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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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V7" title="CONMETR:attr.7">satisfying_OSCH</a>  &amp; <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V6" title="CONMETR:attr.6">satisfying_SCH</a>  )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V7" title="CONMETR:attr.7">satisfying_OSCH</a> 
 <span class="kw">and </span><br/><a NAME="E2:13"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V6" title="CONMETR:attr.6">satisfying_SCH</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">a1</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="Red">:: according to </font></span><a class="ref" href="conmetr.html#D6" target="_self" title="CONMETR:def.6">CONMETR:def 6</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a2</font>, <font color="Olive" title="b2">a3</font>, <font color="Olive" title="b3">a4</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font>, <font color="Olive" title="b7">b4</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b8">M</font>, <font color="Olive" title="b9">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="b8">M</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  &amp; <font color="Olive" title="b9">N</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</font> &amp; <font color="Olive" title="b2">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</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">M</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">M</font> &amp; <font color="Olive" title="b1">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; <font color="Olive" title="b3">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">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="b9">N</font> &amp; <font color="Olive" title="b7">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; not <font color="Olive" title="b3">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</font> &amp; not <font color="Olive" title="b1">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</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="b8">M</font> &amp; not <font color="Olive" title="b7">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</font> &amp; not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; not <font color="Olive" title="b2">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; not <font color="Olive" title="b4">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; not <font color="Olive" title="b6">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; <font color="Olive" title="b2">a3</font>,<font color="Olive" title="b1">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b3</font>,<font color="Olive" title="b5">b2</font> &amp; <font color="Olive" title="b1">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b2</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Olive" title="b3">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b7">b4</font> holds <br/><font color="Olive" title="b2">a3</font>,<font color="Olive" title="b3">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b3</font>,<font color="Olive" title="b7">b4</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c5">a4</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c9">b4</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> holds <br/><font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c11">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">M</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  &amp; <font color="Maroon" title="c11">N</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>  &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> implies <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font> )</span><br/>



















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:13"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c10">M</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E4:13"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c11">N</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E5:13"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E6:13"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E7:13"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E8:13"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E9:13"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E10:13"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E11:13"/><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="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E12:13"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
<font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E13:13"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E14:13"/><span class="lab"><font color="Green" title="E28">A14</font></span>: 
not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E15:13"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E16:13"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E17:13"/><span class="lab"><font color="Green" title="E31">A17</font></span>: 
not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E18:13"/><span class="lab"><font color="Green" title="E32">A18</font></span>: 
not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E19:13"/><span class="lab"><font color="Green" title="E33">A19</font></span>: 
not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E20:13"/><span class="lab"><font color="Green" title="E34">A20</font></span>: 
not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E21:13"/><span class="lab"><font color="Green" title="E35">A21</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">and </span><br/><a NAME="E22:13"/><span class="lab"><font color="Green" title="E36">A22</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E23:13"/><span class="lab"><font color="Green" title="E37">A23</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c12">a19</font> = <font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c13">a29</font> = <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c14">a39</font> = <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c15">a49</font> = <font color="Maroon" title="c5">a4</font>, <font color="Maroon" title="c16">b19</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c17">b29</font> = <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c18">b39</font> = <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c19">b49</font> = <font color="Maroon" title="c9">b4</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#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c20">M9</font> = <font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c21">N9</font> = <font color="Maroon" title="c11">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#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/>
<a NAME="E26:13"/><span class="lab"><font color="Green" title="E38">A24</font></span>: 
<font color="Maroon" title="c20">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="#E3:13"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></span>;<br/>
<a NAME="E27:13"/><span class="lab"><font color="Green" title="E39">A25</font></span>: 
<font color="Maroon" title="c21">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="#E4:13"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></span>;<br/>
<a NAME="E28:13"/><span class="lab"><font color="Green" title="E40">A26</font></span>: 
( <font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> implies ( <font color="Maroon" title="c3">a2</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="c4">a3</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">a4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b4</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_1"/><span class="lab"><font color="Green" title="E41">A27</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a2</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="c4">a3</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">a4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b4</font> )</span><br/>

<div><span class="lab"><font color="Green" title="E42">A28</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_1"/>
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:13"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E3:13_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E4:13_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">a49</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E5:13_1_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="c16">b19</font>,<font color="Maroon" title="c15">a49</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E6:13_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E13:13"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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">A29</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_2"/>
<font color="Maroon" title="c3">a2</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="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E3:13_1_2"/><span class="kw">then </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="c12">a19</font>,<font color="Maroon" title="c16">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E4:13_1_2"/><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="c16">b19</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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">A30</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_1_3"/>
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E3:13_1_3"/><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="c17">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E4:13_1_3"/><span class="kw">then </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="c17">b29</font>,<font color="Maroon" title="c14">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E18:13"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E43">A29</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E5:13_1"/>
( <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> or <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> or <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E6:13_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_1"><span class="lab"><font color="Green" title="E43">A29</font></span></a>, <a class="txt" href="#E2:13_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="txt" href="#E4:13_1"><span class="lab"><font color="Green" title="E44">A30</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E41">A31</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2"/><span class="lab"><font color="Green" title="E42">A32</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><span class="lab"><font color="Green" title="E43">A33</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_2_1"/><span class="lab"><font color="Green" title="E44">A34</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c17">b29</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c17">b29</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_1_1"/><span class="kw">then </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="c17">b29</font>,<font color="Maroon" title="c16">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:13_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E19:13"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E28:13"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:13_2_1"/><span class="lab"><font color="Green" title="E45">A35</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E3:13_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:13"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E4:13_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E5:13_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E6:13_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A36</font></span>: 
<font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c17">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c19">b49</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E7:13_2_1"/>
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c17">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c19">b49</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:13"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E8:13_2_1"/><span class="kw">then </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="c17">b29</font>,<font color="Maroon" title="c19">b49</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="E9:13_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E2:13_2_1"><span class="lab"><font color="Green" title="E45">A35</font></span></a>, <a class="txt" href="#E1:13_2_1"><span class="lab"><font color="Green" title="E44">A34</font></span></a>, <a class="txt" href="#E6:13_2_1"><span class="lab"><font color="Green" title="E46">A36</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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">A37</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13_2_2"/><span class="lab"><font color="Green" title="E45">A38</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a4</font>
 <span class="kw">and </span><br/><a NAME="E2:13_2_2"/><span class="lab"><font color="Green" title="E46">A39</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><span class="lab"><font color="Green" title="E47">A40</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c22">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:13_2_2_1"/><span class="lab"><font color="Green" title="E48">A41</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c22">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:13_2_2_1"/><span class="lab"><font color="Green" title="E49">A42</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="c22">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c23">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="E5:13_2_2_1"/><span class="lab"><font color="Green" title="E50">A43</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c23">x</font>
 <span class="kw">and </span><br/><a NAME="E6:13_2_2_1"/><span class="lab"><font color="Green" title="E51">A44</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">x</font>
 <span class="kw">and </span><br/><a NAME="E7:13_2_2_1"/><span class="lab"><font color="Green" title="E52">A45</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr.html#T2" target="_self" title="CONMETR:th.2">Th2</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">x9</font> = <font color="Maroon" title="c23">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#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c25">e2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E10:13_2_2_1"/><span class="lab"><font color="Green" title="E53">A46</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c25">e2</font>
 <span class="kw">and </span><br/><a NAME="E11:13_2_2_1"/><span class="lab"><font color="Green" title="E54">A47</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">e19</font> = <font color="Maroon" title="c22">e1</font>, <font color="Maroon" title="c27">e29</font> = <font color="Maroon" title="c25">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E13:13_2_2_1"/>
not <font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">x9</font>,<font color="Maroon" title="c27">e29</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_1"/>
<font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">x9</font>,<font color="Maroon" title="c27">e29</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c22">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c25">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E3:13_2_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c25">e2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_1"><span class="lab"><font color="Green" title="E48">A41</font></span></a>, <a class="txt" href="#E3:13_2_2_1"><span class="lab"><font color="Green" title="E49">A42</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E4:13_2_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_2_2_1"><span class="lab"><font color="Green" title="E53">A46</font></span></a>, <a class="txt" href="#E11:13_2_2_1"><span class="lab"><font color="Green" title="E54">A47</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E5:13_2_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E6:13_2_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E7:13_2_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c17">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:13_2_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E15:13"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c28">y9</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="E15:13_2_2_1"/><span class="lab"><font color="Green" title="E55">A48</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c28">y9</font>
 <span class="kw">and </span><br/><a NAME="E16:13_2_2_1"/><span class="lab"><font color="Green" title="E56">A49</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">x9</font>,<font color="Maroon" title="c27">e29</font>,<font color="Maroon" title="c28">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c29">y</font> = <font color="Maroon" title="c28">y9</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#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E18:13_2_2_1"/><span class="lab"><font color="Green" title="E57">A50</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c23">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E19:13_2_2_1"/><span class="lab"><font color="Green" title="E58">A51</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c23">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:13_2_2_1_2"/><span class="lab"><font color="Green" title="E59">A52</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_2_1"/>
<font color="Maroon" title="c3">a2</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="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:13_2_2_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="c13">a29</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:13_2_2_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="c12">a19</font>,<font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c13">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:13_2_2_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:13_2_2_1_2"/>
 <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="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:13_2_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A53</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="c24">x9</font>,<font color="Maroon" title="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:13_2_2_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c23">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:13_2_2_1_2"/><span class="kw">then </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="c17">b29</font>,<font color="Maroon" title="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E6:13_2_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c21">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E1:13_2_2_1_2"><span class="lab"><font color="Green" title="E59">A52</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:13_2_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E7:13_2_2_1"><span class="lab"><font color="Green" title="E52">A45</font></span></a>, <a class="txt" href="#E3:13_2_2_1_2"><span class="lab"><font color="Green" title="E60">A53</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E20:13_2_2_1"/><span class="lab"><font color="Green" title="E59">A54</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_3"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_1_3"/><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="c16">b19</font>,<font color="Maroon" title="c15">a49</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:13_2_2_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E13:13"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E21:13_2_2_1"/><span class="lab"><font color="Green" title="E60">A55</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c23">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_4"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c23">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_1_4"/><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="c16">b19</font>,<font color="Maroon" title="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:13_2_2_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A56</font></span>: 
<font color="Maroon" title="c24">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<a NAME="E4:13_2_2_1_4"/>
 <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="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:13_2_2_1_4"/><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="c24">x9</font>,<font color="Maroon" title="c13">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:13_2_2_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E6:13_2_2_1"><span class="lab"><font color="Green" title="E51">A44</font></span></a>, <a class="txt" href="#E3:13_2_2_1_4"><span class="lab"><font color="Green" title="E61">A56</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E22:13_2_2_1"/><span class="lab"><font color="Green" title="E61">A57</font></span>: 
<font color="Maroon" title="c10">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c11">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E23:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c20">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></span>;<br/><a NAME="E24:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c18">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c17">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></span>;<br/><a NAME="E25:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E26:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A58</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E27:13_2_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c25">e2</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:13_2_2_1"><span class="lab"><font color="Green" title="E56">A49</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E28:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c25">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E29:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A59</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13_2_2_1"><span class="lab"><font color="Green" title="E53">A46</font></span></a>, <a class="txt" href="#E11:13_2_2_1"><span class="lab"><font color="Green" title="E54">A47</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E30:13_2_2_1"/><span class="lab"><font color="Green" title="E64">A60</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="c29">y</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_5"/>
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_1_5"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c23">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:13_2_2_1"><span class="lab"><font color="Green" title="E63">A59</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E3:13_2_2_1_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c23">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E4:13_2_2_1_5"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:13_2_2_1_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A61</font></span>: 
<font color="Maroon" title="c24">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<a NAME="E6:13_2_2_1_5"/>
 <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="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E7:13_2_2_1_5"/><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="c24">x9</font>,<font color="Maroon" title="c13">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:13_2_2_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E6:13_2_2_1"><span class="lab"><font color="Green" title="E51">A44</font></span></a>, <a class="txt" href="#E5:13_2_2_1_5"><span class="lab"><font color="Green" title="E65">A61</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E31:13_2_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c22">e1</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:13_2_2_1"><span class="lab"><font color="Green" title="E55">A48</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E32:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c22">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E33:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A62</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_1"><span class="lab"><font color="Green" title="E48">A41</font></span></a>, <a class="txt" href="#E3:13_2_2_1"><span class="lab"><font color="Green" title="E49">A42</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E34:13_2_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E35:13_2_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c17">b29</font>,<font color="Maroon" title="c28">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E36:13_2_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c28">y9</font>,<font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c17">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E37:13_2_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E38:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E39:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A63</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E40:13_2_2_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E41:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E15:13"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E33:13_2_2_1"><span class="lab"><font color="Green" title="E65">A62</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E42:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A64</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c23">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E18:13_2_2_1"><span class="lab"><font color="Green" title="E57">A50</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E43:13_2_2_1"/><span class="lab"><font color="Green" title="E68">A65</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c4">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_6"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:13_2_2_1_6"/><span class="lab"><font color="Green" title="E69">A66</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_6_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_6_1"/>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_1_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:13_2_2_1"><span class="lab"><font color="Green" title="E67">A64</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E3:13_2_2_1_6_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E4:13_2_2_1_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">x9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:13_2_2_1_6_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="c16">b19</font>,<font color="Maroon" title="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:13_2_2_1_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A67</font></span>: 
<font color="Maroon" title="c24">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<a NAME="E7:13_2_2_1_6_1"/>
 <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="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E8:13_2_2_1_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">x9</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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:13_2_2_1_6_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E6:13_2_2_1"><span class="lab"><font color="Green" title="E51">A44</font></span></a>, <a class="txt" href="#E6:13_2_2_1_6_1"><span class="lab"><font color="Green" title="E70">A67</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:13_2_2_1_6"/>
<font color="Maroon" title="c12">a19</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="c16">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/>
<a NAME="E3:13_2_2_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E4:13_2_2_1_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A68</font></span>: 
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="txt" href="#E29:13_2_2_1"><span class="lab"><font color="Green" title="E63">A59</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<span class="kw">assume </span><a NAME="E5:13_2_2_1_6"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c4">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E6:13_2_2_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c4">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E7:13_2_2_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_6"><span class="lab"><font color="Green" title="E69">A66</font></span></a>, <a class="txt" href="#E4:13_2_2_1_6"><span class="lab"><font color="Green" title="E70">A68</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E8:13_2_2_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c23">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E9:13_2_2_1_6"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c23">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E10:13_2_2_1_6"/><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="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E11:13_2_2_1_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A69</font></span>: 
<font color="Maroon" title="c24">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E2:13_2_2"><span class="lab"><font color="Green" title="E46">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<a NAME="E12:13_2_2_1_6"/>
 <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="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E13:13_2_2_1_6"/><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="c24">x9</font>,<font color="Maroon" title="c13">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:13_2_2_1_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E6:13_2_2_1"><span class="lab"><font color="Green" title="E51">A44</font></span></a>, <a class="txt" href="#E11:13_2_2_1_6"><span class="lab"><font color="Green" title="E71">A69</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E44:13_2_2_1"/><span class="lab"><font color="Green" title="E69">A70</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c5">a4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_7"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:13_2_2_1_7"/><span class="lab"><font color="Green" title="E70">A71</font></span>: 
<font color="Maroon" title="c23">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_7_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_7_1"/>
<font color="Maroon" title="c23">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_1_7_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E42:13_2_2_1"><span class="lab"><font color="Green" title="E67">A64</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E3:13_2_2_1_7_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E4:13_2_2_1_7_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">x9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:13_2_2_1_7_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="c16">b19</font>,<font color="Maroon" title="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:13_2_2_1_7_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A72</font></span>: 
<font color="Maroon" title="c24">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<a NAME="E7:13_2_2_1_7_1"/>
 <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="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E8:13_2_2_1_7_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">x9</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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:13_2_2_1_7_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E6:13_2_2_1"><span class="lab"><font color="Green" title="E51">A44</font></span></a>, <a class="txt" href="#E6:13_2_2_1_7_1"><span class="lab"><font color="Green" title="E71">A72</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:13_2_2_1_7"/>
<font color="Maroon" title="c20">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13_2_2_1"><span class="lab"><font color="Green" title="E61">A57</font></span></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></span>;<br/>
<a NAME="E3:13_2_2_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c15">a49</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></span>;<br/>
<a NAME="E4:13_2_2_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E5:13_2_2_1_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A73</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="txt" href="#E29:13_2_2_1"><span class="lab"><font color="Green" title="E63">A59</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<span class="kw">assume </span><a NAME="E6:13_2_2_1_7"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c5">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E7:13_2_2_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E8:13_2_2_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_1_7"><span class="lab"><font color="Green" title="E70">A71</font></span></a>, <a class="txt" href="#E5:13_2_2_1_7"><span class="lab"><font color="Green" title="E71">A73</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E9:13_2_2_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c23">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E10:13_2_2_1_7"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c23">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E11:13_2_2_1_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">a49</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E12:13_2_2_1_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A74</font></span>: 
<font color="Maroon" title="c24">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c21">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E1:13_2_2"><span class="lab"><font color="Green" title="E45">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<a NAME="E13:13_2_2_1_7"/>
 <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="c24">x9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E14:13_2_2_1_7"/><span class="kw">then </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="c24">x9</font>,<font color="Maroon" title="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:13_2_2_1_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E7:13_2_2_1"><span class="lab"><font color="Green" title="E52">A45</font></span></a>, <a class="txt" href="#E12:13_2_2_1_7"><span class="lab"><font color="Green" title="E72">A74</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E45:13_2_2_1"/><span class="lab"><font color="Green" title="E70">A75</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c4">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_8"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:13_2_2_1_8"/><span class="lab"><font color="Green" title="E71">A76</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_8_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_8_1"/>
<font color="Maroon" title="c3">a2</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="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_1_8_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:13_2_2_1_8_1"/><span class="kw">then </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="c12">a19</font>,<font color="Maroon" title="c16">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:13_2_2_1_8_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="c16">b19</font>,<font color="Maroon" title="c13">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:13_2_2_1_8_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:13_2_2_1_8"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c4">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:13_2_2_1_8"/><span class="kw">then </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="c17">b29</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:13_2_2_1_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E18:13"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E1:13_2_2_1_8"><span class="lab"><font color="Green" title="E71">A76</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E46:13_2_2_1"/><span class="lab"><font color="Green" title="E71">A77</font></span>: 
( <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_1_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_1_9"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a> </span><br/>

<a NAME="E2:13_2_2_1_9"/><span class="kw">then </span>
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr.html#T7" target="_self" title="CONMETR:th.7">Th7</a></span>;<br/>
<a NAME="E3:13_2_2_1_9"/><span class="kw">then </span>
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_2.html#T28" title="AFF_2:th.28">AFF_2:28</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:13_2_2_1_9"/>
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr.html#T8" target="_self" title="CONMETR:th.8">Th8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E47:13_2_2_1"/>
 <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="c24">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_1"><span class="lab"><font color="Green" title="E50">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E48:13_2_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">x9</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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E49:13_2_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E50:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E51:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c23">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c23">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E52:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c23">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13_2_2_1"><span class="lab"><font color="Green" title="E51">A44</font></span></a>, <a class="txt" href="#E42:13_2_2_1"><span class="lab"><font color="Green" title="E67">A64</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E53:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A78</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c23">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:13_2_2_1"><span class="lab"><font color="Green" title="E64">A60</font></span></a>, <a class="txt" href="#E39:13_2_2_1"><span class="lab"><font color="Green" title="E66">A63</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E54:13_2_2_1"/>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c18">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E55:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E56:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A79</font></span>: 
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="txt" href="#E29:13_2_2_1"><span class="lab"><font color="Green" title="E63">A59</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E57:13_2_2_1"/>
<font color="Maroon" title="c20">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13_2_2_1"><span class="lab"><font color="Green" title="E61">A57</font></span></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></span>;<br/><a NAME="E58:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">a49</font>,<font color="Maroon" title="c19">b49</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:13"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></span>;<br/><a NAME="E59:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E60:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A80</font></span>: 
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="txt" href="#E29:13_2_2_1"><span class="lab"><font color="Green" title="E63">A59</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E61:13_2_2_1"/>
<font color="Maroon" title="c20">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13_2_2_1"><span class="lab"><font color="Green" title="E61">A57</font></span></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></span>;<br/><a NAME="E62:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c17">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></span>;<br/><a NAME="E63:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E64:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A81</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c29">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="txt" href="#E29:13_2_2_1"><span class="lab"><font color="Green" title="E63">A59</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E65:13_2_2_1"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</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="#E21:13"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E66:13_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A82</font></span>: 
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E46:13_2_2_1"><span class="lab"><font color="Green" title="E71">A77</font></span></a>, <a class="txt" href="#E19:13_2_2_1"><span class="lab"><font color="Green" title="E58">A51</font></span></a>, <a class="txt" href="#E45:13_2_2_1"><span class="lab"><font color="Green" title="E70">A75</font></span></a>, <a class="txt" href="#E64:13_2_2_1"><span class="lab"><font color="Green" title="E75">A81</font></span></a>, <a class="txt" href="#E26:13_2_2_1"><span class="lab"><font color="Green" title="E62">A58</font></span></a>, <a class="txt" href="#E53:13_2_2_1"><span class="lab"><font color="Green" title="E72">A78</font></span></a>, <a class="ref" href="conmetr.html#D8" target="_self" title="CONMETR:def.8">Def8</a></span>;<br/><a NAME="E67:13_2_2_1"/>
<font color="Maroon" title="c20">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13_2_2_1"><span class="lab"><font color="Green" title="E61">A57</font></span></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></span>;<br/><a NAME="E68:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">a49</font>,<font color="Maroon" title="c19">b49</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:13"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></span>;<br/><a NAME="E69:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E70:13_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">x</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E23:13"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E29:13_2_2_1"><span class="lab"><font color="Green" title="E63">A59</font></span></a>, <a class="txt" href="#E46:13_2_2_1"><span class="lab"><font color="Green" title="E71">A77</font></span></a>, <a class="txt" href="#E21:13_2_2_1"><span class="lab"><font color="Green" title="E60">A55</font></span></a>, <a class="txt" href="#E20:13_2_2_1"><span class="lab"><font color="Green" title="E59">A54</font></span></a>, <a class="txt" href="#E42:13_2_2_1"><span class="lab"><font color="Green" title="E67">A64</font></span></a>, <a class="ref" href="conmetr.html#D8" target="_self" title="CONMETR:def.8">Def8</a></span>;<br/><span class="kw">hence </span><a NAME="E71:13_2_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E46:13_2_2_1"><span class="lab"><font color="Green" title="E71">A77</font></span></a>, <a class="txt" href="#E66:13_2_2_1"><span class="lab"><font color="Green" title="E76">A82</font></span></a>, <a class="txt" href="#E43:13_2_2_1"><span class="lab"><font color="Green" title="E68">A65</font></span></a>, <a class="txt" href="#E44:13_2_2_1"><span class="lab"><font color="Green" title="E69">A70</font></span></a>, <a class="txt" href="#E56:13_2_2_1"><span class="lab"><font color="Green" title="E73">A79</font></span></a>, <a class="txt" href="#E60:13_2_2_1"><span class="lab"><font color="Green" title="E74">A80</font></span></a>, <a class="ref" href="conmetr.html#D8" target="_self" title="CONMETR:def.8">Def8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="13_2_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_2_2"/>
not <font color="Maroon" title="c10">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c11">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:13_2_2_2"/><span class="kw">then </span>
not <font color="Maroon" title="c20">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c22">o9</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="E4:13_2_2_2"/><span class="lab"><font color="Green" title="E48">A83</font></span>: 
<font color="Maroon" title="c22">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M9</font>
 <span class="kw">and </span><br/><a NAME="E5:13_2_2_2"/><span class="lab"><font color="Green" title="E49">A84</font></span>: 
<font color="Maroon" title="c22">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="aff_1.html#T72" title="AFF_1:th.72">AFF_1:72</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c23">o</font> = <font color="Maroon" title="c22">o9</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#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c24">K</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E8:13_2_2_2"/><span class="lab"><font color="Green" title="E50">A85</font></span>: 
<font color="Maroon" title="c23">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 <span class="kw">and </span><br/><a NAME="E9:13_2_2_2"/><span class="lab"><font color="Green" title="E51">A86</font></span>: 
<font color="Maroon" title="c11">N</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c24">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="ref" href="conmetr.html#T3" target="_self" title="CONMETR:th.3">Th3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c25">K9</font> = <font color="Maroon" title="c24">K</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#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/><a NAME="E11:13_2_2_2"/><span class="lab"><font color="Green" title="E52">A87</font></span>: 
<font color="Maroon" title="c24">K</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13_2_2_2"><span class="lab"><font color="Green" title="E51">A86</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E12:13_2_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A88</font></span>: 
<font color="Maroon" title="c25">K9</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="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_2_2_2_1"/><span class="lab"><font color="Green" title="E54">A89</font></span>: 
( not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</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="c24">K</font> &amp; not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E55">A90</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c26">x</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c26">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">x</font> implies  not <font color="Maroon" title="c26">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13_2_2_2_1_1_1"/><span class="lab"><font color="Green" title="E56">A91</font></span>: 
<font color="Maroon" title="c26">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E2:13_2_2_2_1_1_1"/><span class="lab"><font color="Green" title="E57">A92</font></span>: 
<font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c26">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font></span><br/><span class="kw">assume </span><a NAME="E3:13_2_2_2_1_1_1"/>
<font color="Maroon" title="c26">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:13_2_2_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c26">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c26">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E8:13_2_2_2"><span class="lab"><font color="Green" title="E50">A85</font></span></a>, <a class="txt" href="#E9:13_2_2_2"><span class="lab"><font color="Green" title="E51">A86</font></span></a>, <a class="txt" href="#E1:13_2_2_2_1_1_1"><span class="lab"><font color="Green" title="E56">A91</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/><span class="kw">hence </span><a NAME="E5:13_2_2_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_2_1_1_1"><span class="lab"><font color="Green" title="E57">A92</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:13_2_2_2_1_1"/>
( <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> or <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> or <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> or <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E3:13_2_2_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:13"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E13:13"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:13"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:13"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E1:13_2_2_2_1_1"><span class="lab"><font color="Green" title="E55">A90</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:13_2_2_2_1"/><span class="lab"><font color="Green" title="E55">A93</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="ref" href="conmetr.html#T4" target="_self" title="CONMETR:th.4">Th4</a></span>;<br/><div><span class="lab"><font color="Green" title="E56">A94</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_2_2_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_2_2_1_2"/><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="c16">b19</font>,<font color="Maroon" title="c15">a49</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_2_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E13:13"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E4:13_2_2_2_1"/><span class="lab"><font color="Green" title="E57">A95</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="ref" href="conmetr.html#T4" target="_self" title="CONMETR:th.4">Th4</a></span>;<br/><div><span class="lab"><font color="Green" title="E58">A96</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_2_2_1_3"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c3">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_2_2_1_3"/><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="c18">b39</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_2_2_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E28:13"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E6:13_2_2_2_1"/><span class="lab"><font color="Green" title="E59">A97</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="ref" href="conmetr.html#T4" target="_self" title="CONMETR:th.4">Th4</a></span>;<br/><div><span class="lab"><font color="Green" title="E60">A98</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_4"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c26">x9</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">y9</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> st <br/>( <font color="Olive" title="b1">y9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K9</font> &amp; <font color="Maroon" title="c26">x9</font>,<font color="Olive" title="b1">y9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font> )</span><br/><span class="kw">consider </span><font color="Maroon" title="c27">D9</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="E2:13_2_2_2_1_4"/><span class="lab"><font color="Green" title="E61">A99</font></span>: 
<font color="Maroon" title="c26">x9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">D9</font>
 <span class="kw">and </span><br/><a NAME="E3:13_2_2_2_1_4"/><span class="lab"><font color="Green" title="E62">A100</font></span>: 
<font color="Maroon" title="c21">N9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c27">D9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="aff_1.html#T63" title="AFF_1:th.63">AFF_1:63</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c28">D</font> = <font color="Maroon" title="c27">D9</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/><a NAME="E5:13_2_2_2_1_4"/>
<font color="Maroon" title="c11">N</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c28">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_2_2_1_4"><span class="lab"><font color="Green" title="E62">A100</font></span></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></span>;<br/><a NAME="E6:13_2_2_2_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c24">K</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c28">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13_2_2_2"><span class="lab"><font color="Green" title="E51">A86</font></span></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c29">y</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="E8:13_2_2_2_1_4"/><span class="lab"><font color="Green" title="E63">A101</font></span>: 
<font color="Maroon" title="c29">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 <span class="kw">and </span><br/><a NAME="E9:13_2_2_2_1_4"/><span class="lab"><font color="Green" title="E64">A102</font></span>: 
<font color="Maroon" title="c29">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c28">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T88" title="ANALMETR:th.88">ANALMETR:88</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">y9</font> = <font color="Maroon" title="c29">y</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#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c31">y9</font> = <font color="Maroon" title="c30">y9</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c31">y9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K9</font> &amp; <font color="Maroon" title="c26">x9</font>,<font color="Maroon" title="c31">y9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font> )</span><br/><span class="kw">thus </span><a NAME="E11:13_2_2_2_1_4"/>
( <font color="Maroon" title="c31">y9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K9</font> &amp; <font color="Maroon" title="c26">x9</font>,<font color="Maroon" title="c31">y9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2_2_2_1_4"><span class="lab"><font color="Green" title="E61">A99</font></span></a>, <a class="txt" href="#E3:13_2_2_2_1_4"><span class="lab"><font color="Green" title="E62">A100</font></span></a>, <a class="txt" href="#E8:13_2_2_2_1_4"><span class="lab"><font color="Green" title="E63">A101</font></span></a>, <a class="txt" href="#E9:13_2_2_2_1_4"><span class="lab"><font color="Green" title="E64">A102</font></span></a>, <a class="ref" href="aff_1.html#T54" title="AFF_1:th.54">AFF_1:54</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="c26">d19</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="E9:13_2_2_2_1"/><span class="lab"><font color="Green" title="E61">A103</font></span>: 
<font color="Maroon" title="c26">d19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K9</font>
 <span class="kw">and </span><br/><a NAME="E10:13_2_2_2_1"/><span class="lab"><font color="Green" title="E62">A104</font></span>: 
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c26">d19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font>
 ;<br/><span class="kw">consider </span><font color="Maroon" title="c27">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="E12:13_2_2_2_1"/><span class="lab"><font color="Green" title="E63">A105</font></span>: 
<font color="Maroon" title="c27">e19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K9</font>
 <span class="kw">and </span><br/><a NAME="E13:13_2_2_2_1"/><span class="lab"><font color="Green" title="E64">A106</font></span>: 
<font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c27">e19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_2_2_2_1"><span class="lab"><font color="Green" title="E60">A98</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c28">d39</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="E15:13_2_2_2_1"/><span class="lab"><font color="Green" title="E65">A107</font></span>: 
<font color="Maroon" title="c28">d39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K9</font>
 <span class="kw">and </span><br/><a NAME="E16:13_2_2_2_1"/><span class="lab"><font color="Green" title="E66">A108</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c28">d39</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_2_2_2_1"><span class="lab"><font color="Green" title="E60">A98</font></span></a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c29">e39</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="E18:13_2_2_2_1"/><span class="lab"><font color="Green" title="E67">A109</font></span>: 
<font color="Maroon" title="c29">e39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K9</font>
 <span class="kw">and </span><br/><a NAME="E19:13_2_2_2_1"/><span class="lab"><font color="Green" title="E68">A110</font></span>: 
<font color="Maroon" title="c18">b39</font>,<font color="Maroon" title="c29">e39</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:13_2_2_2_1"><span class="lab"><font color="Green" title="E60">A98</font></span></a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">d1</font> = <font color="Maroon" title="c26">d19</font>, <font color="Maroon" title="c31">d3</font> = <font color="Maroon" title="c28">d39</font>, <font color="Maroon" title="c32">e1</font> = <font color="Maroon" title="c27">e19</font>, <font color="Maroon" title="c33">e3</font> = <font color="Maroon" title="c29">e39</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#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E21:13_2_2_2_1"/><span class="lab"><font color="Green" title="E69">A111</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c30">d1</font>,<font color="Maroon" title="c32">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2_2_2"><span class="lab"><font color="Green" title="E50">A85</font></span></a>, <a class="txt" href="#E11:13_2_2_2"><span class="lab"><font color="Green" title="E52">A87</font></span></a>, <a class="txt" href="#E9:13_2_2_2_1"><span class="lab"><font color="Green" title="E61">A103</font></span></a>, <a class="txt" href="#E12:13_2_2_2_1"><span class="lab"><font color="Green" title="E63">A105</font></span></a>, <a class="ref" href="conmetr.html#T4" target="_self" title="CONMETR:th.4">Th4</a></span>;<br/><a NAME="E22:13_2_2_2_1"/><span class="lab"><font color="Green" title="E70">A112</font></span>: 
( <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c32">e1</font> &amp; <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">e3</font> &amp; <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">d1</font> &amp; <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c31">d3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_5"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E71">A113</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_5_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c34">x</font>, <font color="Maroon" title="c35">y</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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">x9</font>, <font color="Olive" title="b2">y9</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>  st <font color="Olive" title="b1">x9</font>,<font color="Olive" title="b2">y9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font> &amp; <font color="Maroon" title="c34">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x9</font> &amp; <font color="Maroon" title="c35">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y9</font> &amp; <font color="Maroon" title="c34">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c35">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; not <font color="Maroon" title="c34">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> holds <br/> not <font color="Maroon" title="c23">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">y</font></span><br/><span class="kw">let </span><font color="Maroon" title="c36">x9</font>, <font color="Maroon" title="c37">y9</font> be   <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c36">x9</font>,<font color="Maroon" title="c37">y9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font> &amp; <font color="Maroon" title="c34">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">x9</font> &amp; <font color="Maroon" title="c35">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">y9</font> &amp; <font color="Maroon" title="c34">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c35">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> &amp; not <font color="Maroon" title="c34">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> implies  not <font color="Maroon" title="c23">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">y</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:13_2_2_2_1_5_1"/><span class="lab"><font color="Green" title="E72">A114</font></span>: 
<font color="Maroon" title="c36">x9</font>,<font color="Maroon" title="c37">y9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">and </span><br/><a NAME="E2:13_2_2_2_1_5_1"/><span class="lab"><font color="Green" title="E73">A115</font></span>: 
<font color="Maroon" title="c34">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">x9</font>
 <span class="kw">and </span><br/><a NAME="E3:13_2_2_2_1_5_1"/><span class="lab"><font color="Green" title="E74">A116</font></span>: 
<font color="Maroon" title="c35">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">y9</font>
 <span class="kw">and </span><br/><a NAME="E4:13_2_2_2_1_5_1"/>
<font color="Maroon" title="c34">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E5:13_2_2_2_1_5_1"/>
<font color="Maroon" title="c35">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font>
 <span class="kw">and </span><br/><a NAME="E6:13_2_2_2_1_5_1"/><span class="lab"><font color="Green" title="E75">A117</font></span>: 
not <font color="Maroon" title="c34">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c23">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">y</font></span><br/><span class="kw">assume </span><a NAME="E7:13_2_2_2_1_5_1"/>
<font color="Maroon" title="c23">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c35">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E8:13_2_2_2_1_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c36">x9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13_2_2_2_1_5_1"><span class="lab"><font color="Green" title="E72">A114</font></span></a>, <a class="txt" href="#E3:13_2_2_2_1_5_1"><span class="lab"><font color="Green" title="E74">A116</font></span></a>, <a class="ref" href="aff_1.html#T48" title="AFF_1:th.48">AFF_1:48</a></span>;<br/><span class="kw">hence </span><a NAME="E9:13_2_2_2_1_5_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E2:13_2_2_2_1_5_1"><span class="lab"><font color="Green" title="E73">A115</font></span></a>, <a class="txt" href="#E6:13_2_2_2_1_5_1"><span class="lab"><font color="Green" title="E75">A117</font></span></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:13_2_2_2_1_5"/>
(  not <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c32">e1</font> or  not <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">e3</font> or  not <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c30">d1</font> or  not <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c31">d3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E3:13_2_2_2_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E18:13"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E19:13"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E20:13"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E9:13_2_2_2_1"><span class="lab"><font color="Green" title="E61">A103</font></span></a>, <a class="txt" href="#E10:13_2_2_2_1"><span class="lab"><font color="Green" title="E62">A104</font></span></a>, <a class="txt" href="#E15:13_2_2_2_1"><span class="lab"><font color="Green" title="E65">A107</font></span></a>, <a class="txt" href="#E16:13_2_2_2_1"><span class="lab"><font color="Green" title="E66">A108</font></span></a>, <a class="txt" href="#E18:13_2_2_2_1"><span class="lab"><font color="Green" title="E67">A109</font></span></a>, <a class="txt" href="#E19:13_2_2_2_1"><span class="lab"><font color="Green" title="E68">A110</font></span></a>, <a class="txt" href="#E12:13_2_2_2_1"><span class="lab"><font color="Green" title="E63">A105</font></span></a>, <a class="txt" href="#E13:13_2_2_2_1"><span class="lab"><font color="Green" title="E64">A106</font></span></a>, <a class="txt" href="#E1:13_2_2_2_1_5"><span class="lab"><font color="Green" title="E71">A113</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E23:13_2_2_2_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c30">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E10:13_2_2_2_1"><span class="lab"><font color="Green" title="E62">A104</font></span></a>, <a class="ref" href="conmetr.html#T6" target="_self" title="CONMETR:th.6">Th6</a></span>;<br/><a NAME="E24:13_2_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A118</font></span>: 
<font color="Maroon" title="c30">d1</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E25:13_2_2_2_1"/><span class="lab"><font color="Green" title="E72">A119</font></span>: 
not <font color="Maroon" title="c32">e1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:13"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E13:13_2_2_2_1"><span class="lab"><font color="Green" title="E64">A106</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>;<br/><a NAME="E26:13_2_2_2_1"/><span class="lab"><font color="Green" title="E73">A120</font></span>: 
not <font color="Maroon" title="c31">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:13"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E16:13_2_2_2_1"><span class="lab"><font color="Green" title="E66">A108</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>;<br/><a NAME="E27:13_2_2_2_1"/>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c26">d19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b19</font>,<font color="Maroon" title="c27">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E10:13_2_2_2_1"><span class="lab"><font color="Green" title="E62">A104</font></span></a>, <a class="txt" href="#E13:13_2_2_2_1"><span class="lab"><font color="Green" title="E64">A106</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><a NAME="E28:13_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c30">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c32">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E29:13_2_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A121</font></span>: 
<font color="Maroon" title="c30">d1</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">e1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><span class="kw">assume </span><a NAME="E30:13_2_2_2_1"/><span class="lab"><font color="Green" title="E75">A122</font></span>: 
<font color="Maroon" title="c24">K</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">M</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><span class="lab"><font color="Green" title="E76">A123</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_6"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_2_2_1_6"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c31">d3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_2_2_1_6"/><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="c18">b39</font>,<font color="Maroon" title="c28">d39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E3:13_2_2_2_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c31">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E28:13"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_2_1_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E8:13_2_2_2"><span class="lab"><font color="Green" title="E50">A85</font></span></a>, <a class="txt" href="#E11:13_2_2_2"><span class="lab"><font color="Green" title="E52">A87</font></span></a>, <a class="txt" href="#E30:13_2_2_2_1"><span class="lab"><font color="Green" title="E75">A122</font></span></a>, <a class="txt" href="#E15:13_2_2_2_1"><span class="lab"><font color="Green" title="E65">A107</font></span></a>, <a class="txt" href="#E22:13_2_2_2_1"><span class="lab"><font color="Green" title="E70">A112</font></span></a>, <a class="ref" href="conmetr.html#T5" target="_self" title="CONMETR:th.5">Th5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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">A124</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_7"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_2_2_1_7"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c30">d1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_2_2_1_7"/><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="c16">b19</font>,<font color="Maroon" title="c26">d19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E3:13_2_2_2_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c30">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><span class="kw">hence </span><a NAME="E4:13_2_2_2_1_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E8:13_2_2_2"><span class="lab"><font color="Green" title="E50">A85</font></span></a>, <a class="txt" href="#E11:13_2_2_2"><span class="lab"><font color="Green" title="E52">A87</font></span></a>, <a class="txt" href="#E30:13_2_2_2_1"><span class="lab"><font color="Green" title="E75">A122</font></span></a>, <a class="txt" href="#E9:13_2_2_2_1"><span class="lab"><font color="Green" title="E61">A103</font></span></a>, <a class="txt" href="#E22:13_2_2_2_1"><span class="lab"><font color="Green" title="E70">A112</font></span></a>, <a class="ref" href="conmetr.html#T5" target="_self" title="CONMETR:th.5">Th5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E33:13_2_2_2_1"/>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c28">d39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b39</font>,<font color="Maroon" title="c29">e39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E16:13_2_2_2_1"><span class="lab"><font color="Green" title="E66">A108</font></span></a>, <a class="txt" href="#E19:13_2_2_2_1"><span class="lab"><font color="Green" title="E68">A110</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><a NAME="E34:13_2_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A125</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c31">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c33">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E35:13_2_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A126</font></span>: 
<font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">e3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E36:13_2_2_2_1"/><span class="lab"><font color="Green" title="E80">A127</font></span>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c33">e3</font>,<font color="Maroon" title="c4">a3</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c33">e3</font>,<font color="Maroon" title="c5">a4</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_8"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:13_2_2_2_1_8"/><span class="lab"><font color="Green" title="E81">A128</font></span>: 
<font color="Maroon" title="c31">d3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">e3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_8_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_2_2_1_8_1"/>
not <font color="Maroon" title="c31">d3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">e3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_2_2_1_8_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c33">e3</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E35:13_2_2_2_1"><span class="lab"><font color="Green" title="E79">A126</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:13_2_2_2_1_8_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c29">e39</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c18">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:13_2_2_2_1_8_1"/><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="c18">b39</font>,<font color="Maroon" title="c29">e39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E5:13_2_2_2_1_8_1"/><span class="kw">then </span>
<font color="Maroon" title="c29">e39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E28:13"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:13_2_2_2_1_8_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E8:13_2_2_2"><span class="lab"><font color="Green" title="E50">A85</font></span></a>, <a class="txt" href="#E12:13_2_2_2"><span class="lab"><font color="Green" title="E53">A88</font></span></a>, <a class="txt" href="#E30:13_2_2_2_1"><span class="lab"><font color="Green" title="E75">A122</font></span></a>, <a class="txt" href="#E18:13_2_2_2_1"><span class="lab"><font color="Green" title="E67">A109</font></span></a>, <a class="txt" href="#E22:13_2_2_2_1"><span class="lab"><font color="Green" title="E70">A112</font></span></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:13_2_2_2_1_8"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c33">e3</font>,<font color="Maroon" title="c4">a3</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c33">e3</font>,<font color="Maroon" title="c5">a4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:13_2_2_2_1_8"/><span class="kw">then </span>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c28">d39</font>,<font color="Maroon" title="c29">e39</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="c28">d39</font>,<font color="Maroon" title="c29">e39</font>,<font color="Maroon" title="c15">a49</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:13_2_2_2_1_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="c25">K9</font> or <font color="Maroon" title="c15">a49</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:13_2_2_2"><span class="lab"><font color="Green" title="E53">A88</font></span></a>, <a class="txt" href="#E15:13_2_2_2_1"><span class="lab"><font color="Green" title="E65">A107</font></span></a>, <a class="txt" href="#E18:13_2_2_2_1"><span class="lab"><font color="Green" title="E67">A109</font></span></a>, <a class="txt" href="#E1:13_2_2_2_1_8"><span class="lab"><font color="Green" title="E81">A128</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:13_2_2_2_1_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E13:13"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E18:13"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E8:13_2_2_2"><span class="lab"><font color="Green" title="E50">A85</font></span></a>, <a class="txt" href="#E9:13_2_2_2"><span class="lab"><font color="Green" title="E51">A86</font></span></a>, <a class="txt" href="#E12:13_2_2_2"><span class="lab"><font color="Green" title="E53">A88</font></span></a>, <a class="txt" href="#E30:13_2_2_2_1"><span class="lab"><font color="Green" title="E75">A122</font></span></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E81">A129</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_2_2_1_9"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_2_2_2_1_9"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_2_2_2_1_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="c16">b19</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_2_2_2_1_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E38:13_2_2_2_1"/><span class="lab"><font color="Green" title="E82">A130</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:13"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:13"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="ref" href="conmetr.html#T4" target="_self" title="CONMETR:th.4">Th4</a></span>;<br/><a NAME="E39:13_2_2_2_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E40:13_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c30">d1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">e1</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:13"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E19:13"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E22:13_2_2_2_1"><span class="lab"><font color="Green" title="E70">A112</font></span></a>, <a class="txt" href="#E2:13_2_2_2_1"><span class="lab"><font color="Green" title="E55">A93</font></span></a>, <a class="txt" href="#E6:13_2_2_2_1"><span class="lab"><font color="Green" title="E59">A97</font></span></a>, <a class="txt" href="#E21:13_2_2_2_1"><span class="lab"><font color="Green" title="E69">A111</font></span></a>, <a class="txt" href="#E32:13_2_2_2_1"><span class="lab"><font color="Green" title="E77">A124</font></span></a>, <a class="txt" href="#E37:13_2_2_2_1"><span class="lab"><font color="Green" title="E81">A129</font></span></a>, <a class="txt" href="#E29:13_2_2_2_1"><span class="lab"><font color="Green" title="E74">A121</font></span></a>, <a class="txt" href="#E24:13_2_2_2_1"><span class="lab"><font color="Green" title="E71">A118</font></span></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></span>;<br/><a NAME="E41:13_2_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E83">A131</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c30">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c32">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E42:13_2_2_2_1"/><span class="lab"><font color="Green" title="E84">A132</font></span>: 
not <font color="Maroon" title="c33">e3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:13"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E19:13_2_2_2_1"><span class="lab"><font color="Green" title="E68">A110</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>;<br/><a NAME="E43:13_2_2_2_1"/><span class="lab"><font color="Green" title="E85">A133</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c33">e3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:13_2_2_2"><span class="lab"><font color="Green" title="E50">A85</font></span></a>, <a class="txt" href="#E11:13_2_2_2"><span class="lab"><font color="Green" title="E52">A87</font></span></a>, <a class="txt" href="#E15:13_2_2_2_1"><span class="lab"><font color="Green" title="E65">A107</font></span></a>, <a class="txt" href="#E18:13_2_2_2_1"><span class="lab"><font color="Green" title="E67">A109</font></span></a>, <a class="ref" href="conmetr.html#T4" target="_self" title="CONMETR:th.4">Th4</a></span>;<br/><a NAME="E44:13_2_2_2_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c30">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c5">a4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E10:13_2_2_2_1"><span class="lab"><font color="Green" title="E62">A104</font></span></a>, <a class="ref" href="conmetr.html#T6" target="_self" title="CONMETR:th.6">Th6</a></span>;<br/><a NAME="E45:13_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c30">d1</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c5">a4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E46:13_2_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A134</font></span>: 
<font color="Maroon" title="c30">d1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">e1</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E13:13"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E16:13"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E19:13"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E23:13"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E22:13_2_2_2_1"><span class="lab"><font color="Green" title="E70">A112</font></span></a>, <a class="txt" href="#E6:13_2_2_2_1"><span class="lab"><font color="Green" title="E59">A97</font></span></a>, <a class="txt" href="#E38:13_2_2_2_1"><span class="lab"><font color="Green" title="E82">A130</font></span></a>, <a class="txt" href="#E21:13_2_2_2_1"><span class="lab"><font color="Green" title="E69">A111</font></span></a>, <a class="txt" href="#E32:13_2_2_2_1"><span class="lab"><font color="Green" title="E77">A124</font></span></a>, <a class="txt" href="#E3:13_2_2_2_1"><span class="lab"><font color="Green" title="E56">A94</font></span></a>, <a class="txt" href="#E29:13_2_2_2_1"><span class="lab"><font color="Green" title="E74">A121</font></span></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></span>;<br/><a NAME="E47:13_2_2_2_1"/><span class="lab"><font color="Green" title="E87">A135</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c31">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c5">a4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E16:13_2_2_2_1"><span class="lab"><font color="Green" title="E66">A108</font></span></a>, <a class="ref" href="conmetr.html#T6" target="_self" title="CONMETR:th.6">Th6</a></span>;<br/><a NAME="E48:13_2_2_2_1"/><span class="lab"><font color="Green" title="E88">A136</font></span>: 
not <font color="Maroon" title="c30">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E10:13_2_2_2_1"><span class="lab"><font color="Green" title="E62">A104</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>;<br/><a NAME="E49:13_2_2_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c31">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E16:13_2_2_2_1"><span class="lab"><font color="Green" title="E66">A108</font></span></a>, <a class="ref" href="conmetr.html#T6" target="_self" title="CONMETR:th.6">Th6</a></span>;<br/><a NAME="E50:13_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E51:13_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">e3</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:13"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E18:13"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E20:13"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E21:13"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E22:13_2_2_2_1"><span class="lab"><font color="Green" title="E70">A112</font></span></a>, <a class="txt" href="#E2:13_2_2_2_1"><span class="lab"><font color="Green" title="E55">A93</font></span></a>, <a class="txt" href="#E4:13_2_2_2_1"><span class="lab"><font color="Green" title="E57">A95</font></span></a>, <a class="txt" href="#E43:13_2_2_2_1"><span class="lab"><font color="Green" title="E85">A133</font></span></a>, <a class="txt" href="#E31:13_2_2_2_1"><span class="lab"><font color="Green" title="E76">A123</font></span></a>, <a class="txt" href="#E5:13_2_2_2_1"><span class="lab"><font color="Green" title="E58">A96</font></span></a>, <a class="txt" href="#E35:13_2_2_2_1"><span class="lab"><font color="Green" title="E79">A126</font></span></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></span>;<br/><a NAME="E52:13_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c31">d3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">e3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:13"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E9:13_2_2_2"><span class="lab"><font color="Green" title="E51">A86</font></span></a>, <a class="txt" href="#E9:13_2_2_2_1"><span class="lab"><font color="Green" title="E61">A103</font></span></a>, <a class="txt" href="#E15:13_2_2_2_1"><span class="lab"><font color="Green" title="E65">A107</font></span></a>, <a class="txt" href="#E18:13_2_2_2_1"><span class="lab"><font color="Green" title="E67">A109</font></span></a>, <a class="txt" href="#E12:13_2_2_2_1"><span class="lab"><font color="Green" title="E63">A105</font></span></a>, <a class="txt" href="#E41:13_2_2_2_1"><span class="lab"><font color="Green" title="E83">A131</font></span></a>, <a class="txt" href="#E46:13_2_2_2_1"><span class="lab"><font color="Green" title="E86">A134</font></span></a>, <a class="txt" href="#E48:13_2_2_2_1"><span class="lab"><font color="Green" title="E88">A136</font></span></a>, <a class="txt" href="#E26:13_2_2_2_1"><span class="lab"><font color="Green" title="E73">A120</font></span></a>, <a class="txt" href="#E25:13_2_2_2_1"><span class="lab"><font color="Green" title="E72">A119</font></span></a>, <a class="txt" href="#E42:13_2_2_2_1"><span class="lab"><font color="Green" title="E84">A132</font></span></a>, <a class="txt" href="#E1:13_2_2_2_1"><span class="lab"><font color="Green" title="E54">A89</font></span></a>, <a class="ref" href="conmetr.html#D7" target="_self" title="CONMETR:def.7">Def7</a></span>;<br/><span class="kw">hence </span><a NAME="E53:13_2_2_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E13:13"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E16:13"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E18:13"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E20:13"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E4:13_2_2_2"><span class="lab"><font color="Green" title="E48">A83</font></span></a>, <a class="txt" href="#E5:13_2_2_2"><span class="lab"><font color="Green" title="E49">A84</font></span></a>, <a class="txt" href="#E22:13_2_2_2_1"><span class="lab"><font color="Green" title="E70">A112</font></span></a>, <a class="txt" href="#E38:13_2_2_2_1"><span class="lab"><font color="Green" title="E82">A130</font></span></a>, <a class="txt" href="#E4:13_2_2_2_1"><span class="lab"><font color="Green" title="E57">A95</font></span></a>, <a class="txt" href="#E43:13_2_2_2_1"><span class="lab"><font color="Green" title="E85">A133</font></span></a>, <a class="txt" href="#E34:13_2_2_2_1"><span class="lab"><font color="Green" title="E78">A125</font></span></a>, <a class="txt" href="#E36:13_2_2_2_1"><span class="lab"><font color="Green" title="E80">A127</font></span></a>, <a class="txt" href="#E47:13_2_2_2_1"><span class="lab"><font color="Green" title="E87">A135</font></span></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E14:13_2_2_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:13"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:13"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E13:13"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E15:13"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E16:13"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E18:13"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E19:13"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E20:13"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E21:13"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E23:13"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E9:13_2_2_2"><span class="lab"><font color="Green" title="E51">A86</font></span></a>, <a class="ref" href="conmetr.html#D7" target="_self" title="CONMETR:def.7">Def7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:13_2_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_2_2"><span class="lab"><font color="Green" title="E47">A40</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="13_2_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_2_3"/><span class="lab"><font color="Green" title="E45">A137</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c17">b29</font>,<font color="Maroon" title="c16">b19</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_2_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c17">b29</font>,<font color="Maroon" title="c16">b19</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_2_3_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="c16">b19</font>,<font color="Maroon" title="c17">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:13_2_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E15:13"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E1:13_2"><span class="lab"><font color="Green" title="E42">A32</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:13_2_3"/>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c18">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E7:13"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E3:13_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A138</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="c16">b19</font>,<font color="Maroon" title="c18">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="E4:13_2_3"/><span class="lab"><font color="Green" title="E47">A139</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E5:13_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E6:13_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:13"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E7:13_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c17">b29</font>,<font color="Maroon" title="c16">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b29</font>,<font color="Maroon" title="c18">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><span class="kw">hence </span><a NAME="E8:13_2_3"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:13"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E4:13_2_3"><span class="lab"><font color="Green" title="E47">A139</font></span></a>, <a class="txt" href="#E1:13_2_3"><span class="lab"><font color="Green" title="E45">A137</font></span></a>, <a class="txt" href="#E3:13_2_3"><span class="lab"><font color="Green" title="E46">A138</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:13_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:13_2"><span class="lab"><font color="Green" title="E43">A33</font></span></a>, <a class="txt" href="#E3:13_2"><span class="lab"><font color="Green" title="E44">A37</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E30:13"/><span class="lab"><font color="Green" title="E42">A140</font></span>: 
( <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font> implies ( <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:13_3"/><span class="lab"><font color="Green" title="E43">A141</font></span>: 
<font color="Maroon" title="c2">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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</font> )</span><br/>

<div><span class="lab"><font color="Green" title="E44">A142</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_3_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:13"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E1:13_3"><span class="lab"><font color="Green" title="E43">A141</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E2:13_3_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="c15">a49</font>,<font color="Maroon" title="c19">b49</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E3:13_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A143</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">a49</font>,<font color="Maroon" title="c19">b49</font>,<font color="Maroon" title="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">assume </span><a NAME="E4:13_3_1"/>
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">hence </span><a NAME="E5:13_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:13"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:13"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E3:13_3_1"><span class="lab"><font color="Green" title="E45">A143</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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">A144</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_3_2"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:13"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E1:13_3"><span class="lab"><font color="Green" title="E43">A141</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E2:13_3_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E3:13_3_2"/><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="c17">b29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E4:13_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A145</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="c17">b29</font>,<font color="Maroon" title="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">assume </span><a NAME="E5:13_3_2"/>
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">hence </span><a NAME="E6:13_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:13"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:13"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E17:13"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E27:13"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E4:13_3_2"><span class="lab"><font color="Green" title="E46">A145</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E46">A146</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:13_3_3"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:13"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E3:13_3"><span class="lab"><font color="Green" title="E45">A144</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E2:13_3_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E3:13_3_3"/><span class="kw">then </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="c14">a39</font>,<font color="Maroon" title="c18">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E4:13_3_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A147</font></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="c18">b39</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">assume </span><a NAME="E5:13_3_3"/>
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">hence </span><a NAME="E6:13_3_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:13"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:13"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E14:13"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:13"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E4:13_3_3"><span class="lab"><font color="Green" title="E47">A147</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E5:13_3"/>
( <font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> or <font color="Maroon" title="c4">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> or <font color="Maroon" title="c5">a4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">b4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E6:13_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:13_3"><span class="lab"><font color="Green" title="E45">A144</font></span></a>, <a class="txt" href="#E2:13_3"><span class="lab"><font color="Green" title="E44">A142</font></span></a>, <a class="txt" href="#E4:13_3"><span class="lab"><font color="Green" title="E46">A146</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="13_4"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:13_4"/>
<font color="Maroon" title="c2">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="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:13_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">a49</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b39</font>,<font color="Maroon" title="c19">b49</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:13"><span class="lab"><font color="Green" title="E42">A140</font></span></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></span>;<br/><span class="kw">hence </span><a NAME="E3:13_4"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E32:13"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:13"><span class="lab"><font color="Green" title="E41">A31</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
