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<div class="add">

<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"> (  <a href="conmetr.html#NR5" title="CONMETR:NR.5">TDES_holds_in</a> <font color="Maroon" title="c1">X</font> implies  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR7" title="AFF_2:NR.7">satisfies_TDES</a>  )</span><br/>

<b>assume </b><a NAME="E1:9"/><i><font color="Green" title="E14">A1</font></i>: 
 <a href="conmetr.html#NR5" title="CONMETR:NR.5">TDES_holds_in</a> <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">  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> <a href="aff_2.html#NR7" title="AFF_2:NR.7">satisfies_TDES</a> </span><br/>

<b>let </b><font color="Maroon" title="c2">K'</font> be   <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>; <i><font color="Red">:: according to </font></i><a class="ref" href="aff_2.html#D7" title="AFF_2:def.7">AFF_2:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></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>  holds <br/>(  not <font color="Maroon" title="c2">K'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> or  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> or  not <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> or  not <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> or <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>4</sub></font> or <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive">b<sub>3</sub></font> or  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>5</sub></font> or  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>6</sub></font> or  not <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font> or  not <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>7</sub></font> or  not <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K'</font> or <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>7</sub></font> )</span><br/><b>let </b><font color="Maroon" title="c3">o'</font>, <font color="Maroon" title="c4">a'</font>, <font color="Maroon" title="c5">b'</font>, <font color="Maroon" title="c6">c'</font>, <font color="Maroon" title="c7">a1'</font>, <font color="Maroon" title="c8">b1'</font>, <font color="Maroon" title="c9">c1'</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"> (  not <font color="Maroon" title="c2">K'</font> is <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> or  not <font color="Maroon" title="c3">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> or  not <font color="Maroon" title="c6">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> or  not <font color="Maroon" title="c9">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> or <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> or <font color="Maroon" title="c3">o'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c'</font> or <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b'</font> or  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c7">a1'</font> or  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c8">b1'</font> or  not <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a1'</font>,<font color="Maroon" title="c8">b1'</font> or  not <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a1'</font>,<font color="Maroon" title="c9">c1'</font> or  not <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K'</font> or <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font> )</span><br/>



<b>assume </b><a NAME="E2:9"/><i><font color="Green" title="E15">A2</font></i>: 
( <font color="Maroon" title="c2">K'</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c3">o'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> &amp; <font color="Maroon" title="c6">c'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> &amp; <font color="Maroon" title="c9">c1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> &amp; not <font color="Maroon" title="c4">a'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font> &amp; <font color="Maroon" title="c3">o'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c'</font> &amp; <font color="Maroon" title="c4">a'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c7">a1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c8">b1'</font> &amp; <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a1'</font>,<font color="Maroon" title="c8">b1'</font> &amp; <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a1'</font>,<font color="Maroon" title="c9">c1'</font> &amp; <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K'</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c10">o</font> = <font color="Maroon" title="c3">o'</font>, <font color="Maroon" title="c11">a</font> = <font color="Maroon" title="c4">a'</font>, <font color="Maroon" title="c12">a1</font> = <font color="Maroon" title="c7">a1'</font>, <font color="Maroon" title="c13">b</font> = <font color="Maroon" title="c5">b'</font>, <font color="Maroon" title="c14">b1</font> = <font color="Maroon" title="c8">b1'</font>, <font color="Maroon" title="c15">c</font> = <font color="Maroon" title="c6">c'</font>, <font color="Maroon" title="c16">c1</font> = <font color="Maroon" title="c9">c1'</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <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>reconsider </b><font color="Maroon" title="c17">K</font> = <font color="Maroon" title="c2">K'</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></i>;<br/>
<a NAME="E5:9"/><i><font color="Green" title="E16">A3</font></i>: 
( <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c13">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c14">b1</font> &amp; <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c15">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c16">c1</font> )
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1"/><i><font color="Green" title="E17">A4</font></i>: 
not <font color="Maroon" title="c13">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">K</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font></span><br/><a NAME="E2:9_1"/><i><font color="Green" title="E18">A5</font></i>: 
( <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a1</font> implies ( <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">b1</font> &amp; <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">c1</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1"><b>proof </b></a><div class="add">

<b>assume </b><b>that </b><br/><a NAME="E1:9_1_1"/><i><font color="Green" title="E19">A6</font></i>: 
<font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a1</font>
 <b>and </b><br/><a NAME="E2:9_1_1"/><i><font color="Green" title="E20">A7</font></i>: 
( <font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">b1</font> or <font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">c1</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="E21">A8</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_1_1"/><i><font color="Green" title="E22">A9</font></i>: 
<font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">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="E2:9_1_1_1"/>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></i>;<br/><a NAME="E3:9_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/><a NAME="E4:9_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c8">b1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_1"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E5:9_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c8">b1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E6:9_1_1_1"/><b>then </b><i><font color="Green" title="E23">A10</font></i>: 
<font color="Maroon" title="c8">b1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E7:9_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c5">b'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E8:9_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1"><i><font color="Green" title="E17">A4</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_1_1"><i><font color="Green" title="E22">A9</font></i></a>, <a class="txt" href="conmetr.html#E6:9_1_1_1"><i><font color="Green" title="E23">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><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_1_2"/><i><font color="Green" title="E22">A11</font></i>: 
<font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">c1</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="E2:9_1_1_2"/><i><font color="Green" title="E23">A12</font></i>: 
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c9">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_1"><i><font color="Green" title="E19">A6</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E3:9_1_1_2"/>
<font color="Maroon" title="c2">K'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E4:9_1_1_2"/><b>then </b>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c9">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E5:9_1_1_2"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:9_1_1_2"><i><font color="Green" title="E22">A11</font></i></a>, <a class="txt" href="conmetr.html#E2:9_1_1_2"><i><font color="Green" title="E23">A12</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E6:9_1_1_2"/><b>then </b>
<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c4">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E7:9_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E8:9_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c4">a'</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="E9:9_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:9_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9_1_1"><i><font color="Green" title="E20">A7</font></i></a>, <a class="txt" href="conmetr.html#E3:9_1_1"><i><font color="Green" title="E21">A8</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="E19">A13</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_2"/>
<font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font></span><br/><a NAME="E2:9_1_2"/><b>then </b>
<font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c15">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">b1</font>,<font color="Maroon" title="c16">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9_1"><i><font color="Green" title="E18">A5</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><b>hence </b><a NAME="E3:9_1_2"/>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_3"/><i><font color="Green" title="E20">A14</font></i>: 
<font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font></span><br/><a NAME="E2:9_1_3"/><i><font color="Green" title="E21">A15</font></i>: 
( <font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a</font> &amp; <font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b</font> &amp; <font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">c</font> &amp; <font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">c1</font> &amp; <font color="Maroon" title="c10">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">b1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_1_3_1"/><i><font color="Green" title="E22">A16</font></i>: 
( <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a</font> or <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b</font> or <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">c</font> or <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">c1</font> or <font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">b1</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">A17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_3_1_1"/>
<font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">c1</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="E2:9_1_3_1_1"/><b>then </b><i><font color="Green" title="E24">A18</font></i>: 
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c7">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E3:9_1_3_1_1"/>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c7">a1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E4:9_1_3_1_1"/><b>then </b>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c7">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E5:9_1_3_1_1"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:9_1_3"><i><font color="Green" title="E20">A14</font></i></a>, <a class="txt" href="conmetr.html#E2:9_1_3_1_1"><i><font color="Green" title="E24">A18</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E6:9_1_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E7:9_1_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c4">a'</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="E8:9_1_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_3_1_2"/><i><font color="Green" title="E24">A19</font></i>: 
<font color="Maroon" title="c10">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">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="E2:9_1_3_1_2"/>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></i>;<br/><a NAME="E3:9_1_3_1_2"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/><a NAME="E4:9_1_3_1_2"/><b>then </b>
<font color="Maroon" title="c7">a1'</font>,<font color="Maroon" title="c3">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_3_1_2"><i><font color="Green" title="E24">A19</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><a NAME="E5:9_1_3_1_2"/><b>then </b>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c7">a1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E6:9_1_3_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c7">a1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E7:9_1_3_1_2"/><b>then </b><i><font color="Green" title="E25">A20</font></i>: 
<font color="Maroon" title="c7">a1'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>;<br/><a NAME="E8:9_1_3_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c7">a1'</font>,<font color="Maroon" title="c4">a'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>hence </b><a NAME="E9:9_1_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_3"><i><font color="Green" title="E20">A14</font></i></a>, <a class="txt" href="conmetr.html#E7:9_1_3_1_2"><i><font color="Green" title="E25">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="E4:9_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_3_1"><i><font color="Green" title="E22">A16</font></i></a>, <a class="txt" href="conmetr.html#E2:9_1_3_1"><i><font color="Green" title="E23">A17</font></i></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</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="E22">A21</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_3_2"/><i><font color="Green" title="E23">A22</font></i>: 
<font color="Maroon" title="c11">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font></span><br/><a NAME="E2:9_1_3_2"/>
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_1_3_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</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="E2:9_1_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c3">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:9_1_3_2_1"/><b>then </b><i><font color="Green" title="E24">A23</font></i>: 
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c3">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:9_1_3_2_1"/>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></i>;<br/>
<a NAME="E5:9_1_3_2_1"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/>
<a NAME="E6:9_1_3_2_1"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c3">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 
<b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E3:9_1_3_2_1"><i><font color="Green" title="E24">A23</font></i></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/>
<a NAME="E7:9_1_3_2_1"/><b>then </b>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E8:9_1_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c4">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E9:9_1_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:9_1_3_2"/><b>then </b><i><font color="Green" title="E24">A24</font></i>: 
<font color="Maroon" title="c5">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_3_2"><i><font color="Green" title="E23">A22</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><a NAME="E4:9_1_3_2"/><i><font color="Green" title="E25">A25</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_1_3_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</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="E2:9_1_3_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c4">a'</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="E3:9_1_3_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:9_1_3_2"/>
<font color="Maroon" title="c2">K'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E6:9_1_3_2"/><b>then </b>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E7:9_1_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E8:9_1_3_2"/><b>then </b>
<font color="Maroon" title="c6">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_3_2"><i><font color="Green" title="E23">A22</font></i></a>, <a class="txt" href="conmetr.html#E4:9_1_3_2"><i><font color="Green" title="E25">A25</font></i></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></i>;<br/><b>hence </b><a NAME="E9:9_1_3_2"/>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:9_1_3_2"><i><font color="Green" title="E24">A24</font></i></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_3_3"/><i><font color="Green" title="E23">A26</font></i>: 
<font color="Maroon" title="c11">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a1'</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font></span><br/><a NAME="E2:9_1_3_3"/><i><font color="Green" title="E24">A27</font></i>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c13">b</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c15">c</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:9_1_3_3_1"/><i><font color="Green" title="E25">A28</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c13">b</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c15">c</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="E26">A29</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_3_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_3_3_1_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c13">b</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="E2:9_1_3_3_1_1"/><b>then </b><i><font color="Green" title="E27">A30</font></i>: 
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c13">b</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E3:9_1_3_3_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c7">a1'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E4:9_1_3_3_1_1"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c7">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E5:9_1_3_3_1_1"/><b>then </b>
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c10">o</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E6:9_1_3_3_1_1"/><b>then </b>
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c13">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c10">o</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:9_1_3_3"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="conmetr.html#E2:9_1_3_3_1_1"><i><font color="Green" title="E27">A30</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E7:9_1_3_3_1_1"/><b>then </b><i><font color="Green" title="E28">A31</font></i>: 
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c13">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c11">a</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E8:9_1_3_3_1_1"/>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></i>;<br/><a NAME="E9:9_1_3_3_1_1"/><b>then </b>
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c13">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c15">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E10:9_1_3_3_1_1"/><b>then </b>
<font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c15">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c11">a</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="conmetr.html#E7:9_1_3_3_1_1"><i><font color="Green" title="E28">A31</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E11:9_1_3_3_1_1"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c15">c</font>,<font color="Maroon" title="c11">a</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E12:9_1_3_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c4">a'</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="E13:9_1_3_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_3_3_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:9_1_3_3_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font>,<font color="Maroon" title="c15">c</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="E2:9_1_3_3_1_2"/><b>then </b><i><font color="Green" title="E27">A32</font></i>: 
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c15">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E3:9_1_3_3_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c7">a1'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E4:9_1_3_3_1_2"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c7">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E5:9_1_3_3_1_2"/><b>then </b>
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c10">o</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E6:9_1_3_3_1_2"/><b>then </b>
<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c15">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c10">o</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:9_1_3_3"><i><font color="Green" title="E23">A26</font></i></a>, <a class="txt" href="conmetr.html#E2:9_1_3_3_1_2"><i><font color="Green" title="E27">A32</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/><a NAME="E7:9_1_3_3_1_2"/><b>then </b>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c15">c</font>,<font color="Maroon" title="c10">o</font>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E8:9_1_3_3_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c3">o'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E9:9_1_3_3_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">c'</font>,<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c4">a'</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="E10:9_1_3_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:9_1_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conmetr.html#E1:9_1_3_3_1"><i><font color="Green" title="E25">A28</font></i></a>, <a class="txt" href="conmetr.html#E2:9_1_3_3_1"><i><font color="Green" title="E26">A29</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:9_1_3_3"/>
<font color="Maroon" title="c2">K'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E4:9_1_3_3"/><b>then </b>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a></i>;<br/><a NAME="E5:9_1_3_3"/><b>then </b>
<font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c15">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c16">c1</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E6:9_1_3_3"/><b>then </b><i><font color="Green" title="E25">A33</font></i>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c11">a</font>,<font color="Maroon" title="c12">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c14">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c15">c</font>,<font color="Maroon" title="c16">c1</font> )
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E7:9_1_3_3"/><i><font color="Green" title="E26">A34</font></i>: 
<font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c11">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">b1</font>,<font color="Maroon" title="c12">a1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E5:9"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/><a NAME="E8:9_1_3_3"/>
<font color="Maroon" title="c2">K'</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></i>;<br/><a NAME="E9:9_1_3_3"/><b>then </b>
<font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T54" title="AFF_1:th.54">AFF_1:54</a></i>;<br/><a NAME="E10:9_1_3_3"/><b>then </b>
<font color="Maroon" title="c4">a'</font>,<font color="Maroon" title="c5">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></i>;<br/><a NAME="E11:9_1_3_3"/><b>then </b>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c4">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o'</font>,<font color="Maroon" title="c6">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E12:9_1_3_3"/><b>then </b>
<font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c11">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">o</font>,<font color="Maroon" title="c15">c</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E13:9_1_3_3"/><b>then </b>
<font color="Maroon" title="c13">b</font>,<font color="Maroon" title="c15">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">b1</font>,<font color="Maroon" title="c16">c1</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E1:9"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="conmetr.html#E5:9"><i><font color="Green" title="E16">A3</font></i></a>, <a class="txt" href="conmetr.html#E1:9_1_3"><i><font color="Green" title="E20">A14</font></i></a>, <a class="txt" href="conmetr.html#E2:9_1_3"><i><font color="Green" title="E21">A15</font></i></a>, <a class="txt" href="conmetr.html#E2:9_1_3_3"><i><font color="Green" title="E24">A27</font></i></a>, <a class="txt" href="conmetr.html#E6:9_1_3_3"><i><font color="Green" title="E25">A33</font></i></a>, <a class="txt" href="conmetr.html#E7:9_1_3_3"><i><font color="Green" title="E26">A34</font></i></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E14:9_1_3_3"/>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</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="E5:9_1_3"/>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:9_1_3"><i><font color="Green" title="E22">A21</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="E5:9_1"/>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E3:9_1"><i><font color="Green" title="E19">A13</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:9"/>
<font color="Maroon" title="c5">b'</font>,<font color="Maroon" title="c6">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b1'</font>,<font color="Maroon" title="c9">c1'</font>
 <b>by </b><i><a class="txt" href="conmetr.html#E2:9"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</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>
