</font></i>: 
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="#E11:15_2"><i><font color="Green" title="E27">A33</font></i></a>, <a class="txt" href="#E19:15_2"><i><font color="Green" title="E30">A39</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E88:15_2"/><i><font color="Green" title="E60">A98</font></i>: 
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 <b>by </b><i><a class="txt" href="#E28:15_2"><i><font color="Green" title="E35">A48</font></i></a>, <a class="txt" href="#E36:15_2"><i><font color="Green" title="E38">A53</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E89:15_2"/><i><font color="Green" title="E61">A99</font></i>: 
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c40">d4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="txt" href="#E45:15_2"><i><font color="Green" title="E43">A60</font></i></a>, <a class="txt" href="#E53:15_2"><i><font color="Green" title="E46">A66</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E90:15_2"/><i><font color="Green" title="E62">A100</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c33">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_11"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_11"/><i><font color="Green" title="E63">A101</font></i>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c33">d3</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_2_11"/><i><font color="Green" title="E64">A102</font></i>: 
<font color="Maroon" title="c20">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_11_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_11_1"/><i><font color="Green" title="E65">A103</font></i>: 
<font color="Maroon" title="c20">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">d3</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_2_11_1"/><i><font color="Green" title="E66">A104</font></i>: 
<font color="Maroon" title="c20">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_11_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_11_1_1"/>
<font color="Maroon" title="c20">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">d2</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_2_11_1_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">d1'</font>
 
<b>by </b><i><a class="txt" href="#E22:15_2"><i><font color="Green" title="E31">A40</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:15_2_11_1_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c21">d1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">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_2_11_1_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:15_2_11_1_1"/><b>then </b>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E5:15_2"><i><font color="Green" title="E24">A30</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E6:15_2_11_1_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:15_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E8:15_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E9:15_2_11_1_1"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E10:15_2_11_1_1"/><b>then </b><i><font color="Green" title="E67">A105</font></i>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E11:15_2_11_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:15_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E13:15_2_11_1_1"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</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="E14:15_2_11_1_1"/><b>then </b>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:15_2_11_1_1"/><b>then </b>
<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="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E10:15_2_11_1_1"><i><font color="Green" title="E67">A105</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:15_2_11_1_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:15_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:15_2_11_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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="E19:15_2_11_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E3:15_2_11_1"/><i><font color="Green" title="E67">A106</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_11_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_11_1_2"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ; <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_2_11_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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>hence </b><a NAME="E3:15_2_11_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E4:15_2_11_1"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font>
 
<b>by </b><i><a class="txt" href="#E41:15_2"><i><font color="Green" title="E41">A58</font></i></a>, <a class="txt" href="#E1:15_2_11_1"><i><font color="Green" title="E65">A103</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E5:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E24:15_2"><i><font color="Green" title="E33">A46</font></i></a>, <a class="txt" href="#E2:15_2_11_1"><i><font color="Green" title="E66">A104</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E6:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">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="E8:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">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="E9:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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="E10:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">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="E11:15_2_11_1"/><b>then </b><i><font color="Green" title="E68">A107</font></i>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E12:15_2_11_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">o'</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="E14:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">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="E15:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E16:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2_11_1"><i><font color="Green" title="E67">A106</font></i></a>, <a class="txt" href="#E11:15_2_11_1"><i><font color="Green" title="E68">A107</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E17:15_2_11_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E19:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c12">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="E20:15_2_11_1"/><b>then </b><i><font color="Green" title="E69">A108</font></i>: 
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">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="E21:15_2_11_1"/>
( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> )
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E22:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E23:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E24:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E20:15_2_11_1"><i><font color="Green" title="E69">A108</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E25:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E26:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E27:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E28:15_2_11_1"/><b>then </b><i><font color="Green" title="E70">A109</font></i>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E29:15_2_11_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E30:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E31:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">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="E32:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E33:15_2_11_1"/><b>then </b>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E28:15_2_11_1"><i><font color="Green" title="E70">A109</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E34:15_2_11_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E35:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E36:15_2_11_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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="E37:15_2_11_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E3:15_2_11"/><i><font color="Green" title="E65">A110</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E60:15_2"><i><font color="Green" title="E51">A82</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:15_2_11"/><i><font color="Green" title="E66">A111</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E60:15_2"><i><font color="Green" title="E51">A82</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:15_2_11"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c38">d4'</font>,<font color="Maroon" title="c32">d3'</font>
 
<b>by </b><i><a class="txt" href="#E1:15_2_11"><i><font color="Green" title="E63">A101</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c38">d4'</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="E7:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c38">d4'</font>
 
<b>by </b><i><a class="txt" href="#E2:15_2_11"><i><font color="Green" title="E64">A102</font></i></a>, <a class="txt" href="#E3:15_2_11"><i><font color="Green" title="E65">A110</font></i></a>, <a class="txt" href="#E4:15_2_11"><i><font color="Green" title="E66">A111</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<a NAME="E8:15_2_11"/><b>then </b><i><font color="Green" title="E67">A112</font></i>: 
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c38">d4'</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="E9:15_2_11"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E10:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</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="E11:15_2_11"/><b>then </b><i><font color="Green" title="E68">A113</font></i>: 
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">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="E12:15_2_11"/>
<font color="Maroon" title="c16">b2'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b3'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_11_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_11_2"/>
<font color="Maroon" title="c16">b2'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">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="E2:15_2_11_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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>hence </b><a NAME="E3:15_2_11_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E13:15_2_11"/><b>then </b>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c38">d4'</font>
 
<b>by </b><i><a class="txt" href="#E8:15_2_11"><i><font color="Green" title="E67">A112</font></i></a>, <a class="txt" href="#E11:15_2_11"><i><font color="Green" title="E68">A113</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E14:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c38">d4'</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="E15:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c38">d4'</font>,<font color="Maroon" title="c16">b2'</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="E16:15_2_11"/><b>then </b><i><font color="Green" title="E69">A114</font></i>: 
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c38">d4'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E17:15_2_11"/>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c38">d4'</font>
 
<b>by </b><i><a class="txt" href="#E56:15_2"><i><font color="Green" title="E47">A67</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E18:15_2_11"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c38">d4'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">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="E19:15_2_11"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="#E57:15_2"><i><font color="Green" title="E48">A68</font></i></a>, <a class="txt" href="#E16:15_2_11"><i><font color="Green" title="E69">A114</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E20:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">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="E21:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</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="E22:15_2_11"/><b>then </b><i><font color="Green" title="E70">A115</font></i>: 
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">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="E23:15_2_11"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E24:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</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="E25:15_2_11"/><b>then </b>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">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="E26:15_2_11"/><b>then </b>
<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E22:15_2_11"><i><font color="Green" title="E70">A115</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E27:15_2_11"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">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/>
<b>hence </b><a NAME="E28:15_2_11"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E91:15_2"/><i><font color="Green" title="E63">A116</font></i>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c40">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_12"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_12"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c40">d4</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_2_12"/><b>then </b><i><font color="Green" title="E64">A117</font></i>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font>
 
<b>by </b><i><a class="txt" href="#E58:15_2"><i><font color="Green" title="E49">A71</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:15_2_12"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_12_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_12_1"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">d3</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_2_12_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c32">d3'</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>hence </b><a NAME="E3:15_2_12_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E59:15_2"><i><font color="Green" title="E50">A72</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E4:15_2_12"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<b>by </b><i><a class="txt" href="#E41:15_2"><i><font color="Green" title="E41">A58</font></i></a>, <a class="txt" href="#E2:15_2_12"><i><font color="Green" title="E64">A117</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E5:15_2_12"/><b>then </b>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:15_2_12"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:15_2_12"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:15_2_12"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c14">a3'</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="E9:15_2_12"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E7:15"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E2:15_2"><i><font color="Green" title="E22">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><a NAME="E92:15_2"/><i><font color="Green" title="E64">A118</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c17">b3'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c16">b2'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c38">d4'</font>,<font color="Maroon" title="c12">a1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c38">d4'</font>,<font color="Maroon" title="c14">a3'</font> )
 <b>by </b><i><a class="txt" href="#E60:15_2"><i><font color="Green" title="E51">A82</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon" title="c41">A'</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E94:15_2"/><i><font color="Green" title="E65">A119</font></i>: 
( <font color="Maroon" title="c41">A'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c21">d1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">A'</font> &amp; <font color="Maroon" title="c32">d3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">A'</font> &amp; <font color="Maroon" title="c17">b3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">A'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c42">A</font> = <font color="Maroon" title="c41">A'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/><a NAME="E96:15_2"/><i><font color="Green" title="E66">A120</font></i>: 
<font color="Maroon" title="c21">d1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c32">d3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_13"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_13"/>
<font color="Maroon" title="c21">d1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">d3'</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_2_13"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c32">d3'</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>hence </b><a NAME="E3:15_2_13"/>
contradiction
 <b>by </b><i><a class="txt" href="#E59:15_2"><i><font color="Green" title="E50">A72</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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>consider </b><font color="Maroon" title="c43">K'</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E98:15_2"/><i><font color="Green" title="E67">A121</font></i>: 
( <font color="Maroon" title="c43">K'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c26">d2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c43">K'</font> &amp; <font color="Maroon" title="c38">d4'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c43">K'</font> &amp; <font color="Maroon" title="c12">a1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c43">K'</font> )
 <b>by </b><i><a class="txt" href="#E92:15_2"><i><font color="Green" title="E64">A118</font></i></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c44">K</font> = <font color="Maroon" title="c43">K'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/><a NAME="E100:15_2"/><i><font color="Green" title="E68">A122</font></i>: 
not <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_14"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_14"/><i><font color="Green" title="E69">A123</font></i>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</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_2_14"/>
<font color="Maroon" title="c41">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c41">A'</font>
 
<b>by </b><i><a class="txt" href="#E94:15_2"><i><font color="Green" title="E65">A119</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_2_14"/><b>then </b>
<font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c26">d2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>
 
<b>by </b><i><a class="txt" href="#E94:15_2"><i><font color="Green" title="E65">A119</font></i></a>, <a class="txt" href="#E1:15_2_14"><i><font color="Green" title="E69">A123</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_2_14"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c32">d3'</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_2_14"/>
contradiction
 <b>by </b><i><a class="txt" href="#E59:15_2"><i><font color="Green" title="E50">A72</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E101:15_2"/><i><font color="Green" title="E69">A124</font></i>: 
not <font color="Maroon" title="c40">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_15"/><i><font color="Green" title="E70">A125</font></i>: 
<font color="Maroon" title="c40">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</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_2_15"/>
<font color="Maroon" title="c41">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c41">A'</font>
 
<b>by </b><i><a class="txt" href="#E94:15_2"><i><font color="Green" title="E65">A119</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_2_15"/><b>then </b>
<font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c38">d4'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>
 
<b>by </b><i><a class="txt" href="#E94:15_2"><i><font color="Green" title="E65">A119</font></i></a>, <a class="txt" href="#E1:15_2_15"><i><font color="Green" title="E70">A125</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_2_15"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c38">d4'</font>,<font color="Maroon" title="c32">d3'</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_2_15"/>
contradiction
 <b>by </b><i><a class="txt" href="#E90:15_2"><i><font color="Green" title="E62">A100</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E102:15_2"/>
<font color="Maroon" title="c42">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c44">K</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_16"><b>proof </b></a><div class="add">

<a NAME="E1:15_2_16"/>
<font color="Maroon" title="c41">A'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>
 
<b>by </b><i><a class="txt" href="#E94:15_2"><i><font color="Green" title="E65">A119</font></i></a>, <a class="txt" href="#E96:15_2"><i><font color="Green" title="E66">A120</font></i></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></i>;<br/>
<a NAME="E2:15_2_16"/><b>then </b><i><font color="Green" title="E70">A126</font></i>: 
<font color="Maroon" title="c42">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></i>;<br/>
<a NAME="E3:15_2_16"/>
<font color="Maroon" title="c43">K'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c26">d2'</font>,<font color="Maroon" title="c38">d4'</font>
 
<b>by </b><i><a class="txt" href="#E91:15_2"><i><font color="Green" title="E63">A116</font></i></a>, <a class="txt" href="#E98:15_2"><i><font color="Green" title="E67">A121</font></i></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></i>;<br/>
<a NAME="E4:15_2_16"/><b>then </b>
<font color="Maroon" title="c44">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></i>;<br/>
<b>hence </b><a NAME="E5:15_2_16"/>
<font color="Maroon" title="c42">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c44">K</font>
 <b>by </b><i><a class="txt" href="#E86:15_2"><i><font color="Green" title="E58">A96</font></i></a>, <a class="txt" href="#E91:15_2"><i><font color="Green" title="E63">A116</font></i></a>, <a class="txt" href="#E96:15_2"><i><font color="Green" title="E66">A120</font></i></a>, <a class="txt" href="#E2:15_2_16"><i><font color="Green" title="E70">A126</font></i></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</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="E103:15_2"/><b>then </b>
( <font color="Maroon" title="c42">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c44">K</font> &amp; <font color="Maroon" title="c20">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</font> &amp; <font color="Maroon" title="c33">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</font> &amp; <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c44">K</font> &amp; <font color="Maroon" title="c40">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c44">K</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c44">K</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c44">K</font> &amp; not <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</font> &amp; not <font color="Maroon" title="c40">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c42">A</font> )
 <b>by </b><i><a class="txt" href="#E91:15_2"><i><font color="Green" title="E63">A116</font></i></a>, <a class="txt" href="#E92:15_2"><i><font color="Green" title="E64">A118</font></i></a>, <a class="txt" href="#E94:15_2"><i><font color="Green" title="E65">A119</font></i></a>, <a class="txt" href="#E96:15_2"><i><font color="Green" title="E66">A120</font></i></a>, <a class="txt" href="#E98:15_2"><i><font color="Green" title="E67">A121</font></i></a>, <a class="txt" href="#E100:15_2"><i><font color="Green" title="E68">A122</font></i></a>, <a class="txt" href="#E101:15_2"><i><font color="Green" title="E69">A124</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E104:15_2"/><b>then </b><i><font color="Green" title="E70">A127</font></i>: 
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c40">d4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="txt" href="#E2:15"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E87:15_2"><i><font color="Green" title="E59">A97</font></i></a>, <a class="txt" href="#E88:15_2"><i><font color="Green" title="E60">A98</font></i></a>, <a class="txt" href="#E89:15_2"><i><font color="Green" title="E61">A99</font></i></a>, <a class="ref" href="conmetr.html#D4" target="_self" title="CONMETR:def.4">Def4</a></i>;<br/><a NAME="E105:15_2"/><i><font color="Green" title="E71">A128</font></i>: 
( <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c40">d4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c3">a1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_17"><b>proof </b></a><div class="add">

<a NAME="E1:15_2_17"/><i><font color="Green" title="E72">A129</font></i>: 
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<b>by </b><i><a class="txt" href="#E41:15_2"><i><font color="Green" title="E41">A58</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E2:15_2_17"/><i><font color="Green" title="E73">A130</font></i>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_17_1"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">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="E2:15_2_17_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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>hence </b><a NAME="E3:15_2_17_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E3:15_2_17"/><i><font color="Green" title="E74">A131</font></i>: 
( <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c40">d4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> or <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> )
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E58:15_2"><i><font color="Green" title="E49">A71</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E4:15_2_17"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_17_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_17_2"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">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="E2:15_2_17_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b2'</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>hence </b><a NAME="E3:15_2_17_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E5:15_2_17"/>
( <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c40">d4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c3">a1</font> )
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E24:15_2"><i><font color="Green" title="E33">A46</font></i></a>, <a class="txt" href="#E1:15_2_17"><i><font color="Green" title="E72">A129</font></i></a>, <a class="txt" href="#E2:15_2_17"><i><font color="Green" title="E73">A130</font></i></a>, <a class="txt" href="#E3:15_2_17"><i><font color="Green" title="E74">A131</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="E106:15_2"/><i><font color="Green" title="E72">A132</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c8">b3</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c4">a2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_18"><b>proof </b></a><div class="add">

<a NAME="E1:15_2_18"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:15_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c15">b1'</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="E3:15_2_18"/><b>then </b><i><font color="Green" title="E73">A133</font></i>: 
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</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="E4:15_2_18"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c17">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:15_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</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="E6:15_2_18"/><b>then </b><i><font color="Green" title="E74">A134</font></i>: 
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">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="E7:15_2_18"/>
<font color="Maroon" title="c17">b3'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b2'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_18_1"/>
<font color="Maroon" title="c17">b3'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">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="E2:15_2_18_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c17">b3'</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>hence </b><a NAME="E3:15_2_18_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E8:15_2_18"/><b>then </b>
<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c11">o'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2_18"><i><font color="Green" title="E73">A133</font></i></a>, <a class="txt" href="#E6:15_2_18"><i><font color="Green" title="E74">A134</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E9:15_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</font>,<font color="Maroon" title="c11">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="E10:15_2_18"/><b>then </b><i><font color="Green" title="E75">A135</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c15">b1'</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="E11:15_2_18"/><i><font color="Green" title="E76">A136</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c21">d1'</font>
 
<b>by </b><i><a class="txt" href="#E6:15_2"><i><font color="Green" title="E25">A31</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:15_2_18"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c17">b3'</font>,<font color="Maroon" title="c32">d3'</font>
 
<b>by </b><i><a class="txt" href="#E41:15_2"><i><font color="Green" title="E41">A58</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:15_2_18"/><b>then </b><i><font color="Green" title="E77">A137</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">d1'</font>,<font color="Maroon" title="c32">d3'</font>,<font color="Maroon" title="c15">b1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E10:15_2_18"><i><font color="Green" title="E75">A135</font></i></a>, <a class="txt" href="#E11:15_2_18"><i><font color="Green" title="E76">A136</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c45">o'</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c46">a1'</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c47">a2'</font> = <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c48">a3'</font> = <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c49">d2'</font> = <font color="Maroon" title="c27">d2</font>, <font color="Maroon" title="c50">d4'</font> = <font color="Maroon" title="c40">d4</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E15:15_2_18"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c46">a1'</font>,<font color="Maroon" title="c47">a2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E16:15_2_18"/><b>then </b><i><font color="Green" title="E78">A138</font></i>: 
<font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c46">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c47">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="E17:15_2_18"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">o'</font>,<font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c46">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:15_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c46">a1'</font>,<font color="Maroon" title="c45">o'</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="E19:15_2_18"/><b>then </b><i><font color="Green" title="E79">A139</font></i>: 
<font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c46">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c45">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="E20:15_2_18"/>
<font color="Maroon" title="c48">a3'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c46">a1'</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_18_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_18_2"/>
<font color="Maroon" title="c46">a1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c48">a3'</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_2_18_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c46">a1'</font>,<font color="Maroon" title="c16">b2'</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>hence </b><a NAME="E3:15_2_18_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E21:15_2_18"/><b>then </b>
<font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c47">a2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c45">o'</font>
 
<b>by </b><i><a class="txt" href="#E16:15_2_18"><i><font color="Green" title="E78">A138</font></i></a>, <a class="txt" href="#E19:15_2_18"><i><font color="Green" title="E79">A139</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E22:15_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c47">a2'</font>,<font color="Maroon" title="c45">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="E23:15_2_18"/><b>then </b><i><font color="Green" title="E80">A140</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">o'</font>,<font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c47">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="E24:15_2_18"/><i><font color="Green" title="E81">A141</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">o'</font>,<font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c49">d2'</font>
 
<b>by </b><i><a class="txt" href="#E24:15_2"><i><font color="Green" title="E33">A46</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E25:15_2_18"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">o'</font>,<font color="Maroon" title="c48">a3'</font>,<font color="Maroon" title="c50">d4'</font>
 
<b>by </b><i><a class="txt" href="#E58:15_2"><i><font color="Green" title="E49">A71</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E26:15_2_18"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c49">d2'</font>,<font color="Maroon" title="c50">d4'</font>,<font color="Maroon" title="c47">a2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E23:15_2_18"><i><font color="Green" title="E80">A140</font></i></a>, <a class="txt" href="#E24:15_2_18"><i><font color="Green" title="E81">A141</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<b>hence </b><a NAME="E27:15_2_18"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c8">b3</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>,<font color="Maroon" title="c4">a2</font> )
 <b>by </b><i><a class="txt" href="#E60:15_2"><i><font color="Green" title="E51">A82</font></i></a>, <a class="txt" href="#E13:15_2_18"><i><font color="Green" title="E77">A137</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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>reconsider </b><font color="Maroon" title="c45">d1'</font> = <font color="Maroon" title="c20">d1</font>, <font color="Maroon" title="c46">d2'</font> = <font color="Maroon" title="c27">d2</font>, <font color="Maroon" title="c47">d3'</font> = <font color="Maroon" title="c33">d3</font>, <font color="Maroon" title="c48">d4'</font> = <font color="Maroon" title="c40">d4</font>, <font color="Maroon" title="c49">b3'</font> = <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c50">a1'</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c51">b1'</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c52">a2'</font> = <font color="Maroon" title="c4">a2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E108:15_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c47">d3'</font>,<font color="Maroon" title="c49">b3'</font>
 <b>by </b><i><a class="txt" href="#E106:15_2"><i><font color="Green" title="E72">A132</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon" title="c53">A'</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E110:15_2"/><i><font color="Green" title="E73">A142</font></i>: 
( <font color="Maroon" title="c53">A'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c45">d1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c53">A'</font> &amp; <font color="Maroon" title="c47">d3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c53">A'</font> &amp; <font color="Maroon" title="c49">b3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c53">A'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c54">A</font> = <font color="Maroon" title="c53">A'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/><a NAME="E112:15_2"/><i><font color="Green" title="E74">A143</font></i>: 
<font color="Maroon" title="c45">d1'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c47">d3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_19"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_19"/>
<font color="Maroon" title="c45">d1'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c47">d3'</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_2_19"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c46">d2'</font>,<font color="Maroon" title="c47">d3'</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>hence </b><a NAME="E3:15_2_19"/>
contradiction
 <b>by </b><i><a class="txt" href="#E59:15_2"><i><font color="Green" title="E50">A72</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E113:15_2"/><i><font color="Green" title="E75">A144</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c47">d3'</font>,<font color="Maroon" title="c51">b1'</font>
 <b>by </b><i><a class="txt" href="#E106:15_2"><i><font color="Green" title="E72">A132</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E114:15_2"/><i><font color="Green" title="E76">A145</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c46">d2'</font>,<font color="Maroon" title="c48">d4'</font>,<font color="Maroon" title="c50">a1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c46">d2'</font>,<font color="Maroon" title="c48">d4'</font>,<font color="Maroon" title="c52">a2'</font> )
 <b>by </b><i><a class="txt" href="#E106:15_2"><i><font color="Green" title="E72">A132</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><b>then consider </b><font color="Maroon" title="c55">K'</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E116:15_2"/><i><font color="Green" title="E77">A146</font></i>: 
( <font color="Maroon" title="c55">K'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c46">d2'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">K'</font> &amp; <font color="Maroon" title="c48">d4'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">K'</font> &amp; <font color="Maroon" title="c50">a1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">K'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c56">K</font> = <font color="Maroon" title="c55">K'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/><a NAME="E118:15_2"/><i><font color="Green" title="E78">A147</font></i>: 
not <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_20"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_20"/><i><font color="Green" title="E79">A148</font></i>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</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_2_20"/>
<font color="Maroon" title="c53">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c53">A'</font>
 
<b>by </b><i><a class="txt" href="#E110:15_2"><i><font color="Green" title="E73">A142</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_2_20"/><b>then </b>
<font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c46">d2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c47">d3'</font>
 
<b>by </b><i><a class="txt" href="#E110:15_2"><i><font color="Green" title="E73">A142</font></i></a>, <a class="txt" href="#E1:15_2_20"><i><font color="Green" title="E79">A148</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_2_20"/><b>then </b>
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E5:15_2_20"/>
contradiction
 <b>by </b><i><a class="txt" href="#E59:15_2"><i><font color="Green" title="E50">A72</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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><a NAME="E119:15_2"/><i><font color="Green" title="E79">A149</font></i>: 
not <font color="Maroon" title="c40">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_21"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_21"/><i><font color="Green" title="E80">A150</font></i>: 
<font color="Maroon" title="c40">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</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_2_21"/>
<font color="Maroon" title="c53">A'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c53">A'</font>
 
<b>by </b><i><a class="txt" href="#E110:15_2"><i><font color="Green" title="E73">A142</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E3:15_2_21"/><b>then </b>
<font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c48">d4'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c47">d3'</font>
 
<b>by </b><i><a class="txt" href="#E110:15_2"><i><font color="Green" title="E73">A142</font></i></a>, <a class="txt" href="#E1:15_2_21"><i><font color="Green" title="E80">A150</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E4:15_2_21"/><b>then </b>
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c40">d4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E5:15_2_21"/>
contradiction
 <b>by </b><i><a class="txt" href="#E90:15_2"><i><font color="Green" title="E62">A100</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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><a NAME="E120:15_2"/>
<font color="Maroon" title="c54">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c56">K</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_22"><b>proof </b></a><div class="add">

<a NAME="E1:15_2_22"/>
<font color="Maroon" title="c53">A'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c47">d3'</font>
 
<b>by </b><i><a class="txt" href="#E110:15_2"><i><font color="Green" title="E73">A142</font></i></a>, <a class="txt" href="#E112:15_2"><i><font color="Green" title="E74">A143</font></i></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></i>;<br/>
<a NAME="E2:15_2_22"/><b>then </b><i><font color="Green" title="E80">A151</font></i>: 
<font color="Maroon" title="c54">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c33">d3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></i>;<br/>
<a NAME="E3:15_2_22"/>
<font color="Maroon" title="c55">K'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c46">d2'</font>,<font color="Maroon" title="c48">d4'</font>
 
<b>by </b><i><a class="txt" href="#E91:15_2"><i><font color="Green" title="E63">A116</font></i></a>, <a class="txt" href="#E116:15_2"><i><font color="Green" title="E77">A146</font></i></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></i>;<br/>
<a NAME="E4:15_2_22"/><b>then </b>
<font color="Maroon" title="c56">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c40">d4</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></i>;<br/>
<b>hence </b><a NAME="E5:15_2_22"/>
<font color="Maroon" title="c54">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c56">K</font>
 <b>by </b><i><a class="txt" href="#E86:15_2"><i><font color="Green" title="E58">A96</font></i></a>, <a class="txt" href="#E91:15_2"><i><font color="Green" title="E63">A116</font></i></a>, <a class="txt" href="#E112:15_2"><i><font color="Green" title="E74">A143</font></i></a>, <a class="txt" href="#E2:15_2_22"><i><font color="Green" title="E80">A151</font></i></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</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="E121:15_2"/><b>then </b>
( <font color="Maroon" title="c54">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c56">K</font> &amp; <font color="Maroon" title="c20">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font> &amp; <font color="Maroon" title="c33">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font> &amp; <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c56">K</font> &amp; <font color="Maroon" title="c40">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c56">K</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c56">K</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c56">K</font> &amp; not <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font> &amp; not <font color="Maroon" title="c40">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font> )
 <b>by </b><i><a class="txt" href="#E91:15_2"><i><font color="Green" title="E63">A116</font></i></a>, <a class="txt" href="#E110:15_2"><i><font color="Green" title="E73">A142</font></i></a>, <a class="txt" href="#E112:15_2"><i><font color="Green" title="E74">A143</font></i></a>, <a class="txt" href="#E113:15_2"><i><font color="Green" title="E75">A144</font></i></a>, <a class="txt" href="#E114:15_2"><i><font color="Green" title="E76">A145</font></i></a>, <a class="txt" href="#E116:15_2"><i><font color="Green" title="E77">A146</font></i></a>, <a class="txt" href="#E118:15_2"><i><font color="Green" title="E78">A147</font></i></a>, <a class="txt" href="#E119:15_2"><i><font color="Green" title="E79">A149</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E122:15_2"/><b>then </b>
<font color="Maroon" title="c20">d1</font>,<font color="Maroon" title="c40">d4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c4">a2</font>
 <b>by </b><i><a class="txt" href="#E1:15"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E105:15_2"><i><font color="Green" title="E71">A128</font></i></a>, <a class="ref" href="conmetr.html#D3" target="_self" title="CONMETR:def.3">Def3</a></i>;<br/><a NAME="E123:15_2"/><b>then </b><i><font color="Green" title="E80">A152</font></i>: 
( <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c4">a2</font> or <font color="Maroon" title="c20">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c40">d4</font> )
 <b>by </b><i><a class="txt" href="#E104:15_2"><i><font color="Green" title="E70">A127</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E124:15_2"/>
<font color="Maroon" title="c20">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c40">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_23"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:15_2_23"/><i><font color="Green" title="E81">A153</font></i>: 
<font color="Maroon" title="c20">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c40">d4</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_2_23"/><i><font color="Green" title="E82">A154</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c49">b3'</font>,<font color="Maroon" title="c11">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<a NAME="E3:15_2_23"/><i><font color="Green" title="E83">A155</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c49">b3'</font>,<font color="Maroon" title="c45">d1'</font>
 
<b>by </b><i><a class="txt" href="#E6:15_2"><i><font color="Green" title="E25">A31</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:15_2_23"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c49">b3'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:15_2_23"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c49">b3'</font>,<font color="Maroon" title="c16">b2'</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="E6:15_2_23"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c45">d1'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E2:15_2_23"><i><font color="Green" title="E82">A154</font></i></a>, <a class="txt" href="#E3:15_2_23"><i><font color="Green" title="E83">A155</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/>
<a NAME="E7:15_2_23"/><b>then </b><i><font color="Green" title="E84">A156</font></i>: 
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c45">d1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</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="E8:15_2_23"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c48">d4'</font>
 
<b>by </b><i><a class="txt" href="#E58:15_2"><i><font color="Green" title="E49">A71</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:15_2_23"/><b>then </b><i><font color="Green" title="E85">A157</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c48">d4'</font>,<font color="Maroon" title="c14">a3'</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="E10:15_2_23"/><i><font color="Green" title="E86">A158</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c50">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:15_2_23"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c48">d4'</font>,<font color="Maroon" title="c11">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<a NAME="E12:15_2_23"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c48">d4'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="txt" href="#E9:15_2_23"><i><font color="Green" title="E85">A157</font></i></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></i>;<br/>
<a NAME="E13:15_2_23"/><b>then </b>
<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c16">b2'</font>
 
<b>by </b><i><a class="txt" href="#E57:15_2"><i><font color="Green" title="E48">A68</font></i></a>, <a class="txt" href="#E1:15_2_23"><i><font color="Green" title="E81">A153</font></i></a>, <a class="txt" href="#E7:15_2_23"><i><font color="Green" title="E84">A156</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E14:15_2_23"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</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="E15:15_2_23"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c11">o'</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="E16:15_2_23"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">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="E17:15_2_23"/><b>then </b><i><font color="Green" title="E87">A159</font></i>: 
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</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="E18:15_2_23"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">o'</font>,<font color="Maroon" title="c50">a1'</font>
 
<b>by </b><i><a class="txt" href="#E10:15_2_23"><i><font color="Green" title="E86">A158</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E19:15_2_23"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c11">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c50">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="E20:15_2_23"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c50">a1'</font>
 
<b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="#E17:15_2_23"><i><font color="Green" title="E87">A159</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E21:15_2_23"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c16">b2'</font>,<font color="Maroon" title="c50">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="E22:15_2_23"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c50">a1'</font>,<font color="Maroon" title="c16">b2'</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="E23:15_2_23"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:15_2"><i><font color="Green" title="E23">A26</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E125:15_2"/><b>then </b>
<font color="Maroon" title="c50">a1'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c49">b3'</font>,<font color="Maroon" title="c52">a2'</font>
 <b>by </b><i><a class="txt" href="#E123:15_2"><i><font color="Green" title="E80">A152</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E126:15_2"/><b>then </b>
<font color="Maroon" title="c50">a1'</font>,<font color="Maroon" title="c16">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c52">a2'</font>,<font color="Maroon" title="c49">b3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><b>hence </b><a NAME="E127:15_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</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="E11:15"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <b>by </b><i><a class="txt" href="#E9:15"><i><font color="Green" title="E20">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>
