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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V1" title="CONMETR:attr.1">satisfying_OPAP</a>  &amp; <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V2" title="CONMETR:attr.2">satisfying_PAP</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V1" title="CONMETR:attr.1">satisfying_OPAP</a> 
 <span class="kw">and </span><br/><a NAME="E2:14"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V1" title="CONAFFM:attr.1">satisfying_DES</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V2" title="CONMETR:attr.2">satisfying_PAP</a> </span><br/>

<span class="kw">let </span><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>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="conmetr.html#D2" target="_self" title="CONMETR:def.2">CONMETR:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">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="Olive" title="b7">M</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  &amp; <font color="Olive" title="b8">N</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="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="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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M</font>, <font color="Olive" title="b2">N</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">M</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  &amp; <font color="Olive" title="b2">N</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="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="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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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>  &amp; <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="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/>

















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:14"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c9">M</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E4:14"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c10">N</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E5:14"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E6:14"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E7:14"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E8:14"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E9:14"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E10:14"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">and </span><br/><a NAME="E11:14"/><span class="lab"><font color="Green" title="E25">A11</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E12:14"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
<font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">and </span><br/><a NAME="E13:14"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
 not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">and </span><br/><a NAME="E14:14"/><span class="lab"><font color="Green" title="E28">A14</font></span>: 
 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>
 <span class="kw">and </span><br/><a NAME="E15:14"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E16:14"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E17:14"/>
<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>
 <span class="kw">and </span><br/><a NAME="E18:14"/><span class="lab"><font color="Green" title="E31">A17</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E19:14"/>
<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>
 <span class="kw">and </span><br/><a NAME="E20:14"/><span class="lab"><font color="Green" title="E32">A18</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E21:14"/><span class="lab"><font color="Green" title="E33">A19</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E22:14"/><span class="lab"><font color="Green" title="E34">A20</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">reconsider </span><font color="Maroon" title="c11">o9</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c12">a19</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c13">a29</font> = <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c14">a39</font> = <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c15">b19</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c16">b29</font> = <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c17">b39</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">M9</font> = <font color="Maroon" title="c9">M</font>, <font color="Maroon" title="c19">N9</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T42" title="ANALMETR:th.42">ANALMETR:42</a></span>;<br/>
<a NAME="E25:14"/><span class="lab"><font color="Green" title="E35">A21</font></span>: 
<font color="Maroon" title="c18">M9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="analmetr.html#T43" title="ANALMETR:th.43">ANALMETR:43</a></span>;<br/>
<a NAME="E26:14"/><span class="lab"><font color="Green" title="E36">A22</font></span>: 
<font color="Maroon" title="c19">N9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="analmetr.html#T43" title="ANALMETR:th.43">ANALMETR:43</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1"/><span class="lab"><font color="Green" title="E37">A23</font></span>: 
 not <font color="Maroon" title="c9">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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><span class="lab"><font color="Green" title="E38">A24</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:14_1_1"/><span class="lab"><font color="Green" title="E39">A25</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E2:14_1_1"/><span class="lab"><font color="Green" title="E40">A26</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E3:14_1_1"/><span class="lab"><font color="Green" title="E41">A27</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E4:14_1_1"/><span class="lab"><font color="Green" title="E42">A28</font></span>: 
( <font color="Maroon" title="c6">b1</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="c7">b2</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="c6">b1</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="14_1_1_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E43">A29</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_1_1_1"/><span class="lab"><font color="Green" title="E44">A30</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_1_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A31</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:14_1_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E2:14_1_1_1_1_1"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_1"/>
<font color="Maroon" title="c6">b1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E4:14_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A32</font></span>: 
<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E5:14_1_1_1_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E6:14_1_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:14_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="txt" href="#E1:14_1_1_1_1"><span class="lab"><font color="Green" title="E44">A30</font></span></a>, <a class="txt" href="#E4:14_1_1_1_1"><span class="lab"><font color="Green" title="E45">A32</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E44">A33</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_1_1_2"/><span class="lab"><font color="Green" title="E45">A34</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_1_2_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_1_1_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A35</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_1_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:14_1_1_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E2:14_1_1_1_2_1"><span class="lab"><font color="Green" title="E46">A35</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_2"/>
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_2"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E4:14_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E5:14_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A36</font></span>: 
<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E6:14_1_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E7:14_1_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E8:14_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E1:14_1_1_1_2"><span class="lab"><font color="Green" title="E45">A34</font></span></a>, <a class="txt" href="#E5:14_1_1_1_2"><span class="lab"><font color="Green" title="E46">A36</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E45">A37</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_1_1_3"/><span class="lab"><font color="Green" title="E46">A38</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c13">a29</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_1_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c13">a29</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_1_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:14_1_1_1_3"/>
<font color="Maroon" title="c6">b1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:14_1_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E4:14_1_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A39</font></span>: 
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c13">a29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E5:14_1_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E6:14_1_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:14_1_1_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E1:14_1_1_1_3"><span class="lab"><font color="Green" title="E46">A38</font></span></a>, <a class="txt" href="#E4:14_1_1_1_3"><span class="lab"><font color="Green" title="E47">A39</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E4:14_1_1_1"/>
( <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> or <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> or <font color="Maroon" title="c6">b1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E5:14_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_1"><span class="lab"><font color="Green" title="E45">A37</font></span></a>, <a class="txt" href="#E2:14_1_1_1"><span class="lab"><font color="Green" title="E44">A33</font></span></a>, <a class="txt" href="#E1:14_1_1_1"><span class="lab"><font color="Green" title="E43">A29</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E43">A40</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_1_2"/><span class="lab"><font color="Green" title="E44">A41</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E4:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A42</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E5:14_1_1_2"/><span class="lab"><font color="Green" title="E46">A43</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E7:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E8:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A44</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c20">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E10:14_1_1_2"/><span class="lab"><font color="Green" title="E48">A45</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>
 <span class="kw">and </span><br/><a NAME="E11:14_1_1_2"/><span class="lab"><font color="Green" title="E49">A46</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T39" title="ANALMETR:th.39">ANALMETR:39</a></span>;<br/><a NAME="E12:14_1_1_2"/><span class="lab"><font color="Green" title="E50">A47</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E10:14_1_1_2"><span class="lab"><font color="Green" title="E48">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c21">e19</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><span class="kw"> such that </span><br/><a NAME="E14:14_1_1_2"/><span class="lab"><font color="Green" title="E51">A48</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c21">e19</font>
 <span class="kw">and </span><br/><a NAME="E15:14_1_1_2"/><span class="lab"><font color="Green" title="E52">A49</font></span>: 
<font color="Maroon" title="c16">b29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c22">x9</font> = <font color="Maroon" title="c20">x</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E17:14_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c22">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">A9</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><span class="kw"> such that </span><br/><a NAME="E19:14_1_1_2"/><span class="lab"><font color="Green" title="E53">A50</font></span>: 
<font color="Maroon" title="c23">A9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E20:14_1_1_2"/><span class="lab"><font color="Green" title="E54">A51</font></span>: 
<font color="Maroon" title="c11">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E21:14_1_1_2"/><span class="lab"><font color="Green" title="E55">A52</font></span>: 
<font color="Maroon" title="c22">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E22:14_1_1_2"/>
<font color="Maroon" title="c22">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T21" title="AFF_1:th.21">AFF_1:21</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">A</font> = <font color="Maroon" title="c23">A9</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T42" title="ANALMETR:th.42">ANALMETR:42</a></span>;<br/><a NAME="E24:14_1_1_2"/><span class="lab"><font color="Green" title="E56">A53</font></span>: 
 for <font color="Olive" title="b1">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font> holds <br/> <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Olive" title="b1">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c25">e1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font> implies  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:14_1_1_2_3"/><span class="lab"><font color="Green" title="E57">A54</font></span>: 
<font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c26">e19</font> = <font color="Maroon" title="c25">e1</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E3:14_1_1_2_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">x9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c26">e19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E21:14_1_1_2"><span class="lab"><font color="Green" title="E55">A52</font></span></a>, <a class="txt" href="#E1:14_1_1_2_3"><span class="lab"><font color="Green" title="E57">A54</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c26">e19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_2_3"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E25:14_1_1_2"/>
 for <font color="Olive" title="b1">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Olive" title="b1">e1</font> holds <br/><font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c25">e1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font> implies <font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:14_1_1_2_4"/><span class="lab"><font color="Green" title="E57">A55</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c26">e19</font> = <font color="Maroon" title="c25">e1</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E3:14_1_1_2_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c26">e19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_2_4"><span class="lab"><font color="Green" title="E57">A55</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_2_4"/>
<font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1_2"><span class="lab"><font color="Green" title="E49">A46</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E21:14_1_1_2"><span class="lab"><font color="Green" title="E55">A52</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E26:14_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">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="c2">o</font>,<font color="Maroon" title="c20">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:14_1_1_2"><span class="lab"><font color="Green" title="E56">A53</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E27:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A56</font></span>: 
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14_1_1_2"><span class="lab"><font color="Green" title="E49">A46</font></span></a>, <a class="txt" href="#E12:14_1_1_2"><span class="lab"><font color="Green" title="E50">A47</font></span></a>, <a class="ref" href="analmetr.html#D14" title="ANALMETR:def.14">ANALMETR:def 14</a></span>;<br/><a NAME="E28:14_1_1_2"/><span class="lab"><font color="Green" title="E58">A57</font></span>: 
 not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_5"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_5"/><span class="lab"><font color="Green" title="E59">A58</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_5"/>
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E1:14_1_1_2_5"><span class="lab"><font color="Green" title="E59">A58</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E4:14_1_1_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_2_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E29:14_1_1_2"/><span class="lab"><font color="Green" title="E59">A59</font></span>: 
 not <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="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E30:14_1_1_2"/>
 not <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c21">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_6"/><span class="lab"><font color="Green" title="E60">A60</font></span>: 
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c21">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c25">d19</font>, <font color="Maroon" title="c26">d29</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><span class="kw"> such that </span><br/><a NAME="E3:14_1_1_2_6"/><span class="lab"><font color="Green" title="E61">A61</font></span>: 
<font color="Maroon" title="c25">d19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d29</font>
 <span class="kw">and </span><br/><a NAME="E4:14_1_1_2_6"/><span class="lab"><font color="Green" title="E62">A62</font></span>: 
<font color="Maroon" title="c23">A9</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="c25">d19</font>,<font color="Maroon" title="c26">d29</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/>
<a NAME="E5:14_1_1_2_6"/><span class="lab"><font color="Green" title="E63">A63</font></span>: 
<font color="Maroon" title="c26">d29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_2_6"><span class="lab"><font color="Green" title="E62">A62</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c27">d1</font> = <font color="Maroon" title="c25">d19</font>, <font color="Maroon" title="c28">d2</font> = <font color="Maroon" title="c26">d29</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E7:14_1_1_2_6"/>
<font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E8:14_1_1_2_6"/><span class="kw">then </span>
<font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_2_6"><span class="lab"><font color="Green" title="E61">A61</font></span></a>, <a class="txt" href="#E4:14_1_1_2_6"><span class="lab"><font color="Green" title="E62">A62</font></span></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></span>;<br/>
<a NAME="E9:14_1_1_2_6"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c21">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E1:14_1_1_2_6"><span class="lab"><font color="Green" title="E60">A60</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/>
<a NAME="E10:14_1_1_2_6"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14_1_1_2"><span class="lab"><font color="Green" title="E51">A48</font></span></a>, <a class="txt" href="#E15:14_1_1_2"><span class="lab"><font color="Green" title="E52">A49</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E11:14_1_1_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A64</font></span>: 
<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="c27">d1</font>,<font color="Maroon" title="c28">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E12:14_1_1_2_6"/>
<font color="Maroon" title="c25">d19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_2_6"><span class="lab"><font color="Green" title="E62">A62</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E13:14_1_1_2_6"/><span class="kw">then </span>
<font color="Maroon" title="c27">d1</font>,<font color="Maroon" title="c28">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="txt" href="#E5:14_1_1_2_6"><span class="lab"><font color="Green" title="E63">A63</font></span></a>, <a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:14_1_1_2_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:14_1_1_2"><span class="lab"><font color="Green" title="E59">A59</font></span></a>, <a class="txt" href="#E3:14_1_1_2_6"><span class="lab"><font color="Green" title="E61">A61</font></span></a>, <a class="txt" href="#E11:14_1_1_2_6"><span class="lab"><font color="Green" title="E64">A64</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">c39</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><span class="kw"> such that </span><br/><a NAME="E32:14_1_1_2"/><span class="lab"><font color="Green" title="E60">A65</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E33:14_1_1_2"/><span class="lab"><font color="Green" title="E61">A66</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c21">e19</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></span>;<br/><a NAME="E34:14_1_1_2"/>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c21">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:14_1_1_2"><span class="lab"><font color="Green" title="E61">A66</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E35:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A67</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:14_1_1_2"><span class="lab"><font color="Green" title="E51">A48</font></span></a>, <a class="txt" href="#E15:14_1_1_2"><span class="lab"><font color="Green" title="E52">A49</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c26">e19</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><span class="kw"> such that </span><br/><a NAME="E37:14_1_1_2"/><span class="lab"><font color="Green" title="E63">A68</font></span>: 
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">and </span><br/><a NAME="E38:14_1_1_2"/><span class="lab"><font color="Green" title="E64">A69</font></span>: 
<font color="Maroon" title="c12">a19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/><a NAME="E39:14_1_1_2"/>
 not <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c26">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_7"/><span class="lab"><font color="Green" title="E65">A70</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">o9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_7_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_7_1"/>
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_7_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A71</font></span>: 
<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="c7">b2</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:14_1_1_2"><span class="lab"><font color="Green" title="E62">A67</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E3:14_1_1_2_7_1"/>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_2_7_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E5:14_1_1_2_7_1"/><span class="kw">then </span>
<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="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7_1"><span class="lab"><font color="Green" title="E66">A71</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E6:14_1_1_2_7_1"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E7:14_1_1_2_7_1"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E8:14_1_1_2_7_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:14_1_1_2_7_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_7"/><span class="lab"><font color="Green" title="E66">A72</font></span>: 
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c26">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_7"/><span class="lab"><font color="Green" title="E67">A73</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E4:14_1_1_2_7"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E5:14_1_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E2:14_1_1_2_7"><span class="lab"><font color="Green" title="E66">A72</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/>
<a NAME="E6:14_1_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:14_1_1_2"><span class="lab"><font color="Green" title="E63">A68</font></span></a>, <a class="txt" href="#E38:14_1_1_2"><span class="lab"><font color="Green" title="E64">A69</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E7:14_1_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E8:14_1_1_2_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E1:14_1_1_2_7"><span class="lab"><font color="Green" title="E65">A70</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E10:14_1_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E3:14_1_1_2_7"><span class="lab"><font color="Green" title="E67">A73</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E11:14_1_1_2_7"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:14_1_1_2_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c27">c19</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><span class="kw"> such that </span><br/><a NAME="E41:14_1_1_2"/><span class="lab"><font color="Green" title="E65">A74</font></span>: 
<font color="Maroon" title="c27">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E42:14_1_1_2"/><span class="lab"><font color="Green" title="E66">A75</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c27">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c28">c1</font> = <font color="Maroon" title="c27">c19</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">c3</font> = <font color="Maroon" title="c25">c39</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E45:14_1_1_2"/>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c27">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:14_1_1_2"><span class="lab"><font color="Green" title="E66">A75</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E46:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A76</font></span>: 
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c27">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:14_1_1_2"><span class="lab"><font color="Green" title="E63">A68</font></span></a>, <a class="txt" href="#E38:14_1_1_2"><span class="lab"><font color="Green" title="E64">A69</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E47:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A77</font></span>: 
<font color="Maroon" title="c29">c3</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="c28">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c30">e19</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><span class="kw"> such that </span><br/><a NAME="E49:14_1_1_2"/><span class="lab"><font color="Green" title="E69">A78</font></span>: 
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c30">e19</font>
 <span class="kw">and </span><br/><a NAME="E50:14_1_1_2"/><span class="lab"><font color="Green" title="E70">A79</font></span>: 
<font color="Maroon" title="c13">a29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/><a NAME="E51:14_1_1_2"/>
 not <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c30">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_8"/><span class="lab"><font color="Green" title="E71">A80</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">o9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_8_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_8_1"/>
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_8_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A81</font></span>: 
<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="c7">b2</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:14_1_1_2"><span class="lab"><font color="Green" title="E62">A67</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E3:14_1_1_2_8_1"/>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_2_8_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E5:14_1_1_2_8_1"/><span class="kw">then </span>
<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="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E2:14_1_1_2_8_1"><span class="lab"><font color="Green" title="E72">A81</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E6:14_1_1_2_8_1"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E7:14_1_1_2_8_1"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E8:14_1_1_2_8_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:14_1_1_2_8_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_8"/><span class="lab"><font color="Green" title="E72">A82</font></span>: 
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c30">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_8"/><span class="lab"><font color="Green" title="E73">A83</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E4:14_1_1_2_8"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E5:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c30">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E2:14_1_1_2_8"><span class="lab"><font color="Green" title="E72">A82</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/>
<a NAME="E6:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:14_1_1_2"><span class="lab"><font color="Green" title="E69">A78</font></span></a>, <a class="txt" href="#E50:14_1_1_2"><span class="lab"><font color="Green" title="E70">A79</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E7:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E8:14_1_1_2_8"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E1:14_1_1_2_8"><span class="lab"><font color="Green" title="E71">A80</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E10:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E3:14_1_1_2_8"><span class="lab"><font color="Green" title="E73">A83</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E11:14_1_1_2_8"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:14_1_1_2_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c31">c29</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><span class="kw"> such that </span><br/><a NAME="E53:14_1_1_2"/><span class="lab"><font color="Green" title="E71">A84</font></span>: 
<font color="Maroon" title="c31">c29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E54:14_1_1_2"/><span class="lab"><font color="Green" title="E72">A85</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c30">e19</font>,<font color="Maroon" title="c31">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c32">c2</font> = <font color="Maroon" title="c31">c29</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E56:14_1_1_2"/>
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c30">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c31">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:14_1_1_2"><span class="lab"><font color="Green" title="E72">A85</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E57:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A86</font></span>: 
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c31">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:14_1_1_2"><span class="lab"><font color="Green" title="E69">A78</font></span></a>, <a class="txt" href="#E50:14_1_1_2"><span class="lab"><font color="Green" title="E70">A79</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E58:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A87</font></span>: 
<font color="Maroon" title="c29">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E59:14_1_1_2"/><span class="lab"><font color="Green" title="E75">A88</font></span>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">c3</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="c32">c2</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">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_9"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E76">A89</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_9_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_2_9_1"/><span class="lab"><font color="Green" title="E77">A90</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">c3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_2_9_1"/>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_1_2_9_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E35:14_1_1_2"><span class="lab"><font color="Green" title="E62">A67</font></span></a>, <a class="txt" href="#E1:14_1_1_2_9_1"><span class="lab"><font color="Green" title="E77">A90</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E4:14_1_1_2_9_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/><a NAME="E5:14_1_1_2_9_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E6:14_1_1_2_9_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E77">A91</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_9_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_1_2_9_2"/>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E2:14_1_1_2_9_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A92</font></span>: 
<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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><span class="kw">assume </span><a NAME="E3:14_1_1_2_9_2"/>
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">c2</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:14_1_1_2_9_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A93</font></span>: 
( <font color="Maroon" title="c29">c3</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> or <font color="Maroon" title="c29">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:14_1_1_2"><span class="lab"><font color="Green" title="E67">A76</font></span></a>, <a class="txt" href="#E57:14_1_1_2"><span class="lab"><font color="Green" title="E73">A86</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E5:14_1_1_2_9_2"/>
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E6:14_1_1_2_9_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E7:14_1_1_2_9_2"/><span class="kw">then </span>
<font color="Maroon" title="c29">c3</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="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E4:14_1_1_2_9_2"><span class="lab"><font color="Green" title="E79">A93</font></span></a>, <a class="txt" href="#E2:14_1_1_2_9_2"><span class="lab"><font color="Green" title="E78">A92</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E8:14_1_1_2_9_2"/><span class="kw">then </span>
<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="c29">c3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E9:14_1_1_2_9_2"/><span class="kw">then </span>
 <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="c29">c3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/><a NAME="E10:14_1_1_2_9_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E11:14_1_1_2_9_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A94</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/><a NAME="E12:14_1_1_2_9_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/><a NAME="E13:14_1_1_2_9_2"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E1:14_1_1_2_9"><span class="lab"><font color="Green" title="E76">A89</font></span></a>, <a class="txt" href="#E11:14_1_1_2_9_2"><span class="lab"><font color="Green" title="E80">A94</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/><a NAME="E14:14_1_1_2_9_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/><span class="kw">hence </span><a NAME="E15:14_1_1_2_9_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:14_1_1_2_9"/>
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">c3</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">c2</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_2_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_2_9"><span class="lab"><font color="Green" title="E76">A89</font></span></a>, <a class="txt" href="#E2:14_1_1_2_9"><span class="lab"><font color="Green" title="E77">A91</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E60:14_1_1_2"/><span class="lab"><font color="Green" title="E76">A95</font></span>: 
 not <font color="Maroon" title="c29">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_10"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_10"/><span class="lab"><font color="Green" title="E77">A96</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_10"/>
<font color="Maroon" title="c29">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_10"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E1:14_1_1_2_10"><span class="lab"><font color="Green" title="E77">A96</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E4:14_1_1_2_10"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_2_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E61:14_1_1_2"/><span class="lab"><font color="Green" title="E77">A97</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_11"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_11"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_11"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:14_1_1_2_11"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A98</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_2_11"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E5:14_1_1_2_11"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E3:14_1_1_2_11"><span class="lab"><font color="Green" title="E78">A98</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E6:14_1_1_2_11"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_2_11"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E62:14_1_1_2"/><span class="lab"><font color="Green" title="E78">A99</font></span>: 
 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="c29">c3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_12"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_12"/>
 <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="c29">c3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_12"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:14_1_1_2_12"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A100</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_2_12"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E5:14_1_1_2_12"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E3:14_1_1_2_12"><span class="lab"><font color="Green" title="E79">A100</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E6:14_1_1_2_12"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_2_12"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E63:14_1_1_2"/><span class="lab"><font color="Green" title="E79">A101</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c28">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_13"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_2_13"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c28">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_2_13"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c27">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:14_1_1_2_13"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A102</font></span>: 
<font color="Maroon" title="c27">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_2_13"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E5:14_1_1_2_13"/><span class="kw">then </span>
<font color="Maroon" title="c18">M9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E41:14_1_1_2"><span class="lab"><font color="Green" title="E65">A74</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E3:14_1_1_2_13"><span class="lab"><font color="Green" title="E80">A102</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E6:14_1_1_2_13"/><span class="kw">then </span>
<font color="Maroon" title="c9">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c24">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_2_13"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E64:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E65:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E66:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A103</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E67:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E68:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E69:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A104</font></span>: 
 <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="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E70:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E41:14_1_1_2"><span class="lab"><font color="Green" title="E65">A74</font></span></a>, <a class="txt" href="#E53:14_1_1_2"><span class="lab"><font color="Green" title="E71">A84</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E71:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c19</font>,<font color="Maroon" title="c31">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E72:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A105</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c32">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E73:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E53:14_1_1_2"><span class="lab"><font color="Green" title="E71">A84</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E74:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c31">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E75:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A106</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">c3</font>,<font color="Maroon" title="c32">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E76:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E41:14_1_1_2"><span class="lab"><font color="Green" title="E65">A74</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E77:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c27">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E78:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A107</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c29">c3</font>,<font color="Maroon" title="c28">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E79:14_1_1_2"/>
<font color="Maroon" title="c29">c3</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="14_1_1_2_14"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_14"/><span class="lab"><font color="Green" title="E85">A108</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_14"/>
<font color="Maroon" title="c29">c3</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_14"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E1:14_1_1_2_14"><span class="lab"><font color="Green" title="E85">A108</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E4:14_1_1_2_14"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_2_14"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E80:14_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c28">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:14_1_1_2"><span class="lab"><font color="Green" title="E68">A77</font></span></a>, <a class="txt" href="#E58:14_1_1_2"><span class="lab"><font color="Green" title="E74">A87</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E81:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A109</font></span>: 
<font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E82:14_1_1_2"/><span class="lab"><font color="Green" title="E86">A110</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c7">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_15"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_15"/><span class="lab"><font color="Green" title="E87">A111</font></span>: 
<font color="Maroon" title="c27">c19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c31">c29</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_2_15_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_15_1"/><span class="lab"><font color="Green" title="E88">A112</font></span>: 
<font color="Maroon" title="c29">c3</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="14_1_1_2_15_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_2_15_1_1"/><span class="lab"><font color="Green" title="E89">A113</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_15_1_1"/>
<font color="Maroon" title="c29">c3</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E1:14_1_1_2_15_1_1"><span class="lab"><font color="Green" title="E89">A113</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E4:14_1_1_2_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_2_15_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_15_1"/>
<font color="Maroon" title="c27">c19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c31">c29</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c28">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c28">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:14_1_1_2"><span class="lab"><font color="Green" title="E68">A77</font></span></a>, <a class="txt" href="#E58:14_1_1_2"><span class="lab"><font color="Green" title="E74">A87</font></span></a>, <a class="txt" href="#E1:14_1_1_2_15_1"><span class="lab"><font color="Green" title="E88">A112</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E4:14_1_1_2_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E5:14_1_1_2_15_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E6:14_1_1_2_15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c27">c19</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E7:14_1_1_2_15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c27">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E8:14_1_1_2_15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A114</font></span>: 
<font color="Maroon" title="c27">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E9:14_1_1_2_15_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E10:14_1_1_2_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E41:14_1_1_2"><span class="lab"><font color="Green" title="E65">A74</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E8:14_1_1_2_15_1"><span class="lab"><font color="Green" title="E89">A114</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E11:14_1_1_2_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:14_1_1_2_15_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_2_15"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_2_15"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c27">c19</font>,<font color="Maroon" title="c31">c29</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E4:14_1_1_2_15"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E41:14_1_1_2"><span class="lab"><font color="Green" title="E65">A74</font></span></a>, <a class="txt" href="#E53:14_1_1_2"><span class="lab"><font color="Green" title="E71">A84</font></span></a>, <a class="txt" href="#E1:14_1_1_2_15"><span class="lab"><font color="Green" title="E87">A111</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E5:14_1_1_2_15"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E19:14_1_1_2"><span class="lab"><font color="Green" title="E53">A50</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="ref" href="aff_1.html#T18" title="AFF_1:th.18">AFF_1:18</a></span>;<br/>
<a NAME="E6:14_1_1_2_15"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E7:14_1_1_2_15"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:14_1_1_2_15"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E83:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E84:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E85:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A115</font></span>: 
 <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="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E86:14_1_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E87:14_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E88:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A116</font></span>: 
 <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="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E89:14_1_1_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c29">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c28">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:14_1_1_2"><span class="lab"><font color="Green" title="E68">A77</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E90:14_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c29">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c28">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E62:14_1_1_2"><span class="lab"><font color="Green" title="E78">A99</font></span></a>, <a class="txt" href="#E1:14_1_1_2"><span class="lab"><font color="Green" title="E44">A41</font></span></a>, <a class="txt" href="#E8:14_1_1_2"><span class="lab"><font color="Green" title="E47">A44</font></span></a>, <a class="txt" href="#E88:14_1_1_2"><span class="lab"><font color="Green" title="E88">A116</font></span></a>, <a class="txt" href="#E78:14_1_1_2"><span class="lab"><font color="Green" title="E84">A107</font></span></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></span>;<br/><a NAME="E91:14_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A117</font></span>: 
<font color="Maroon" title="c29">c3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E92:14_1_1_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c29">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E58:14_1_1_2"><span class="lab"><font color="Green" title="E74">A87</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E93:14_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c29">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c32">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E85:14_1_1_2"><span class="lab"><font color="Green" title="E87">A115</font></span></a>, <a class="txt" href="#E69:14_1_1_2"><span class="lab"><font color="Green" title="E81">A104</font></span></a>, <a class="txt" href="#E75:14_1_1_2"><span class="lab"><font color="Green" title="E83">A106</font></span></a>, <a class="txt" href="#E5:14_1_1_2"><span class="lab"><font color="Green" title="E46">A43</font></span></a>, <a class="txt" href="#E61:14_1_1_2"><span class="lab"><font color="Green" title="E77">A97</font></span></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></span>;<br/><a NAME="E94:14_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c29">c3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E95:14_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c28">c1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E20:14_1_1_2"><span class="lab"><font color="Green" title="E54">A51</font></span></a>, <a class="txt" href="#E27:14_1_1_2"><span class="lab"><font color="Green" title="E57">A56</font></span></a>, <a class="txt" href="#E32:14_1_1_2"><span class="lab"><font color="Green" title="E60">A65</font></span></a>, <a class="txt" href="#E41:14_1_1_2"><span class="lab"><font color="Green" title="E65">A74</font></span></a>, <a class="txt" href="#E53:14_1_1_2"><span class="lab"><font color="Green" title="E71">A84</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E91:14_1_1_2"><span class="lab"><font color="Green" title="E89">A117</font></span></a>, <a class="txt" href="#E28:14_1_1_2"><span class="lab"><font color="Green" title="E58">A57</font></span></a>, <a class="txt" href="#E60:14_1_1_2"><span class="lab"><font color="Green" title="E76">A95</font></span></a>, <a class="ref" href="conmetr.html#D1" target="_self" title="CONMETR:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E96:14_1_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E59:14_1_1_2"><span class="lab"><font color="Green" title="E75">A88</font></span></a>, <a class="txt" href="#E66:14_1_1_2"><span class="lab"><font color="Green" title="E80">A103</font></span></a>, <a class="txt" href="#E4:14_1_1_2"><span class="lab"><font color="Green" title="E45">A42</font></span></a>, <a class="txt" href="#E72:14_1_1_2"><span class="lab"><font color="Green" title="E82">A105</font></span></a>, <a class="txt" href="#E63:14_1_1_2"><span class="lab"><font color="Green" title="E79">A101</font></span></a>, <a class="txt" href="#E82:14_1_1_2"><span class="lab"><font color="Green" title="E86">A110</font></span></a>, <a class="txt" href="#E81:14_1_1_2"><span class="lab"><font color="Green" title="E85">A109</font></span></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E2:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E3:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A118</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E4:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E5:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E6:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A119</font></span>: 
 <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="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E7:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E8:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E9:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A120</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E10:14_1_1_3"/><span class="lab"><font color="Green" title="E47">A121</font></span>: 
(  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</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="c6">b1</font>,<font color="Maroon" title="c5">a3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_3_1"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_3_1"/><span class="kw">then </span>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">a39</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">a39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E11:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E12:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E13:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A122</font></span>: 
 <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="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E14:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E15:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E16:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A123</font></span>: 
 <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="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E17:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E18:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E19:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A124</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c20">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E21:14_1_1_3"/><span class="lab"><font color="Green" title="E51">A125</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>
 <span class="kw">and </span><br/><a NAME="E22:14_1_1_3"/><span class="lab"><font color="Green" title="E52">A126</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T39" title="ANALMETR:th.39">ANALMETR:39</a></span>;<br/><a NAME="E23:14_1_1_3"/><span class="lab"><font color="Green" title="E53">A127</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font> <a href="analmetr.html#R6" title="ANALMETR:pred.6">_|_</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E21:14_1_1_3"><span class="lab"><font color="Green" title="E51">A125</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c21">e19</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><span class="kw"> such that </span><br/><a NAME="E25:14_1_1_3"/><span class="lab"><font color="Green" title="E54">A128</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c21">e19</font>
 <span class="kw">and </span><br/><a NAME="E26:14_1_1_3"/><span class="lab"><font color="Green" title="E55">A129</font></span>: 
<font color="Maroon" title="c17">b39</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c22">x9</font> = <font color="Maroon" title="c20">x</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E28:14_1_1_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c22">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T7" title="AFF_1:th.7">AFF_1:7</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">A9</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><span class="kw"> such that </span><br/><a NAME="E30:14_1_1_3"/><span class="lab"><font color="Green" title="E56">A130</font></span>: 
<font color="Maroon" title="c23">A9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E31:14_1_1_3"/><span class="lab"><font color="Green" title="E57">A131</font></span>: 
<font color="Maroon" title="c11">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E32:14_1_1_3"/><span class="lab"><font color="Green" title="E58">A132</font></span>: 
<font color="Maroon" title="c22">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E33:14_1_1_3"/>
<font color="Maroon" title="c22">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T21" title="AFF_1:th.21">AFF_1:21</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">A</font> = <font color="Maroon" title="c23">A9</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T42" title="ANALMETR:th.42">ANALMETR:42</a></span>;<br/><a NAME="E35:14_1_1_3"/><span class="lab"><font color="Green" title="E59">A133</font></span>: 
 for <font color="Olive" title="b1">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font> holds <br/> <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Olive" title="b1">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c25">e1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font> implies  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:14_1_1_3_2"/><span class="lab"><font color="Green" title="E60">A134</font></span>: 
<font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c26">e19</font> = <font color="Maroon" title="c25">e1</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E3:14_1_1_3_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">x9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c26">e19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E32:14_1_1_3"><span class="lab"><font color="Green" title="E58">A132</font></span></a>, <a class="txt" href="#E1:14_1_1_3_2"><span class="lab"><font color="Green" title="E60">A134</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_3_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c26">e19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_3_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E36:14_1_1_3"/>
 for <font color="Olive" title="b1">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Olive" title="b1">e1</font> holds <br/><font color="Olive" title="b1">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c25">e1</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font> implies <font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:14_1_1_3_3"/><span class="lab"><font color="Green" title="E60">A135</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">x</font>,<font color="Maroon" title="c25">e1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c26">e19</font> = <font color="Maroon" title="c25">e1</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E3:14_1_1_3_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">x9</font>,<font color="Maroon" title="c26">e19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_3_3"><span class="lab"><font color="Green" title="E60">A135</font></span></a>, <a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_3_3"/>
<font color="Maroon" title="c25">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1_1_3"><span class="lab"><font color="Green" title="E52">A126</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E32:14_1_1_3"><span class="lab"><font color="Green" title="E58">A132</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E37:14_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c24">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="c2">o</font>,<font color="Maroon" title="c20">x</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:14_1_1_3"><span class="lab"><font color="Green" title="E59">A133</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E38:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A136</font></span>: 
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14_1_1_3"><span class="lab"><font color="Green" title="E52">A126</font></span></a>, <a class="txt" href="#E23:14_1_1_3"><span class="lab"><font color="Green" title="E53">A127</font></span></a>, <a class="ref" href="analmetr.html#D14" title="ANALMETR:def.14">ANALMETR:def 14</a></span>;<br/><span class="kw">assume </span><a NAME="E39:14_1_1_3"/><span class="lab"><font color="Green" title="E61">A137</font></span>: 
<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="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E40:14_1_1_3"/>
 not <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c21">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_3_4"/><span class="lab"><font color="Green" title="E62">A138</font></span>: 
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c21">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">consider </span><font color="Maroon" title="c25">d19</font>, <font color="Maroon" title="c26">d29</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><span class="kw"> such that </span><br/><a NAME="E3:14_1_1_3_4"/><span class="lab"><font color="Green" title="E63">A139</font></span>: 
<font color="Maroon" title="c25">d19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d29</font>
 <span class="kw">and </span><br/><a NAME="E4:14_1_1_3_4"/><span class="lab"><font color="Green" title="E64">A140</font></span>: 
<font color="Maroon" title="c23">A9</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="c25">d19</font>,<font color="Maroon" title="c26">d29</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/>
<a NAME="E5:14_1_1_3_4"/><span class="lab"><font color="Green" title="E65">A141</font></span>: 
<font color="Maroon" title="c26">d29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_3_4"><span class="lab"><font color="Green" title="E64">A140</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c27">d1</font> = <font color="Maroon" title="c25">d19</font>, <font color="Maroon" title="c28">d2</font> = <font color="Maroon" title="c26">d29</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/>
<a NAME="E7:14_1_1_3_4"/>
<font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E8:14_1_1_3_4"/><span class="kw">then </span>
<font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_3_4"><span class="lab"><font color="Green" title="E63">A139</font></span></a>, <a class="txt" href="#E4:14_1_1_3_4"><span class="lab"><font color="Green" title="E64">A140</font></span></a>, <a class="ref" href="aff_1.html#D4" title="AFF_1:def.4">AFF_1:def 4</a></span>;<br/>
<a NAME="E9:14_1_1_3_4"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c21">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E1:14_1_1_3_4"><span class="lab"><font color="Green" title="E62">A138</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/>
<a NAME="E10:14_1_1_3_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">d19</font>,<font color="Maroon" title="c26">d29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:14_1_1_3"><span class="lab"><font color="Green" title="E54">A128</font></span></a>, <a class="txt" href="#E26:14_1_1_3"><span class="lab"><font color="Green" title="E55">A129</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E11:14_1_1_3_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A142</font></span>: 
<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="c27">d1</font>,<font color="Maroon" title="c28">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<a NAME="E12:14_1_1_3_4"/>
<font color="Maroon" title="c25">d19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1_1_3_4"><span class="lab"><font color="Green" title="E64">A140</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E13:14_1_1_3_4"/><span class="kw">then </span>
<font color="Maroon" title="c27">d1</font>,<font color="Maroon" title="c28">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="txt" href="#E5:14_1_1_3_4"><span class="lab"><font color="Green" title="E65">A141</font></span></a>, <a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></span>;<br/>
<a NAME="E14:14_1_1_3_4"/><span class="kw">then </span>
<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="c2">o</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_1_3_4"><span class="lab"><font color="Green" title="E63">A139</font></span></a>, <a class="txt" href="#E11:14_1_1_3_4"><span class="lab"><font color="Green" title="E66">A142</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E15:14_1_1_3_4"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E39:14_1_1_3"><span class="lab"><font color="Green" title="E61">A137</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/>
<a NAME="E16:14_1_1_3_4"/><span class="kw">then </span>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E17:14_1_1_3_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E18:14_1_1_3_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E19:14_1_1_3_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">c39</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><span class="kw"> such that </span><br/><a NAME="E42:14_1_1_3"/><span class="lab"><font color="Green" title="E62">A143</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E43:14_1_1_3"/><span class="lab"><font color="Green" title="E63">A144</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c21">e19</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></span>;<br/><a NAME="E44:14_1_1_3"/><span class="lab"><font color="Green" title="E64">A145</font></span>: 
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c21">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:14_1_1_3"><span class="lab"><font color="Green" title="E63">A144</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c26">e19</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><span class="kw"> such that </span><br/><a NAME="E46:14_1_1_3"/><span class="lab"><font color="Green" title="E65">A146</font></span>: 
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">and </span><br/><a NAME="E47:14_1_1_3"/><span class="lab"><font color="Green" title="E66">A147</font></span>: 
<font color="Maroon" title="c13">a29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/><a NAME="E48:14_1_1_3"/>
 not <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c26">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_5"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_3_5"/><span class="lab"><font color="Green" title="E67">A148</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">o9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_5_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_3_5_1"/>
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_3_5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A149</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:14_1_1_3"><span class="lab"><font color="Green" title="E54">A128</font></span></a>, <a class="txt" href="#E26:14_1_1_3"><span class="lab"><font color="Green" title="E55">A129</font></span></a>, <a class="txt" href="#E44:14_1_1_3"><span class="lab"><font color="Green" title="E64">A145</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_3_5_1"/>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_3_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E2:14_1_1_3_5_1"><span class="lab"><font color="Green" title="E68">A149</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_3_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E6:14_1_1_3_5_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_3_5_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_3_5"/><span class="lab"><font color="Green" title="E68">A150</font></span>: 
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c26">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_3_5"/><span class="lab"><font color="Green" title="E69">A151</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E4:14_1_1_3_5"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E5:14_1_1_3_5"/><span class="kw">then </span>
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E2:14_1_1_3_5"><span class="lab"><font color="Green" title="E68">A150</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/>
<a NAME="E6:14_1_1_3_5"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:14_1_1_3"><span class="lab"><font color="Green" title="E65">A146</font></span></a>, <a class="txt" href="#E47:14_1_1_3"><span class="lab"><font color="Green" title="E66">A147</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E7:14_1_1_3_5"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E8:14_1_1_3_5"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_3_5"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E1:14_1_1_3_5"><span class="lab"><font color="Green" title="E67">A148</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E10:14_1_1_3_5"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E3:14_1_1_3_5"><span class="lab"><font color="Green" title="E69">A151</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E11:14_1_1_3_5"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:14_1_1_3_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c27">c29</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><span class="kw"> such that </span><br/><a NAME="E50:14_1_1_3"/><span class="lab"><font color="Green" title="E67">A152</font></span>: 
<font color="Maroon" title="c27">c29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E51:14_1_1_3"/><span class="lab"><font color="Green" title="E68">A153</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c27">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c28">c3</font> = <font color="Maroon" title="c25">c39</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">c2</font> = <font color="Maroon" title="c27">c29</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E54:14_1_1_3"/>
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c27">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:14_1_1_3"><span class="lab"><font color="Green" title="E68">A153</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E55:14_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c27">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:14_1_1_3"><span class="lab"><font color="Green" title="E65">A146</font></span></a>, <a class="txt" href="#E47:14_1_1_3"><span class="lab"><font color="Green" title="E66">A147</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E56:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A154</font></span>: 
<font color="Maroon" title="c28">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E57:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A155</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c28">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c30">e19</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><span class="kw"> such that </span><br/><a NAME="E59:14_1_1_3"/><span class="lab"><font color="Green" title="E71">A156</font></span>: 
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c30">e19</font>
 <span class="kw">and </span><br/><a NAME="E60:14_1_1_3"/><span class="lab"><font color="Green" title="E72">A157</font></span>: 
<font color="Maroon" title="c12">a19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></span>;<br/><a NAME="E61:14_1_1_3"/>
 not <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c30">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_6"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_3_6"/><span class="lab"><font color="Green" title="E73">A158</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">o9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_6_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_3_6_1"/>
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">o9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_3_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A159</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:14_1_1_3"><span class="lab"><font color="Green" title="E54">A128</font></span></a>, <a class="txt" href="#E26:14_1_1_3"><span class="lab"><font color="Green" title="E55">A129</font></span></a>, <a class="txt" href="#E44:14_1_1_3"><span class="lab"><font color="Green" title="E64">A145</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E3:14_1_1_3_6_1"/>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E4:14_1_1_3_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E2:14_1_1_3_6_1"><span class="lab"><font color="Green" title="E74">A159</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E5:14_1_1_3_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E6:14_1_1_3_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_3_6_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_3_6"/><span class="lab"><font color="Green" title="E74">A160</font></span>: 
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c30">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_3_6"/><span class="lab"><font color="Green" title="E75">A161</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E4:14_1_1_3_6"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="ref" href="aff_1.html#T40" title="AFF_1:th.40">AFF_1:40</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E5:14_1_1_3_6"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c30">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E2:14_1_1_3_6"><span class="lab"><font color="Green" title="E74">A160</font></span></a>, <a class="ref" href="aff_1.html#T31" title="AFF_1:th.31">AFF_1:31</a></span>;<br/>
<a NAME="E6:14_1_1_3_6"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:14_1_1_3"><span class="lab"><font color="Green" title="E71">A156</font></span></a>, <a class="txt" href="#E60:14_1_1_3"><span class="lab"><font color="Green" title="E72">A157</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/>
<a NAME="E7:14_1_1_3_6"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T4" title="AFF_1:th.4">AFF_1:4</a></span>;<br/>
<a NAME="E8:14_1_1_3_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:14_1_1_3_6"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E1:14_1_1_3_6"><span class="lab"><font color="Green" title="E73">A158</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E10:14_1_1_3_6"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E3:14_1_1_3_6"><span class="lab"><font color="Green" title="E75">A161</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E11:14_1_1_3_6"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:14_1_1_3_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c31">c19</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><span class="kw"> such that </span><br/><a NAME="E63:14_1_1_3"/><span class="lab"><font color="Green" title="E73">A162</font></span>: 
<font color="Maroon" title="c31">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c23">A9</font>
 <span class="kw">and </span><br/><a NAME="E64:14_1_1_3"/><span class="lab"><font color="Green" title="E74">A163</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c30">e19</font>,<font color="Maroon" title="c31">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="ref" href="aff_1.html#T59" title="AFF_1:th.59">AFF_1:59</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c32">c1</font> = <font color="Maroon" title="c31">c19</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E66:14_1_1_3"/>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c30">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c31">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E64:14_1_1_3"><span class="lab"><font color="Green" title="E74">A163</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E67:14_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c31">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:14_1_1_3"><span class="lab"><font color="Green" title="E71">A156</font></span></a>, <a class="txt" href="#E60:14_1_1_3"><span class="lab"><font color="Green" title="E72">A157</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E68:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A164</font></span>: 
<font color="Maroon" title="c28">c3</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="c32">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E69:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A165</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c28">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c32">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E70:14_1_1_3"/><span class="lab"><font color="Green" title="E77">A166</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:14_1_1_3"><span class="lab"><font color="Green" title="E54">A128</font></span></a>, <a class="txt" href="#E26:14_1_1_3"><span class="lab"><font color="Green" title="E55">A129</font></span></a>, <a class="txt" href="#E44:14_1_1_3"><span class="lab"><font color="Green" title="E64">A145</font></span></a>, <a class="ref" href="aff_1.html#T5" title="AFF_1:th.5">AFF_1:5</a></span>;<br/><a NAME="E71:14_1_1_3"/><span class="lab"><font color="Green" title="E78">A167</font></span>: 
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">c3</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="c29">c2</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="c32">c1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_7"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E79">A168</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_7_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:14_1_1_3_7_1"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">c3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:14_1_1_3_7_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A169</font></span>: 
<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="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E70:14_1_1_3"><span class="lab"><font color="Green" title="E77">A166</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E3:14_1_1_3_7_1"/>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E4:14_1_1_3_7_1"/><span class="kw">then </span>
<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="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E5:14_1_1_3_7_1"/><span class="kw">then </span>
<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="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E2:14_1_1_3_7_1"><span class="lab"><font color="Green" title="E80">A169</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E6:14_1_1_3_7_1"/><span class="kw">then </span>
<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="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E7:14_1_1_3_7_1"/><span class="kw">then </span>
 <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="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/><a NAME="E8:14_1_1_3_7_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><span class="kw">hence </span><a NAME="E9:14_1_1_3_7_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:14_1_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E80">A170</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_7_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_1_3_7_2"/>
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E2:14_1_1_3_7_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A171</font></span>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><span class="kw">assume </span><a NAME="E3:14_1_1_3_7_2"/>
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">c2</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:14_1_1_3_7_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A172</font></span>: 
( <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c28">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c2">o</font> or <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c28">c3</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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E56:14_1_1_3"><span class="lab"><font color="Green" title="E69">A154</font></span></a>, <a class="txt" href="#E68:14_1_1_3"><span class="lab"><font color="Green" title="E75">A164</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E5:14_1_1_3_7_2"/>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E6:14_1_1_3_7_2"/><span class="kw">then </span>
<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="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E7:14_1_1_3_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c28">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E4:14_1_1_3_7_2"><span class="lab"><font color="Green" title="E82">A172</font></span></a>, <a class="txt" href="#E2:14_1_1_3_7_2"><span class="lab"><font color="Green" title="E81">A171</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E8:14_1_1_3_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c28">c3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E9:14_1_1_3_7_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c28">c3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/><a NAME="E10:14_1_1_3_7_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E11:14_1_1_3_7_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A173</font></span>: 
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/><a NAME="E12:14_1_1_3_7_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/><a NAME="E13:14_1_1_3_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E1:14_1_1_3_7"><span class="lab"><font color="Green" title="E79">A168</font></span></a>, <a class="txt" href="#E11:14_1_1_3_7_2"><span class="lab"><font color="Green" title="E83">A173</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/><a NAME="E14:14_1_1_3_7_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/><span class="kw">hence </span><a NAME="E15:14_1_1_3_7_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:14_1_1_3_7"/>
( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">c3</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">c2</font> or <font color="Maroon" title="c2">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_1_3_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1_3_7"><span class="lab"><font color="Green" title="E79">A168</font></span></a>, <a class="txt" href="#E2:14_1_1_3_7"><span class="lab"><font color="Green" title="E80">A170</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E72:14_1_1_3"/><span class="lab"><font color="Green" title="E79">A174</font></span>: 
 not <font color="Maroon" title="c28">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_8"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_3_8"/><span class="lab"><font color="Green" title="E80">A175</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_3_8"/>
<font color="Maroon" title="c28">c3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_3_8"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E71:14_1_1_3"><span class="lab"><font color="Green" title="E78">A167</font></span></a>, <a class="txt" href="#E1:14_1_1_3_8"><span class="lab"><font color="Green" title="E80">A175</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E4:14_1_1_3_8"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_3_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E73:14_1_1_3"/><span class="lab"><font color="Green" title="E80">A176</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_3_9"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_3_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c31">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:14_1_1_3_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A177</font></span>: 
<font color="Maroon" title="c31">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_3_9"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E5:14_1_1_3_9"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E63:14_1_1_3"><span class="lab"><font color="Green" title="E73">A162</font></span></a>, <a class="txt" href="#E71:14_1_1_3"><span class="lab"><font color="Green" title="E78">A167</font></span></a>, <a class="txt" href="#E3:14_1_1_3_9"><span class="lab"><font color="Green" title="E81">A177</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E6:14_1_1_3_9"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_3_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E74:14_1_1_3"/><span class="lab"><font color="Green" title="E81">A178</font></span>: 
(  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="c28">c3</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="c4">a2</font>,<font color="Maroon" title="c28">c3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_10"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_1_3_10"/>
(  <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="c28">c3</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c28">c3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_1_3_10"/><span class="kw">then </span>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c25">c39</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c25">c39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:14_1_1_3_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E82">A179</font></span>: 
( <font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font> or <font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E2:14_1_1"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E3:14_1_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E4:14_1_1_3_10"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E5:14_1_1_3_10"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E71:14_1_1_3"><span class="lab"><font color="Green" title="E78">A167</font></span></a>, <a class="txt" href="#E3:14_1_1_3_10"><span class="lab"><font color="Green" title="E82">A179</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E6:14_1_1_3_10"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:14_1_1_3_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E75:14_1_1_3"/><span class="lab"><font color="Green" title="E82">A180</font></span>: 
 not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_11"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_3_11"/><span class="lab"><font color="Green" title="E83">A181</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_3_11"/>
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_3_11"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E1:14_1_1_3_11"><span class="lab"><font color="Green" title="E83">A181</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E4:14_1_1_3_11"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c10">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_3_11"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E76:14_1_1_3"/><span class="lab"><font color="Green" title="E83">A182</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c7">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_12"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_3_12"/><span class="lab"><font color="Green" title="E84">A183</font></span>: 
<font color="Maroon" title="c31">c19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">c29</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_12_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_3_12_1"/><span class="lab"><font color="Green" title="E85">A184</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">c3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_12_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_3_12_1_1"/><span class="lab"><font color="Green" title="E86">A185</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_3_12_1_1"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">c3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_3_12_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E1:14_1_1_3_12_1_1"><span class="lab"><font color="Green" title="E86">A185</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E4:14_1_1_3_12_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_3_12_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_3_12_1"/>
<font color="Maroon" title="c31">c19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">c29</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_3_12_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c32">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c32">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:14_1_1_3"><span class="lab"><font color="Green" title="E70">A155</font></span></a>, <a class="txt" href="#E69:14_1_1_3"><span class="lab"><font color="Green" title="E76">A165</font></span></a>, <a class="txt" href="#E1:14_1_1_3_12_1"><span class="lab"><font color="Green" title="E85">A184</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/>
<a NAME="E4:14_1_1_3_12_1"/><span class="kw">then </span>
<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/>
<a NAME="E5:14_1_1_3_12_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>;<br/>
<a NAME="E6:14_1_1_3_12_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c31">c19</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E7:14_1_1_3_12_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c31">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<a NAME="E8:14_1_1_3_12_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A186</font></span>: 
<font color="Maroon" title="c31">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<a NAME="E9:14_1_1_3_12_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<a NAME="E10:14_1_1_3_12_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E63:14_1_1_3"><span class="lab"><font color="Green" title="E73">A162</font></span></a>, <a class="txt" href="#E71:14_1_1_3"><span class="lab"><font color="Green" title="E78">A167</font></span></a>, <a class="txt" href="#E8:14_1_1_3_12_1"><span class="lab"><font color="Green" title="E86">A186</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E11:14_1_1_3_12_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:14_1_1_3_12_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:14_1_1_3_12"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_3_12"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c31">c19</font>,<font color="Maroon" title="c27">c29</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:14_1_1_3_12"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E50:14_1_1_3"><span class="lab"><font color="Green" title="E67">A152</font></span></a>, <a class="txt" href="#E63:14_1_1_3"><span class="lab"><font color="Green" title="E73">A162</font></span></a>, <a class="txt" href="#E75:14_1_1_3"><span class="lab"><font color="Green" title="E82">A180</font></span></a>, <a class="txt" href="#E1:14_1_1_3_12"><span class="lab"><font color="Green" title="E84">A183</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E77:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E50:14_1_1_3"><span class="lab"><font color="Green" title="E67">A152</font></span></a>, <a class="txt" href="#E63:14_1_1_3"><span class="lab"><font color="Green" title="E73">A162</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E78:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c19</font>,<font color="Maroon" title="c27">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E79:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A187</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c29">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E80:14_1_1_3"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">c3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_3_13"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_1_3_13"/><span class="lab"><font color="Green" title="E85">A188</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:14_1_1_3_13"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">c3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:14_1_1_3_13"/><span class="kw">then </span>
<font color="Maroon" title="c23">A9</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E1:14_1_1_3_13"><span class="lab"><font color="Green" title="E85">A188</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/>
<a NAME="E4:14_1_1_3_13"/><span class="kw">then </span>
<font color="Maroon" title="c24">A</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c9">M</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T46" title="ANALMETR:th.46">ANALMETR:46</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:14_1_1_3_13"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="ref" href="analmetr.html#T52" title="ANALMETR:th.52">ANALMETR:52</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E81:14_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c29">c2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c32">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:14_1_1_3"><span class="lab"><font color="Green" title="E70">A155</font></span></a>, <a class="txt" href="#E69:14_1_1_3"><span class="lab"><font color="Green" title="E76">A165</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E82:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A189</font></span>: 
<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E83:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c31">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E63:14_1_1_3"><span class="lab"><font color="Green" title="E73">A162</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E84:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c31">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E85:14_1_1_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">c3</font>,<font color="Maroon" title="c32">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E86:14_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c28">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c32">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E69:14_1_1_3"><span class="lab"><font color="Green" title="E76">A165</font></span></a>, <a class="txt" href="#E71:14_1_1_3"><span class="lab"><font color="Green" title="E78">A167</font></span></a>, <a class="txt" href="#E10:14_1_1_3"><span class="lab"><font color="Green" title="E47">A121</font></span></a>, <a class="txt" href="#E74:14_1_1_3"><span class="lab"><font color="Green" title="E81">A178</font></span></a>, <a class="txt" href="#E19:14_1_1_3"><span class="lab"><font color="Green" title="E50">A124</font></span></a>, <a class="txt" href="#E16:14_1_1_3"><span class="lab"><font color="Green" title="E49">A123</font></span></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></span>;<br/><a NAME="E87:14_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A190</font></span>: 
<font color="Maroon" title="c28">c3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E88:14_1_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c27">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:14_1_1_3"><span class="lab"><font color="Green" title="E56">A130</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E50:14_1_1_3"><span class="lab"><font color="Green" title="E67">A152</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E89:14_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>,<font color="Maroon" title="c27">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E90:14_1_1_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">c3</font>,<font color="Maroon" title="c29">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/><a NAME="E91:14_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c28">c3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E57:14_1_1_3"><span class="lab"><font color="Green" title="E70">A155</font></span></a>, <a class="txt" href="#E71:14_1_1_3"><span class="lab"><font color="Green" title="E78">A167</font></span></a>, <a class="txt" href="#E10:14_1_1_3"><span class="lab"><font color="Green" title="E47">A121</font></span></a>, <a class="txt" href="#E74:14_1_1_3"><span class="lab"><font color="Green" title="E81">A178</font></span></a>, <a class="txt" href="#E13:14_1_1_3"><span class="lab"><font color="Green" title="E48">A122</font></span></a>, <a class="txt" href="#E6:14_1_1_3"><span class="lab"><font color="Green" title="E45">A119</font></span></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></span>;<br/><a NAME="E92:14_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c28">c3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>;<br/><a NAME="E93:14_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c32">c1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">c2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E31:14_1_1_3"><span class="lab"><font color="Green" title="E57">A131</font></span></a>, <a class="txt" href="#E38:14_1_1_3"><span class="lab"><font color="Green" title="E60">A136</font></span></a>, <a class="txt" href="#E42:14_1_1_3"><span class="lab"><font color="Green" title="E62">A143</font></span></a>, <a class="txt" href="#E50:14_1_1_3"><span class="lab"><font color="Green" title="E67">A152</font></span></a>, <a class="txt" href="#E63:14_1_1_3"><span class="lab"><font color="Green" title="E73">A162</font></span></a>, <a class="txt" href="#E71:14_1_1_3"><span class="lab"><font color="Green" title="E78">A167</font></span></a>, <a class="txt" href="#E87:14_1_1_3"><span class="lab"><font color="Green" title="E86">A190</font></span></a>, <a class="txt" href="#E75:14_1_1_3"><span class="lab"><font color="Green" title="E82">A180</font></span></a>, <a class="txt" href="#E72:14_1_1_3"><span class="lab"><font color="Green" title="E79">A174</font></span></a>, <a class="ref" href="conmetr.html#D1" target="_self" title="CONMETR:def.1">Def1</a></span>;<br/><span class="kw">hence </span><a NAME="E94:14_1_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:14"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E71:14_1_1_3"><span class="lab"><font color="Green" title="E78">A167</font></span></a>, <a class="txt" href="#E3:14_1_1_3"><span class="lab"><font color="Green" title="E44">A118</font></span></a>, <a class="txt" href="#E9:14_1_1_3"><span class="lab"><font color="Green" title="E46">A120</font></span></a>, <a class="txt" href="#E79:14_1_1_3"><span class="lab"><font color="Green" title="E84">A187</font></span></a>, <a class="txt" href="#E73:14_1_1_3"><span class="lab"><font color="Green" title="E80">A176</font></span></a>, <a class="txt" href="#E76:14_1_1_3"><span class="lab"><font color="Green" title="E83">A182</font></span></a>, <a class="txt" href="#E82:14_1_1_3"><span class="lab"><font color="Green" title="E85">A189</font></span></a>, <a class="ref" href="conaffm.html#D1" title="CONAFFM:def.1">CONAFFM:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E7:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14_1_1"><span class="lab"><font color="Green" title="E43">A40</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E39">A191</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_2"/><span class="lab"><font color="Green" title="E40">A192</font></span>: 
 not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:14_1_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:14_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:14_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:14_1_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E3:14_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A193</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E4:14_1_2"/><span class="lab"><font color="Green" title="E42">A194</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E5:14_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><span class="kw">hence </span><a NAME="E6:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E4:14_1_2"><span class="lab"><font color="Green" title="E42">A194</font></span></a>, <a class="txt" href="#E1:14_1_2"><span class="lab"><font color="Green" title="E40">A192</font></span></a>, <a class="txt" href="#E3:14_1_2"><span class="lab"><font color="Green" title="E41">A193</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E40">A195</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E2:14_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A196</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E3:14_1_3"/><span class="lab"><font color="Green" title="E42">A197</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E4:14_1_3"/>
<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="14_1_3_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:14_1_3_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/>
<a NAME="E2:14_1_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A198</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:14_1_3_1"/>
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:14_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E2:14_1_3_1"><span class="lab"><font color="Green" title="E43">A198</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:14_1_3"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E3:14_1_3"><span class="lab"><font color="Green" title="E42">A197</font></span></a>, <a class="ref" href="analmetr.html#T60" title="ANALMETR:th.60">ANALMETR:60</a></span>;<br/><a NAME="E6:14_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E7:14_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E2:14_1_3"><span class="lab"><font color="Green" title="E41">A196</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/><a NAME="E8:14_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:14_1_3"><span class="lab"><font color="Green" title="E42">A197</font></span></a>, <a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>;<br/><span class="kw">hence </span><a NAME="E9:14_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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_4"><span class="kw">now </span></a><div class="add"><a NAME="E1:14_1_4"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E26:14"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E2:14_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A199</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E3:14_1_4"/><span class="lab"><font color="Green" title="E42">A200</font></span>: 
<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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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="E4:14_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E5:14_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:14"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E2:14_1_4"><span class="lab"><font color="Green" title="E41">A199</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/><span class="kw">hence </span><a NAME="E6:14_1_4"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E3:14_1_4"><span class="lab"><font color="Green" title="E42">A200</font></span></a>, <a class="ref" href="analmetr.html#T59" title="ANALMETR:th.59">ANALMETR:59</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E6:14_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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:14_1"><span class="lab"><font color="Green" title="E40">A195</font></span></a>, <a class="txt" href="#E3:14_1"><span class="lab"><font color="Green" title="E39">A191</font></span></a>, <a class="txt" href="#E2:14_1"><span class="lab"><font color="Green" title="E38">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E28:14"/>
<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E5:14"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:14"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:14"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:14"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:14"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:14"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:14"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:14"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E13:14"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:14"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:14"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:14"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E18:14"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E20:14"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E21:14"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E22:14"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="conmetr.html#D1" target="_self" title="CONMETR:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
