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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is <a href="conmetr.html#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/>

<b>assume </b><b>that </b><br/><a NAME="E1:13"/><i><font color="Green" title="E15">A1</font></i>: 
<font color="Maroon" title="c1">X</font> is <a href="conmetr.html#V7" title="CONMETR:attr.7">satisfying_OSCH</a>
 <b>and </b><br/><a NAME="E2:13"/><i><font color="Green" title="E16">A2</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>let </b><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>; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c5">a4</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c9">b4</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">M</font>, <font color="Olive" title="b2">N</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">M</font> 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/><b>let </b><font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c11">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">M</font> 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/>



















<b>assume </b><b>that </b><br/><a NAME="E3:13"/><i><font color="Green" title="E17">A3</font></i>: 
( <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> )
 <b>and </b><br/><a NAME="E4:13"/><i><font color="Green" title="E18">A4</font></i>: 
( <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c12">a1'</font> = <font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c13">a2'</font> = <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c14">a3'</font> = <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c15">a4'</font> = <font color="Maroon" title="c5">a4</font>, <font color="Maroon" title="c16">b1'</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c17">b2'</font> = <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c18">b3'</font> = <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c19">b4'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c20">M'</font> = <font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c21">N'</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> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/>
<a NAME="E7:13"/><i><font color="Green" title="E19">A5</font></i>: 
( <font color="Maroon" title="c20">M'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c21">N'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> )
 
<b>by </b><i><a class="txt" href="#E3:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></i>;<br/>
<a NAME="E8:13"/><i><font color="Green" title="E20">A6</font></i>: 
( <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_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_1"/><i><font color="Green" title="E21">A7</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E2:13_1"/><i><font color="Green" title="E22">A8</font></i>: 
( <font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E23">A9</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_1"/><i><font color="Green" title="E24">A10</font></i>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_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="c2">a1</font>,<font color="Maroon" title="c7">b2</font>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E1:13_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E3:13_1_1"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E4:13_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E5:13_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c12">a1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E6:13_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_1_1"><i><font color="Green" title="E24">A10</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E24">A11</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_2"/><i><font color="Green" title="E25">A12</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_2"/>
 <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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E1:13_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E3:13_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c15">a4'</font>,<font color="Maroon" title="c19">b4'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E4:13_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">a4'</font>,<font color="Maroon" title="c19">b4'</font>,<font color="Maroon" title="c12">a1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E5:13_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_1_2"><i><font color="Green" title="E25">A12</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_1_3"/><i><font color="Green" title="E25">A13</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_1_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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E3:13_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E3:13_1_3"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E4:13_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c18">b3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E5:13_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c18">b3'</font>,<font color="Maroon" title="c13">a2'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E6:13_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_1_3"><i><font color="Green" title="E25">A13</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:13_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:13_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="txt" href="#E3:13_1"><i><font color="Green" title="E23">A9</font></i></a>, <a class="txt" href="#E4:13_1"><i><font color="Green" title="E24">A11</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<div><i><font color="Green" title="E21">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_2"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:13_2"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c15">a4'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b3'</font>,<font color="Maroon" title="c19">b4'</font>
 <b>by </b><i><a class="txt" href="#E8:13"><i><font color="Green" title="E20">A6</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>;<br/><b>hence </b><a NAME="E3:13_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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E10:13"/><i><font color="Green" title="E22">A15</font></i>: 
( <font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="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_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_3"/><i><font color="Green" title="E23">A16</font></i>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">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/>

<b>assume </b><a NAME="E2:13_3"/><i><font color="Green" title="E24">A17</font></i>: 
( <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><i><font color="Green" title="E25">A18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_3_1"/><b>then </b>
 <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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E3:13_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E4:13_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">a2'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E5:13_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_3"><i><font color="Green" title="E23">A16</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E26">A19</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3_2"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_3_2"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E3:13_3_2"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E4:13_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">a4'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E5:13_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c15">a4'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E6:13_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_3"><i><font color="Green" title="E23">A16</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_3_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_3_3"/><b>then </b>
 <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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E3:13_3_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E4:13_3_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E5:13_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E3:13_3"><i><font color="Green" title="E25">A18</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:13_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E2:13_3"><i><font color="Green" title="E24">A17</font></i></a>, <a class="txt" href="#E3:13_3"><i><font color="Green" title="E25">A18</font></i></a>, <a class="txt" href="#E4:13_3"><i><font color="Green" title="E26">A19</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4"/><i><font color="Green" title="E23">A20</font></i>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="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><i><font color="Green" title="E24">A21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_1"/><i><font color="Green" title="E25">A22</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:13_4_1"/><i><font color="Green" title="E26">A23</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">b2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">b2'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E10:13"><i><font color="Green" title="E22">A15</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:13_4_1"/><i><font color="Green" title="E27">A24</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c19">b4'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_1_2"/>
<font color="Maroon" title="c21">N'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N'</font>
 
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:13_4_1_2"/><b>then </b>
<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c19">b4'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c19">b4'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:13_4_1"/>
<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c19">b4'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_1_3"/>
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E1:13_4_1"><i><font color="Green" title="E25">A22</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E2:13_4_1_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E3:13_4_1_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E4:13_4_1_3"/>
<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">b2'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c19">b4'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:13_4_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E1:13_4_1"><i><font color="Green" title="E25">A22</font></i></a>, <a class="txt" href="#E2:13_4_1"><i><font color="Green" title="E26">A23</font></i></a>, <a class="txt" href="#E3:13_4_1"><i><font color="Green" title="E27">A24</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><i><font color="Green" title="E25">A25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_2"/><i><font color="Green" title="E26">A26</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:13_4_2"/><i><font color="Green" title="E27">A27</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c16">b1'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c16">b1'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:13_4_2"/><i><font color="Green" title="E28">A28</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c18">b3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_2_2"/>
<font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:13_4_2_2"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c18">b3'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c18">b3'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:13_4_2"/>
<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c18">b3'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_2_3"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_2_3"/>
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E1:13_4_2"><i><font color="Green" title="E26">A26</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E2:13_4_2_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_2_3"/>
<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c18">b3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:13_4_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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E1:13_4_2"><i><font color="Green" title="E26">A26</font></i></a>, <a class="txt" href="#E2:13_4_2"><i><font color="Green" title="E27">A27</font></i></a>, <a class="txt" href="#E3:13_4_2"><i><font color="Green" title="E28">A28</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3"/><i><font color="Green" title="E26">A29</font></i>: 
( <font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a4</font> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><i><font color="Green" title="E27">A30</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3_1"/><i><font color="Green" title="E28">A31</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><b>consider </b><font color="Maroon" title="c22">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E3:13_4_3_1"/><i><font color="Green" title="E29">A32</font></i>: 
(  <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="c22">x</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">x</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">x</font> )
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="conmetr.html#T2" target="_self" title="CONMETR:th.2">Th2</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c23">x'</font> = <font color="Maroon" title="c22">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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><b>consider </b><font color="Maroon" title="c24">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><b> such that </b><br/><a NAME="E6:13_4_3_1"/><i><font color="Green" title="E30">A33</font></i>: 
( <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="c24">e1</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">e1</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>consider </b><font color="Maroon" title="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><b> such that </b><br/><a NAME="E8:13_4_3_1"/><i><font color="Green" title="E31">A34</font></i>: 
( <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="c22">x</font>,<font color="Maroon" title="c25">e2</font> &amp; <font color="Maroon" title="c22">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">e2</font> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c26">e1'</font> = <font color="Maroon" title="c24">e1</font>, <font color="Maroon" title="c27">e2'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E10:13_4_3_1"/>
not <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c27">e2'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_1"/>
<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c27">e2'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_1"/><b>then </b>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c24">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c25">e2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:13_4_3_1_1"/><b>then </b>
<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="c22">x</font>,<font color="Maroon" title="c25">e2</font>
 
<b>by </b><i><a class="txt" href="#E6:13_4_3_1"><i><font color="Green" title="E30">A33</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:13_4_3_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="#E8:13_4_3_1"><i><font color="Green" title="E31">A34</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E5:13_4_3_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:13_4_3_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:13_4_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c17">b2'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:13_4_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c28">y'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E12:13_4_3_1"/><i><font color="Green" title="E32">A35</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c28">y'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c27">e2'</font>,<font color="Maroon" title="c28">y'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c29">y</font> = <font color="Maroon" title="c28">y'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E14:13_4_3_1"/><i><font color="Green" title="E33">A36</font></i>: 
 <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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c24">e1</font>,<font color="Maroon" title="c29">y</font>
 
<b>by </b><i><a class="txt" href="#E12:13_4_3_1"><i><font color="Green" title="E32">A35</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:13_4_3_1_2"/><b>then </b>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c24">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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_4_3_1_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="#E6:13_4_3_1"><i><font color="Green" title="E30">A33</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E4:13_4_3_1_2"/>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E15:13_4_3_1"/><i><font color="Green" title="E34">A37</font></i>: 
<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="c22">x</font>,<font color="Maroon" title="c29">y</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_3"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_3"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c25">e2</font>,<font color="Maroon" title="c29">y</font>
 
<b>by </b><i><a class="txt" href="#E12:13_4_3_1"><i><font color="Green" title="E32">A35</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:13_4_3_1_3"/><b>then </b>
<font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c25">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c29">y</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_3_1_3"/>
<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="c22">x</font>,<font color="Maroon" title="c29">y</font>
 <b>by </b><i><a class="txt" href="#E8:13_4_3_1"><i><font color="Green" title="E31">A34</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E16:13_4_3_1"/><i><font color="Green" title="E35">A38</font></i>: 
( <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_4_3_1_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_4"/>
<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:()"><i><font color="Red">::  thesis: </font></i></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_4_3_1_4"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="conmetr.html#T7" target="_self" title="CONMETR:th.7">Th7</a></i>;<br/>
<a NAME="E3:13_4_3_1_4"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="aff_2.html#T28" title="AFF_2:th.28">AFF_2:28</a></i>;<br/>
<b>hence </b><a NAME="E4:13_4_3_1_4"/>
<font color="Maroon" title="c1">X</font> is <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a>
 <b>by </b><i><a class="ref" href="conmetr.html#T8" target="_self" title="CONMETR:th.8">Th8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E17:13_4_3_1"/><i><font color="Green" title="E36">A39</font></i>: 
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="c22">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_5"/>
 <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="c22">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:13_4_3_1_5"/><b>then </b><i><font color="Green" title="E37">A40</font></i>: 
<font color="Maroon" title="c23">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E4:13_4_3_1_5"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:13_4_3_1_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E6:13_4_3_1_5"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="#E3:13_4_3_1_5"><i><font color="Green" title="E37">A40</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E18:13_4_3_1"/><i><font color="Green" title="E37">A41</font></i>: 
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_4_3_1_6"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_6"/>
 <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_6"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c15">a4'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_3_1_6"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E19:13_4_3_1"/><i><font color="Green" title="E38">A42</font></i>: 
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_7"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_7"/>
<font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N'</font>
 
<b>by </b><i><a class="txt" href="#E1:13_4_3_1"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<a NAME="E2:13_4_3_1_7"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">a4'</font>,<font color="Maroon" title="c19">b4'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_3_1_7"/>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E20:13_4_3_1"/><i><font color="Green" title="E39">A43</font></i>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c22">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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_8"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_8"/><i><font color="Green" title="E40">A44</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="#E14:13_4_3_1"><i><font color="Green" title="E33">A36</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:13_4_3_1_8"/>
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:13_4_3_1_8"/><b>then </b><i><font color="Green" title="E41">A45</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E1:13_4_3_1_8"><i><font color="Green" title="E40">A44</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:13_4_3_1_8"/>
<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="c22">x</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E5:13_4_3_1_8"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c22">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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E3:13_4_3_1_8"><i><font color="Green" title="E41">A45</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E21:13_4_3_1"/><b>then </b><i><font color="Green" title="E40">A46</font></i>: 
<font color="Maroon" title="c22">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>
 <b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E15:13_4_3_1"><i><font color="Green" title="E34">A37</font></i></a>, <a class="txt" href="#E16:13_4_3_1"><i><font color="Green" title="E35">A38</font></i></a>, <a class="txt" href="#E17:13_4_3_1"><i><font color="Green" title="E36">A39</font></i></a>, <a class="txt" href="#E18:13_4_3_1"><i><font color="Green" title="E37">A41</font></i></a>, <a class="txt" href="#E19:13_4_3_1"><i><font color="Green" title="E38">A42</font></i></a>, <a class="ref" href="conmetr.html#D8" target="_self" title="CONMETR:def.8">Def8</a></i>;<br/><a NAME="E22:13_4_3_1"/><i><font color="Green" title="E41">A47</font></i>: 
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="c22">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_9"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_9"/>
 <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="c22">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_9"/><b>then </b><i><font color="Green" title="E42">A48</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:13_4_3_1_9"/>
<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_4_3_1_9_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_9_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_9_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_4_3_1_9_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:13_4_3_1_9_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E5:13_4_3_1_9_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:13_4_3_1_9"/><b>then </b><i><font color="Green" title="E43">A49</font></i>: 
<font color="Maroon" title="c23">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c21">N'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E2:13_4_3_1_9"><i><font color="Green" title="E42">A48</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E5:13_4_3_1_9"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:13_4_3_1_9"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E7:13_4_3_1_9"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="#E4:13_4_3_1_9"><i><font color="Green" title="E43">A49</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E23:13_4_3_1"/><i><font color="Green" title="E42">A50</font></i>: 
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_4_3_1_10"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_10"/>
 <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_10"/><b>then </b><i><font color="Green" title="E43">A51</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c14">a3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:13_4_3_1_10"/>
<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_4_3_1_10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_10_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_10_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_4_3_1_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:13_4_3_1_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E5:13_4_3_1_10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:13_4_3_1_10"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E2:13_4_3_1_10"><i><font color="Green" title="E43">A51</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E24:13_4_3_1"/><i><font color="Green" title="E43">A52</font></i>: 
<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="c22">x</font>,<font color="Maroon" title="c29">y</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_11"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_11"/>
<font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N'</font>
 
<b>by </b><i><a class="txt" href="#E1:13_4_3_1"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<a NAME="E2:13_4_3_1_11"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:13_4_3_1_11"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E4:13_4_3_1_11"/>
<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="c22">x</font>,<font color="Maroon" title="c29">y</font>
 <b>by </b><i><a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="txt" href="#E15:13_4_3_1"><i><font color="Green" title="E34">A37</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E25:13_4_3_1"/><i><font color="Green" title="E44">A53</font></i>: 
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_12"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_12"/>
<font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N'</font>
 
<b>by </b><i><a class="txt" href="#E1:13_4_3_1"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<a NAME="E2:13_4_3_1_12"/><b>then </b>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c18">b3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c17">b2'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:13_4_3_1_12"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E4:13_4_3_1_12"/>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E26:13_4_3_1"/><i><font color="Green" title="E45">A54</font></i>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c22">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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_13"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_13"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:13_4_3_1_13"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:13_4_3_1_13"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:13_4_3_1_13"/><b>then </b>
<font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c3">a2</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:13_4_3_1_13"/><b>then </b>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c22">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c22">x</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E6:13_4_3_1_13"/><b>then </b><i><font color="Green" title="E46">A55</font></i>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c22">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>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="#E20:13_4_3_1"><i><font color="Green" title="E39">A43</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:13_4_3_1_13"/><i><font color="Green" title="E47">A56</font></i>: 
<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_4_3_1_13_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_13_1"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_13_1"/><b>then </b>
<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="c22">x</font>
 
<b>by </b><i><a class="txt" href="#E15:13_4_3_1"><i><font color="Green" title="E34">A37</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:13_4_3_1_13_1"/><b>then </b>
 <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="c22">x</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:13_4_3_1_13_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:13_4_3_1_13_1"/><b>then </b><i><font color="Green" title="E48">A57</font></i>: 
<font color="Maroon" title="c23">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E6:13_4_3_1_13_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:13_4_3_1_13_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E8:13_4_3_1_13_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="#E5:13_4_3_1_13_1"><i><font color="Green" title="E48">A57</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:13_4_3_1_13"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">b2'</font>,<font color="Maroon" title="c28">y'</font>
 
<b>by </b><i><a class="txt" href="#E14:13_4_3_1"><i><font color="Green" title="E33">A36</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E9:13_4_3_1_13"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c28">y'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c17">b2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E10:13_4_3_1_13"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E11:13_4_3_1_13"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:13_4_3_1_13"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<b>hence </b><a NAME="E13:13_4_3_1_13"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c22">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>
 <b>by </b><i><a class="txt" href="#E6:13_4_3_1_13"><i><font color="Green" title="E46">A55</font></i></a>, <a class="txt" href="#E7:13_4_3_1_13"><i><font color="Green" title="E47">A56</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E27:13_4_3_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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E28:13_4_3_1"/><b>then </b><i><font color="Green" title="E46">A58</font></i>: 
<font color="Maroon" title="c22">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>
 <b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E16:13_4_3_1"><i><font color="Green" title="E35">A38</font></i></a>, <a class="txt" href="#E22:13_4_3_1"><i><font color="Green" title="E41">A47</font></i></a>, <a class="txt" href="#E23:13_4_3_1"><i><font color="Green" title="E42">A50</font></i></a>, <a class="txt" href="#E24:13_4_3_1"><i><font color="Green" title="E43">A52</font></i></a>, <a class="txt" href="#E25:13_4_3_1"><i><font color="Green" title="E44">A53</font></i></a>, <a class="txt" href="#E26:13_4_3_1"><i><font color="Green" title="E45">A54</font></i></a>, <a class="ref" href="conmetr.html#D8" target="_self" title="CONMETR:def.8">Def8</a></i>;<br/><a NAME="E29:13_4_3_1"/><i><font color="Green" title="E47">A59</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">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_4_3_1_14"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_14"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c4">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_14"/><b>then </b><i><font color="Green" title="E48">A60</font></i>: 
<font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c29">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c4">a3</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_4_3_1_14"/><i><font color="Green" title="E49">A61</font></i>: 
<font color="Maroon" title="c22">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_4_3_1_14_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_14_1"/>
<font color="Maroon" title="c22">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_14_1"/><b>then </b>
<font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="#E20:13_4_3_1"><i><font color="Green" title="E39">A43</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:13_4_3_1_14_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:13_4_3_1_14_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:13_4_3_1_14_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:13_4_3_1_14_1"/><b>then </b><i><font color="Green" title="E50">A62</font></i>: 
<font color="Maroon" title="c23">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E7:13_4_3_1_14_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:13_4_3_1_14_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:13_4_3_1_14_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="#E6:13_4_3_1_14_1"><i><font color="Green" title="E50">A62</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:13_4_3_1_14"/>
<font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E5:13_4_3_1_14"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c14">a3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:13_4_3_1_14"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:13_4_3_1_14"/><b>then </b>
<font color="Maroon" title="c22">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>
 
<b>by </b><i><a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="txt" href="#E15:13_4_3_1"><i><font color="Green" title="E34">A37</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:13_4_3_1_14"/><b>then </b>
<font color="Maroon" title="c22">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>
 
<b>by </b><i><a class="txt" href="#E2:13_4_3_1_14"><i><font color="Green" title="E48">A60</font></i></a>, <a class="txt" href="#E3:13_4_3_1_14"><i><font color="Green" title="E49">A61</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E9:13_4_3_1_14"/><b>then </b>
<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="c22">x</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E10:13_4_3_1_14"/><b>then </b>
 <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="c22">x</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:13_4_3_1_14"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:13_4_3_1_14"/><b>then </b><i><font color="Green" title="E50">A63</font></i>: 
<font color="Maroon" title="c23">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4_3"><i><font color="Green" title="E26">A29</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E13:13_4_3_1_14"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:13_4_3_1_14"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:13_4_3_1_14"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="#E12:13_4_3_1_14"><i><font color="Green" title="E50">A63</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E30:13_4_3_1"/><i><font color="Green" title="E48">A64</font></i>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">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_4_3_1_15"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_15"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c29">y</font>,<font color="Maroon" title="c5">a4</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_15"/><b>then </b><i><font color="Green" title="E49">A65</font></i>: 
<font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c29">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c5">a4</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_4_3_1_15"/><i><font color="Green" title="E50">A66</font></i>: 
<font color="Maroon" title="c22">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_4_3_1_15_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_1_15_1"/>
<font color="Maroon" title="c22">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_1_15_1"/><b>then </b>
<font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="txt" href="#E20:13_4_3_1"><i><font color="Green" title="E39">A43</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E3:13_4_3_1_15_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">x</font>,<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c6">b1</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:13_4_3_1_15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:13_4_3_1_15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:13_4_3_1_15_1"/><b>then </b><i><font color="Green" title="E51">A67</font></i>: 
<font color="Maroon" title="c23">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E7:13_4_3_1_15_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:13_4_3_1_15_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E9:13_4_3_1_15_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="#E6:13_4_3_1_15_1"><i><font color="Green" title="E51">A67</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:13_4_3_1_15"/>
<font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N'</font>
 
<b>by </b><i><a class="txt" href="#E1:13_4_3_1"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<a NAME="E5:13_4_3_1_15"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c15">a4'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E6:13_4_3_1_15"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E7:13_4_3_1_15"/><b>then </b>
<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="c22">x</font>,<font color="Maroon" title="c29">y</font>
 
<b>by </b><i><a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="txt" href="#E15:13_4_3_1"><i><font color="Green" title="E34">A37</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E8:13_4_3_1_15"/><b>then </b>
<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="c22">x</font>,<font color="Maroon" title="c5">a4</font>
 
<b>by </b><i><a class="txt" href="#E2:13_4_3_1_15"><i><font color="Green" title="E49">A65</font></i></a>, <a class="txt" href="#E3:13_4_3_1_15"><i><font color="Green" title="E50">A66</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E9:13_4_3_1_15"/><b>then </b>
<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="c22">x</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E10:13_4_3_1_15"/><b>then </b>
 <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="c22">x</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E11:13_4_3_1_15"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">a4'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E12:13_4_3_1_15"/><b>then </b><i><font color="Green" title="E51">A68</font></i>: 
<font color="Maroon" title="c23">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c21">N'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4_3"><i><font color="Green" title="E26">A29</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<a NAME="E13:13_4_3_1_15"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>
 
<b>by </b><i><a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:13_4_3_1_15"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c13">a2'</font>,<font color="Maroon" title="c23">x'</font>,<font color="Maroon" title="c12">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E15:13_4_3_1_15"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E3:13_4_3_1"><i><font color="Green" title="E29">A32</font></i></a>, <a class="txt" href="#E12:13_4_3_1_15"><i><font color="Green" title="E51">A68</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E31:13_4_3_1"/><i><font color="Green" title="E49">A69</font></i>: 
<font color="Maroon" title="c22">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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_16"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_16"/>
<font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/>
<a NAME="E2:13_4_3_1_16"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c18">b3'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:13_4_3_1_16"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E4:13_4_3_1_16"/>
<font color="Maroon" title="c22">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>
 <b>by </b><i><a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="txt" href="#E15:13_4_3_1"><i><font color="Green" title="E34">A37</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E32:13_4_3_1"/>
<font color="Maroon" title="c22">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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_1_17"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_1_17"/>
<font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N'</font>
 
<b>by </b><i><a class="txt" href="#E1:13_4_3_1"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/>
<a NAME="E2:13_4_3_1_17"/><b>then </b>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">a4'</font>,<font color="Maroon" title="c19">b4'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/>
<a NAME="E3:13_4_3_1_17"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E4:13_4_3_1_17"/>
<font color="Maroon" title="c22">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>
 <b>by </b><i><a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="txt" href="#E15:13_4_3_1"><i><font color="Green" title="E34">A37</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E33:13_4_3_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E16:13_4_3_1"><i><font color="Green" title="E35">A38</font></i></a>, <a class="txt" href="#E21:13_4_3_1"><i><font color="Green" title="E40">A46</font></i></a>, <a class="txt" href="#E28:13_4_3_1"><i><font color="Green" title="E46">A58</font></i></a>, <a class="txt" href="#E29:13_4_3_1"><i><font color="Green" title="E47">A59</font></i></a>, <a class="txt" href="#E30:13_4_3_1"><i><font color="Green" title="E48">A64</font></i></a>, <a class="txt" href="#E31:13_4_3_1"><i><font color="Green" title="E49">A69</font></i></a>, <a class="ref" href="conmetr.html#D8" target="_self" title="CONMETR:def.8">Def8</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E2:13_4_3_2"/><b>then </b>
not <font color="Maroon" title="c20">M'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c21">N'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/><b>then consider </b><font color="Maroon" title="c22">o'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E4:13_4_3_2"/><i><font color="Green" title="E28">A70</font></i>: 
( <font color="Maroon" title="c22">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M'</font> &amp; <font color="Maroon" title="c22">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c21">N'</font> )
 <b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T72" title="AFF_1:th.72">AFF_1:72</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c23">o</font> = <font color="Maroon" title="c22">o'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><b>consider </b><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><b> such that </b><br/><a NAME="E7:13_4_3_2"/><i><font color="Green" title="E29">A71</font></i>: 
( <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> &amp; <font color="Maroon" title="c11">N</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c24">K</font> )
 <b>by </b><i><a class="txt" href="#E3:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="conmetr.html#T3" target="_self" title="CONMETR:th.3">Th3</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c25">K'</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> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/><a NAME="E9:13_4_3_2"/><i><font color="Green" title="E30">A72</font></i>: 
<font color="Maroon" title="c24">K</font> is <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a>
 <b>by </b><i><a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></i>;<br/><a NAME="E10:13_4_3_2"/><b>then </b><i><font color="Green" title="E31">A73</font></i>: 
( <font color="Maroon" title="c25">K'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> &amp; <font color="Maroon" title="c21">N'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> )
 <b>by </b><i><a class="txt" href="#E3:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3_2_1"/><i><font color="Green" title="E32">A74</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><i><font color="Green" title="E33">A75</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c26">x'</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">y'</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">y'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> &amp; <font color="Maroon" title="c26">x'</font>,<font color="Olive" title="b1">y'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> )</span><br/><b>consider </b><font color="Maroon" title="c27">D'</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E2:13_4_3_2_1_1"/><i><font color="Green" title="E34">A76</font></i>: 
( <font color="Maroon" title="c26">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c27">D'</font> &amp; <font color="Maroon" title="c21">N'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c27">D'</font> )
 <b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="aff_1.html#T63" title="AFF_1:th.63">AFF_1:63</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c28">D</font> = <font color="Maroon" title="c27">D'</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> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/><a NAME="E4:13_4_3_2_1_1"/>
<font color="Maroon" title="c11">N</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c28">D</font>
 <b>by </b><i><a class="txt" href="#E2:13_4_3_2_1_1"><i><font color="Green" title="E34">A76</font></i></a>, <a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></i>;<br/><a NAME="E5:13_4_3_2_1_1"/><b>then </b>
<font color="Maroon" title="c24">K</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c28">D</font>
 <b>by </b><i><a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></i>;<br/><b>then consider </b><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><b> such that </b><br/><a NAME="E7:13_4_3_2_1_1"/><i><font color="Green" title="E35">A77</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T88" title="ANALMETR:th.88">ANALMETR:88</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c30">y'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><b>take </b><font color="Maroon" title="c31">y'</font> = <font color="Maroon" title="c30">y'</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c31">y'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> &amp; <font color="Maroon" title="c26">x'</font>,<font color="Maroon" title="c31">y'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> )</span><br/><b>thus </b><a NAME="E9:13_4_3_2_1_1"/>
( <font color="Maroon" title="c31">y'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> &amp; <font color="Maroon" title="c26">x'</font>,<font color="Maroon" title="c31">y'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> )
 <b>by </b><i><a class="txt" href="#E2:13_4_3_2_1_1"><i><font color="Green" title="E34">A76</font></i></a>, <a class="txt" href="#E7:13_4_3_2_1_1"><i><font color="Green" title="E35">A77</font></i></a>, <a class="ref" href="aff_1.html#T54" title="AFF_1:th.54">AFF_1:54</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>then consider </b><font color="Maroon" title="c26">d1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E4:13_4_3_2_1"/><i><font color="Green" title="E34">A78</font></i>: 
( <font color="Maroon" title="c26">d1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> &amp; <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c26">d1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c27">d3'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E6:13_4_3_2_1"/><i><font color="Green" title="E35">A79</font></i>: 
( <font color="Maroon" title="c27">d3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> &amp; <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c27">d3'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> )
 <b>by </b><i><a class="txt" href="#E2:13_4_3_2_1"><i><font color="Green" title="E33">A75</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c28">e3'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E8:13_4_3_2_1"/><i><font color="Green" title="E36">A80</font></i>: 
( <font color="Maroon" title="c28">e3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> &amp; <font color="Maroon" title="c18">b3'</font>,<font color="Maroon" title="c28">e3'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> )
 <b>by </b><i><a class="txt" href="#E2:13_4_3_2_1"><i><font color="Green" title="E33">A75</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c29">e1'</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><b> such that </b><br/><a NAME="E10:13_4_3_2_1"/><i><font color="Green" title="E37">A81</font></i>: 
( <font color="Maroon" title="c29">e1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> &amp; <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c29">e1'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> )
 <b>by </b><i><a class="txt" href="#E2:13_4_3_2_1"><i><font color="Green" title="E33">A75</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c30">d1</font> = <font color="Maroon" title="c26">d1'</font>, <font color="Maroon" title="c31">d3</font> = <font color="Maroon" title="c27">d3'</font>, <font color="Maroon" title="c32">e1</font> = <font color="Maroon" title="c29">e1'</font>, <font color="Maroon" title="c33">e3</font> = <font color="Maroon" title="c28">e3'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E12:13_4_3_2_1"/><i><font color="Green" title="E38">A82</font></i>: 
( <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_4_3_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_2_1_2"/><i><font color="Green" title="E39">A83</font></i>: 
(  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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_2_1"><b>now </b></a><div class="add"><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x'</font>, <font color="Olive" title="b2">y'</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span>  st <font color="Olive" title="b1">x'</font>,<font color="Olive" title="b2">y'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> &amp; <font color="Maroon" title="c34">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x'</font> &amp; <font color="Maroon" title="c35">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y'</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/><b>let </b><font color="Maroon" title="c36">x'</font>, <font color="Maroon" title="c37">y'</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c36">x'</font>,<font color="Maroon" title="c37">y'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font> &amp; <font color="Maroon" title="c34">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">x'</font> &amp; <font color="Maroon" title="c35">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">y'</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/><b>assume </b><b>that </b><br/><a NAME="E1:13_4_3_2_1_2_1"/><i><font color="Green" title="E40">A84</font></i>: 
<font color="Maroon" title="c36">x'</font>,<font color="Maroon" title="c37">y'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font>
 <b>and </b><br/><a NAME="E2:13_4_3_2_1_2_1"/><i><font color="Green" title="E41">A85</font></i>: 
( <font color="Maroon" title="c34">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c36">x'</font> &amp; <font color="Maroon" title="c35">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c37">y'</font> )
 <b>and </b><br/><a NAME="E3:13_4_3_2_1_2_1"/><i><font color="Green" title="E42">A86</font></i>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/><b>assume </b><a NAME="E4:13_4_3_2_1_2_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E5:13_4_3_2_1_2_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c36">x'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c21">N'</font>
 <b>by </b><i><a class="txt" href="#E1:13_4_3_2_1_2_1"><i><font color="Green" title="E40">A84</font></i></a>, <a class="txt" href="#E2:13_4_3_2_1_2_1"><i><font color="Green" title="E41">A85</font></i></a>, <a class="ref" href="aff_1.html#T48" title="AFF_1:th.48">AFF_1:48</a></i>;<br/><b>hence </b><a NAME="E6:13_4_3_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E2:13_4_3_2_1_2_1"><i><font color="Green" title="E41">A85</font></i></a>, <a class="txt" href="#E3:13_4_3_2_1_2_1"><i><font color="Green" title="E42">A86</font></i></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:13_4_3_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1"><i><font color="Green" title="E34">A78</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="txt" href="#E8:13_4_3_2_1"><i><font color="Green" title="E36">A80</font></i></a>, <a class="txt" href="#E10:13_4_3_2_1"><i><font color="Green" title="E37">A81</font></i></a>, <a class="txt" href="#E1:13_4_3_2_1_2"><i><font color="Green" title="E39">A83</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E13:13_4_3_2_1"/><i><font color="Green" title="E39">A87</font></i>: 
(  <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> &amp;  <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> &amp;  <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> &amp;  <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> )
 <b>by </b><i><a class="txt" href="#E3:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="ref" href="conmetr.html#T4" target="_self" title="CONMETR:th.4">Th4</a></i>;<br/><a NAME="E14:13_4_3_2_1"/><i><font color="Green" title="E40">A88</font></i>: 
(  <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> &amp;  <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> )
 <b>by </b><i><a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="txt" href="#E9:13_4_3_2"><i><font color="Green" title="E30">A72</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1"><i><font color="Green" title="E34">A78</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="txt" href="#E8:13_4_3_2_1"><i><font color="Green" title="E36">A80</font></i></a>, <a class="txt" href="#E10:13_4_3_2_1"><i><font color="Green" title="E37">A81</font></i></a>, <a class="ref" href="conmetr.html#T4" target="_self" title="CONMETR:th.4">Th4</a></i>;<br/><a NAME="E15:13_4_3_2_1"/><i><font color="Green" title="E41">A89</font></i>: 
( 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="c30">d1</font> &amp; 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="c3">a2</font> &amp; 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> &amp; not  <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> &amp; not  <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_3"><b>proof </b></a><div class="add">

<div><i><font color="Green" title="E42">A90</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3_2_1_3_1"/>
 <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_4_3_2_1_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c26">d1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E3:13_4_3_2_1_3_1"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E4:13_4_3_2_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="txt" href="#E9:13_4_3_2"><i><font color="Green" title="E30">A72</font></i></a>, <a class="txt" href="#E1:13_4_3_2_1"><i><font color="Green" title="E32">A74</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1"><i><font color="Green" title="E34">A78</font></i></a>, <a class="txt" href="#E12:13_4_3_2_1"><i><font color="Green" title="E38">A82</font></i></a>, <a class="ref" href="conmetr.html#T5" target="_self" title="CONMETR:th.5">Th5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E43">A91</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3_2_1_3_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="c3">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_4_3_2_1_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c13">a2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><b>hence </b><a NAME="E3:13_4_3_2_1_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E44">A92</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3_2_1_3_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_4_3_2_1_3_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c15">a4'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><b>hence </b><a NAME="E3:13_4_3_2_1_3_3"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><i><font color="Green" title="E45">A93</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_3_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3_2_1_3_4"/>
 <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_4_3_2_1_3_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c18">b3'</font>,<font color="Maroon" title="c27">d3'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E3:13_4_3_2_1_3_4"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E10:13"><i><font color="Green" title="E22">A15</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><b>hence </b><a NAME="E4:13_4_3_2_1_3_4"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:13"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="txt" href="#E9:13_4_3_2"><i><font color="Green" title="E30">A72</font></i></a>, <a class="txt" href="#E1:13_4_3_2_1"><i><font color="Green" title="E32">A74</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="txt" href="#E12:13_4_3_2_1"><i><font color="Green" title="E38">A82</font></i></a>, <a class="ref" href="conmetr.html#T5" target="_self" title="CONMETR:th.5">Th5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_3_5"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:13_4_3_2_1_3_5"/>
 <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:13_4_3_2_1_3_5"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c18">b3'</font>,<font color="Maroon" title="c13">a2'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><b>hence </b><a NAME="E3:13_4_3_2_1_3_5"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E10:13"><i><font color="Green" title="E22">A15</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:13_4_3_2_1_3"/>
( 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="c30">d1</font> &amp; 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="c3">a2</font> &amp; 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> &amp; not  <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> &amp; not  <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> )
 <b>by </b><i><a class="txt" href="#E1:13_4_3_2_1_3"><i><font color="Green" title="E42">A90</font></i></a>, <a class="txt" href="#E2:13_4_3_2_1_3"><i><font color="Green" title="E43">A91</font></i></a>, <a class="txt" href="#E3:13_4_3_2_1_3"><i><font color="Green" title="E44">A92</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1_3"><i><font color="Green" title="E45">A93</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E16:13_4_3_2_1"/><i><font color="Green" title="E42">A94</font></i>: 
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_4"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_2_1_4"/>
<font color="Maroon" title="c12">a1'</font>,<font color="Maroon" title="c26">d1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b1'</font>,<font color="Maroon" title="c29">e1'</font>
 
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1"><i><font color="Green" title="E34">A78</font></i></a>, <a class="txt" href="#E10:13_4_3_2_1"><i><font color="Green" title="E37">A81</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<a NAME="E2:13_4_3_2_1_4"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_3_2_1_4"/>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E17:13_4_3_2_1"/><i><font color="Green" title="E43">A95</font></i>: 
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_5"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_2_1_5"/>
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1"><i><font color="Green" title="E34">A78</font></i></a>, <a class="ref" href="conmetr.html#T6" target="_self" title="CONMETR:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E2:13_4_3_2_1_5"/>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E18:13_4_3_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>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E19:13_4_3_2_1"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E12:13_4_3_2_1"><i><font color="Green" title="E38">A82</font></i></a>, <a class="txt" href="#E13:13_4_3_2_1"><i><font color="Green" title="E39">A87</font></i></a>, <a class="txt" href="#E14:13_4_3_2_1"><i><font color="Green" title="E40">A88</font></i></a>, <a class="txt" href="#E15:13_4_3_2_1"><i><font color="Green" title="E41">A89</font></i></a>, <a class="txt" href="#E16:13_4_3_2_1"><i><font color="Green" title="E42">A94</font></i></a>, <a class="txt" href="#E17:13_4_3_2_1"><i><font color="Green" title="E43">A95</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></i>;<br/><a NAME="E20:13_4_3_2_1"/><b>then </b><i><font color="Green" title="E44">A96</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E21:13_4_3_2_1"/>
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_6"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_2_1_6"/>
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1"><i><font color="Green" title="E34">A78</font></i></a>, <a class="ref" href="conmetr.html#T6" target="_self" title="CONMETR:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E2:13_4_3_2_1_6"/>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E22:13_4_3_2_1"/><b>then </b><i><font color="Green" title="E45">A97</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E12:13_4_3_2_1"><i><font color="Green" title="E38">A82</font></i></a>, <a class="txt" href="#E13:13_4_3_2_1"><i><font color="Green" title="E39">A87</font></i></a>, <a class="txt" href="#E14:13_4_3_2_1"><i><font color="Green" title="E40">A88</font></i></a>, <a class="txt" href="#E15:13_4_3_2_1"><i><font color="Green" title="E41">A89</font></i></a>, <a class="txt" href="#E16:13_4_3_2_1"><i><font color="Green" title="E42">A94</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></i>;<br/><a NAME="E23:13_4_3_2_1"/><i><font color="Green" title="E46">A98</font></i>: 
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_7"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_2_1_7"/>
<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c27">d3'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b3'</font>,<font color="Maroon" title="c28">e3'</font>
 
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="txt" href="#E8:13_4_3_2_1"><i><font color="Green" title="E36">A80</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<a NAME="E2:13_4_3_2_1_7"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E3:13_4_3_2_1_7"/>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E24:13_4_3_2_1"/>
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_8"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_2_1_8"/>
<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>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="ref" href="conmetr.html#T6" target="_self" title="CONMETR:th.6">Th6</a></i>;<br/>
<b>hence </b><a NAME="E2:13_4_3_2_1_8"/>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E25:13_4_3_2_1"/><b>then </b><i><font color="Green" title="E47">A99</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E12:13_4_3_2_1"><i><font color="Green" title="E38">A82</font></i></a>, <a class="txt" href="#E13:13_4_3_2_1"><i><font color="Green" title="E39">A87</font></i></a>, <a class="txt" href="#E14:13_4_3_2_1"><i><font color="Green" title="E40">A88</font></i></a>, <a class="txt" href="#E15:13_4_3_2_1"><i><font color="Green" title="E41">A89</font></i></a>, <a class="txt" href="#E23:13_4_3_2_1"><i><font color="Green" title="E46">A98</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></i>;<br/><a NAME="E26:13_4_3_2_1"/><i><font color="Green" title="E48">A100</font></i>: 
( 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> &amp; 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> &amp; 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> &amp; 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> )
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1"><i><font color="Green" title="E34">A78</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="txt" href="#E8:13_4_3_2_1"><i><font color="Green" title="E36">A80</font></i></a>, <a class="txt" href="#E10:13_4_3_2_1"><i><font color="Green" title="E37">A81</font></i></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></i>;<br/><a NAME="E27:13_4_3_2_1"/>
( 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_4_3_2_1_9"><b>proof </b></a><div class="add">

<div><i><font color="Green" title="E49">A101</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="13_4_3_2_1_9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c34">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> &amp; <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c34">x</font> implies  not <font color="Maroon" title="c34">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font> )</span><br/><b>assume </b><a NAME="E1:13_4_3_2_1_9_1"/><i><font color="Green" title="E50">A102</font></i>: 
( <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> &amp; <font color="Maroon" title="c23">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c34">x</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c34">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c24">K</font></span><br/><b>assume </b><a NAME="E2:13_4_3_2_1_9_1"/>
<font color="Maroon" title="c34">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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E3:13_4_3_2_1_9_1"/><b>then </b>
<font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c34">x</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">o</font>,<font color="Maroon" title="c34">x</font>
 <b>by </b><i><a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="txt" href="#E1:13_4_3_2_1_9_1"><i><font color="Green" title="E50">A102</font></i></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></i>;<br/><b>hence </b><a NAME="E4:13_4_3_2_1_9_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E1:13_4_3_2_1_9_1"><i><font color="Green" title="E50">A102</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>assume </b><a NAME="E2:13_4_3_2_1_9"/>
( <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>hence </b><a NAME="E3:13_4_3_2_1_9"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E1:13_4_3_2_1_9"><i><font color="Green" title="E49">A101</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E28:13_4_3_2_1"/><b>then </b><i><font color="Green" title="E49">A103</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="txt" href="#E4:13_4_3_2_1"><i><font color="Green" title="E34">A78</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="txt" href="#E8:13_4_3_2_1"><i><font color="Green" title="E36">A80</font></i></a>, <a class="txt" href="#E10:13_4_3_2_1"><i><font color="Green" title="E37">A81</font></i></a>, <a class="txt" href="#E20:13_4_3_2_1"><i><font color="Green" title="E44">A96</font></i></a>, <a class="txt" href="#E22:13_4_3_2_1"><i><font color="Green" title="E45">A97</font></i></a>, <a class="txt" href="#E25:13_4_3_2_1"><i><font color="Green" title="E47">A99</font></i></a>, <a class="txt" href="#E26:13_4_3_2_1"><i><font color="Green" title="E48">A100</font></i></a>, <a class="ref" href="conmetr.html#D7" target="_self" title="CONMETR:def.7">Def7</a></i>;<br/><a NAME="E29:13_4_3_2_1"/><i><font color="Green" title="E50">A104</font></i>: 
( 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_4_3_2_1_10"><b>proof </b></a><div class="add">

<a NAME="E1:13_4_3_2_1_10"/><i><font color="Green" title="E51">A105</font></i>: 
<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_4_3_2_1_10_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:13_4_3_2_1_10_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:13_4_3_2_1_10_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="#E23:13_4_3_2_1"><i><font color="Green" title="E46">A98</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:13_4_3_2_1_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c28">e3'</font>,<font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c18">b3'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:13_4_3_2_1_10_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a3'</font>,<font color="Maroon" title="c18">b3'</font>,<font color="Maroon" title="c28">e3'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:13_4_3_2_1_10_1"/><b>then </b>
<font color="Maroon" title="c28">e3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c20">M'</font>
 
<b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E10:13"><i><font color="Green" title="E22">A15</font></i></a>, <a class="txt" href="#E1:13_4"><i><font color="Green" title="E23">A20</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E6:13_4_3_2_1_10_1"/>
contradiction
 <b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="txt" href="#E10:13_4_3_2"><i><font color="Green" title="E31">A73</font></i></a>, <a class="txt" href="#E1:13_4_3_2_1"><i><font color="Green" title="E32">A74</font></i></a>, <a class="txt" href="#E8:13_4_3_2_1"><i><font color="Green" title="E36">A80</font></i></a>, <a class="txt" href="#E12:13_4_3_2_1"><i><font color="Green" title="E38">A82</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>assume </b><a NAME="E2:13_4_3_2_1_10"/>
(  <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:13_4_3_2_1_10"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c27">d3'</font>,<font color="Maroon" title="c28">e3'</font>,<font color="Maroon" title="c14">a3'</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c27">d3'</font>,<font color="Maroon" title="c28">e3'</font>,<font color="Maroon" title="c15">a4'</font> )
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:13_4_3_2_1_10"/><b>then </b>
( <font color="Maroon" title="c14">a3'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> or <font color="Maroon" title="c15">a4'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c25">K'</font> )
 
<b>by </b><i><a class="txt" href="#E10:13_4_3_2"><i><font color="Green" title="E31">A73</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="txt" href="#E8:13_4_3_2_1"><i><font color="Green" title="E36">A80</font></i></a>, <a class="txt" href="#E1:13_4_3_2_1_10"><i><font color="Green" title="E51">A105</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/>
<b>hence </b><a NAME="E5:13_4_3_2_1_10"/>
contradiction
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="txt" href="#E10:13_4_3_2"><i><font color="Green" title="E31">A73</font></i></a>, <a class="txt" href="#E1:13_4_3_2_1"><i><font color="Green" title="E32">A74</font></i></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E30:13_4_3_2_1"/><i><font color="Green" title="E51">A106</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="#E23:13_4_3_2_1"><i><font color="Green" title="E46">A98</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E31:13_4_3_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="c5">a4</font>
 <b>by </b><i><a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E6:13_4_3_2_1"><i><font color="Green" title="E35">A79</font></i></a>, <a class="ref" href="conmetr.html#T6" target="_self" title="CONMETR:th.6">Th6</a></i>;<br/><b>hence </b><a NAME="E32:13_4_3_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>
 <b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E16">A2</font></i></a>, <a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E4:13_4_3_2"><i><font color="Green" title="E28">A70</font></i></a>, <a class="txt" href="#E12:13_4_3_2_1"><i><font color="Green" title="E38">A82</font></i></a>, <a class="txt" href="#E13:13_4_3_2_1"><i><font color="Green" title="E39">A87</font></i></a>, <a class="txt" href="#E14:13_4_3_2_1"><i><font color="Green" title="E40">A88</font></i></a>, <a class="txt" href="#E28:13_4_3_2_1"><i><font color="Green" title="E49">A103</font></i></a>, <a class="txt" href="#E29:13_4_3_2_1"><i><font color="Green" title="E50">A104</font></i></a>, <a class="txt" href="#E30:13_4_3_2_1"><i><font color="Green" title="E51">A106</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E12:13_4_3_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>
 <b>by </b><i><a class="txt" href="#E1:13"><i><font color="Green" title="E15">A1</font></i></a>, <a class="txt" href="#E4:13"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="#E7:13_4_3_2"><i><font color="Green" title="E29">A71</font></i></a>, <a class="ref" href="conmetr.html#D7" target="_self" title="CONMETR:def.7">Def7</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E4:13_4_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>
 <b>by </b><i><a class="txt" href="#E2:13_4_3"><i><font color="Green" title="E27">A30</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E5:13_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>
 <b>by </b><i><a class="txt" href="#E2:13_4"><i><font color="Green" title="E24">A21</font></i></a>, <a class="txt" href="#E3:13_4"><i><font color="Green" title="E25">A25</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E12:13"/>
<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>
 <b>by </b><i><a class="txt" href="#E9:13"><i><font color="Green" title="E21">A14</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
