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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a>  implies  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:8"/><span class="lab"><font color="Green" title="E14">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V5" title="CONMETR:attr.5">satisfying_TDES</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font> is  <a href="aff_2.html#V7" title="AFF_2:attr.7">Moufangian</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">K9</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>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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">K9</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">K9</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">K9</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">K9</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">K9</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">K9</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/><span class="kw">let </span><font color="Maroon" title="c3">o9</font>, <font color="Maroon" title="c4">a9</font>, <font color="Maroon" title="c5">b9</font>, <font color="Maroon" title="c6">c9</font>, <font color="Maroon" title="c7">a19</font>, <font color="Maroon" title="c8">b19</font>, <font color="Maroon" title="c9">c19</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c2">K9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  or  not <font color="Maroon" title="c3">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font> or  not <font color="Maroon" title="c6">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font> or  not <font color="Maroon" title="c9">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font> or <font color="Maroon" title="c4">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font> or <font color="Maroon" title="c3">o9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">c9</font> or <font color="Maroon" title="c4">a9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b9</font> or  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c7">a19</font> or  not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c8">b19</font> or  not <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a19</font>,<font color="Maroon" title="c8">b19</font> or  not <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a19</font>,<font color="Maroon" title="c9">c19</font> or  not <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K9</font> or <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:8"/><span class="lab"><font color="Green" title="E15">A2</font></span>: 
<font color="Maroon" title="c2">K9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E3:8"/><span class="lab"><font color="Green" title="E16">A3</font></span>: 
<font color="Maroon" title="c3">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">and </span><br/><a NAME="E4:8"/><span class="lab"><font color="Green" title="E17">A4</font></span>: 
<font color="Maroon" title="c6">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">and </span><br/><a NAME="E5:8"/><span class="lab"><font color="Green" title="E18">A5</font></span>: 
<font color="Maroon" title="c9">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">and </span><br/><a NAME="E6:8"/><span class="lab"><font color="Green" title="E19">A6</font></span>: 
not <font color="Maroon" title="c4">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">and </span><br/><a NAME="E7:8"/><span class="lab"><font color="Green" title="E20">A7</font></span>: 
<font color="Maroon" title="c3">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">c9</font>
 <span class="kw">and </span><br/><a NAME="E8:8"/><span class="lab"><font color="Green" title="E21">A8</font></span>: 
<font color="Maroon" title="c4">a9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b9</font>
 <span class="kw">and </span><br/><a NAME="E9:8"/><span class="lab"><font color="Green" title="E22">A9</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c7">a19</font>
 <span class="kw">and </span><br/><a NAME="E10:8"/><span class="lab"><font color="Green" title="E23">A10</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c8">b19</font>
 <span class="kw">and </span><br/><a NAME="E11:8"/><span class="lab"><font color="Green" title="E24">A11</font></span>: 
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a19</font>,<font color="Maroon" title="c8">b19</font>
 <span class="kw">and </span><br/><a NAME="E12:8"/><span class="lab"><font color="Green" title="E25">A12</font></span>: 
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">a19</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">and </span><br/><a NAME="E13:8"/><span class="lab"><font color="Green" title="E26">A13</font></span>: 
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c10">K</font> = <font color="Maroon" title="c2">K9</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">o</font> = <font color="Maroon" title="c3">o9</font>, <font color="Maroon" title="c12">a</font> = <font color="Maroon" title="c4">a9</font>, <font color="Maroon" title="c13">a1</font> = <font color="Maroon" title="c7">a19</font>, <font color="Maroon" title="c14">b</font> = <font color="Maroon" title="c5">b9</font>, <font color="Maroon" title="c15">b1</font> = <font color="Maroon" title="c8">b19</font>, <font color="Maroon" title="c16">c</font> = <font color="Maroon" title="c6">c9</font>, <font color="Maroon" title="c17">c1</font> = <font color="Maroon" title="c9">c19</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/>
<a NAME="E16:8"/><span class="lab"><font color="Green" title="E27">A14</font></span>: 
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c16">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c17">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:8"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E17:8"/><span class="lab"><font color="Green" title="E28">A15</font></span>: 
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c14">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c15">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:8"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E29">A16</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:8_1_1"/><span class="lab"><font color="Green" title="E30">A17</font></span>: 
<font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font></span><br/><a NAME="E2:8_1_1"/><span class="lab"><font color="Green" title="E31">A18</font></span>: 
( <font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">a</font> &amp; <font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">b</font> &amp; <font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">c</font> &amp; <font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c1</font> &amp; <font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">b1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E32">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:8_1_1_1_1"/>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></span>;<br/><a NAME="E2:8_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A20</font></span>: 
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E13:8"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><span class="kw">assume </span><a NAME="E3:8_1_1_1_1"/>
<font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:8_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">a19</font>,<font color="Maroon" title="c3">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:8"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E11:8"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E2:8_1_1_1_1"><span class="lab"><font color="Green" title="E33">A20</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><a NAME="E5:8_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c7">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E6:8_1_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c7">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E7:8_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A21</font></span>: 
<font color="Maroon" title="c7">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E8:8_1_1_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c7">a19</font>,<font color="Maroon" title="c4">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:8"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E9:8_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E1:8_1_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="txt" href="#E7:8_1_1_1_1"><span class="lab"><font color="Green" title="E34">A21</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E33">A22</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:8_1_1_1_2"/>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c7">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:8"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E2:8_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A23</font></span>: 
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c7">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><span class="kw">assume </span><a NAME="E3:8_1_1_1_2"/>
<font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E4:8_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c7">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:8"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E5:8_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8_1_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="txt" href="#E2:8_1_1_1_2"><span class="lab"><font color="Green" title="E34">A23</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><a NAME="E6:8_1_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E7:8_1_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c4">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E8:8_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:8_1_1_1"/>
( <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">a</font> or <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">b</font> or <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">c</font> or <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">c1</font> or <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">b1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:8_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E13:8"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="txt" href="#E2:8_1_1_1"><span class="lab"><font color="Green" title="E33">A22</font></span></a>, <a class="txt" href="#E1:8_1_1_1"><span class="lab"><font color="Green" title="E32">A19</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E32">A24</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:8_1_1_2"/><span class="lab"><font color="Green" title="E33">A25</font></span>: 
<font color="Maroon" title="c12">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">a19</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font></span><br/><a NAME="E2:8_1_1_2"/><span class="lab"><font color="Green" title="E34">A26</font></span>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c14">b</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c16">c</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<div><span class="lab"><font color="Green" title="E35">A27</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_2_1_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:8_1_1_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c7">a19</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:8"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E2:8_1_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c7">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E3:8_1_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A28</font></span>: 
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c11">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><span class="kw">assume </span><a NAME="E4:8_1_1_2_1_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c14">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E5:8_1_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c14">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E6:8_1_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c14">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c11">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8_1_1_2"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E3:8_1_1_2_1_1"><span class="lab"><font color="Green" title="E36">A28</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E7:8_1_1_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A29</font></span>: 
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c14">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c12">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E8:8_1_1_2_1_1"/>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="txt" href="#E13:8"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="aff_1.html#T41" title="AFF_1:th.41">AFF_1:41</a></span>;<br/><a NAME="E9:8_1_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c14">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E10:8_1_1_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c16">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c12">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:8"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E7:8_1_1_2_1_1"><span class="lab"><font color="Green" title="E37">A29</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E11:8_1_1_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c16">c</font>,<font color="Maroon" title="c12">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E12:8_1_1_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c4">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">hence </span><a NAME="E13:8_1_1_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><span class="lab"><font color="Green" title="E36">A30</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_2_1_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:8_1_1_2_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c7">a19</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:8"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E2:8_1_1_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c7">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E3:8_1_1_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A31</font></span>: 
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c11">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><span class="kw">assume </span><a NAME="E4:8_1_1_2_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c16">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E5:8_1_1_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E6:8_1_1_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c16">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c11">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8_1_1_2"><span class="lab"><font color="Green" title="E33">A25</font></span></a>, <a class="txt" href="#E3:8_1_1_2_1_2"><span class="lab"><font color="Green" title="E37">A31</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E7:8_1_1_2_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c16">c</font>,<font color="Maroon" title="c11">o</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E8:8_1_1_2_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E9:8_1_1_2_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E10:8_1_1_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:8_1_1_2_1"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c14">b</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c16">c</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:8_1_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8_1_1_2_1"><span class="lab"><font color="Green" title="E35">A27</font></span></a>, <a class="txt" href="#E2:8_1_1_2_1"><span class="lab"><font color="Green" title="E36">A30</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E3:8_1_1_2"/><span class="lab"><font color="Green" title="E35">A32</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c15">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:8"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E4:8_1_1_2"/>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E5:8"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E5:8_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c16">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c17">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E6:8_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A33</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c16">c</font>,<font color="Maroon" title="c17">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E7:8_1_1_2"/>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="aff_1.html#T54" title="AFF_1:th.54">AFF_1:54</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E8:8_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E13:8"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><a NAME="E9:8_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c4">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E10:8_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A34</font></span>: 
<font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c12">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c16">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E11:8_1_1_2"/><span class="lab"><font color="Green" title="E38">A35</font></span>: 
<font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c12">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1</font>,<font color="Maroon" title="c13">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:8"><span class="lab"><font color="Green" title="E28">A15</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E12:8_1_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c12">a</font>,<font color="Maroon" title="c13">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:8"><span class="lab"><font color="Green" title="E22">A9</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E13:8_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c16">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1</font>,<font color="Maroon" title="c17">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8"><span class="lab"><font color="Green" title="E14">A1</font></span></a>, <a class="txt" href="#E16:8"><span class="lab"><font color="Green" title="E27">A14</font></span></a>, <a class="txt" href="#E1:8_1_1"><span class="lab"><font color="Green" title="E30">A17</font></span></a>, <a class="txt" href="#E2:8_1_1"><span class="lab"><font color="Green" title="E31">A18</font></span></a>, <a class="txt" href="#E2:8_1_1_2"><span class="lab"><font color="Green" title="E34">A26</font></span></a>, <a class="txt" href="#E3:8_1_1_2"><span class="lab"><font color="Green" title="E35">A32</font></span></a>, <a class="txt" href="#E6:8_1_1_2"><span class="lab"><font color="Green" title="E36">A33</font></span></a>, <a class="txt" href="#E11:8_1_1_2"><span class="lab"><font color="Green" title="E38">A35</font></span></a>, <a class="txt" href="#E10:8_1_1_2"><span class="lab"><font color="Green" title="E37">A34</font></span></a>, <a class="ref" href="conmetr.html#D5" target="_self" title="CONMETR:def.5">Def5</a></span>;<br/><span class="kw">hence </span><a NAME="E14:8_1_1_2"/>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:8_1_1_3"/><span class="lab"><font color="Green" title="E33">A36</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:8_1_1_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:8_1_1_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c4">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:8_1_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:8_1_1_3"/><span class="lab"><font color="Green" title="E34">A37</font></span>: 
<font color="Maroon" title="c12">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font></span><br/><a NAME="E3:8_1_1_3"/>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E5:8"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E4:8_1_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E5:8_1_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A38</font></span>: 
<font color="Maroon" title="c6">c9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:8"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E2:8_1_1_3"><span class="lab"><font color="Green" title="E34">A37</font></span></a>, <a class="txt" href="#E1:8_1_1_3"><span class="lab"><font color="Green" title="E33">A36</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>;<br/><a NAME="E6:8_1_1_3"/>
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_1_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:8_1_1_3_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:8_1_1_3_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c3">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E3:8_1_1_3_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A39</font></span>: 
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c3">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E4:8_1_1_3_2"/>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></span>;<br/>
<a NAME="E5:8_1_1_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E13:8"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/>
<a NAME="E6:8_1_1_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c3">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:8"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E3:8_1_1_3_2"><span class="lab"><font color="Green" title="E36">A39</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E7:8_1_1_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c4">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E8:8_1_1_3_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c4">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:8_1_1_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E7:8_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c5">b9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:8"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="txt" href="#E11:8"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E2:8_1_1_3"><span class="lab"><font color="Green" title="E34">A37</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>;<br/><span class="kw">hence </span><a NAME="E8:8_1_1_3"/>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:8_1_1_3"><span class="lab"><font color="Green" title="E35">A38</font></span></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:8_1_1"/>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1_1"><span class="lab"><font color="Green" title="E32">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:8_1"/><span class="lab"><font color="Green" title="E30">A40</font></span>: 
not <font color="Maroon" title="c14">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">K</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font></span><br/><a NAME="E3:8_1"/><span class="lab"><font color="Green" title="E31">A41</font></span>: 
( <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a1</font> implies ( <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">b1</font> &amp; <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">c1</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:8_1_2"/><span class="lab"><font color="Green" title="E32">A42</font></span>: 
<font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a1</font>
 <span class="kw">and </span><br/><a NAME="E2:8_1_2"/><span class="lab"><font color="Green" title="E33">A43</font></span>: 
( <font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">b1</font> or <font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<div><span class="lab"><font color="Green" title="E34">A44</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:8_1_2_1"/><span class="lab"><font color="Green" title="E35">A45</font></span>: 
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c9">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:8"><span class="lab"><font color="Green" title="E25">A12</font></span></a>, <a class="txt" href="#E1:8_1_2"><span class="lab"><font color="Green" title="E32">A42</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><span class="kw">assume </span><a NAME="E2:8_1_2_1"/><span class="lab"><font color="Green" title="E36">A46</font></span>: 
<font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E3:8_1_2_1"/>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c9">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E5:8"><span class="lab"><font color="Green" title="E18">A5</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E4:8_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8_1_2_1"><span class="lab"><font color="Green" title="E36">A46</font></span></a>, <a class="txt" href="#E1:8_1_2_1"><span class="lab"><font color="Green" title="E35">A45</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><a NAME="E5:8_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c4">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E6:8_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c3">o9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E7:8_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c4">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E8:8_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:8_1_2_2"/>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="ref" href="aff_1.html#T37" title="AFF_1:th.37">AFF_1:37</a></span>;<br/><a NAME="E2:8_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a9</font>,<font color="Maroon" title="c5">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E13:8"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><a NAME="E3:8_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c8">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:8"><span class="lab"><font color="Green" title="E21">A8</font></span></a>, <a class="txt" href="#E11:8"><span class="lab"><font color="Green" title="E24">A11</font></span></a>, <a class="txt" href="#E1:8_1_2"><span class="lab"><font color="Green" title="E32">A42</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><a NAME="E4:8_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c6">c9</font>,<font color="Maroon" title="c8">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E5:8_1_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A47</font></span>: 
<font color="Maroon" title="c8">b19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">K9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E4:8"><span class="lab"><font color="Green" title="E17">A4</font></span></a>, <a class="txt" href="#E7:8"><span class="lab"><font color="Green" title="E20">A7</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><span class="kw">assume </span><a NAME="E6:8_1_2_2"/><span class="lab"><font color="Green" title="E36">A48</font></span>: 
<font color="Maroon" title="c11">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E7:8_1_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">o9</font>,<font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c5">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:8"><span class="lab"><font color="Green" title="E23">A10</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><span class="kw">hence </span><a NAME="E8:8_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8"><span class="lab"><font color="Green" title="E15">A2</font></span></a>, <a class="txt" href="#E3:8"><span class="lab"><font color="Green" title="E16">A3</font></span></a>, <a class="txt" href="#E2:8_1"><span class="lab"><font color="Green" title="E30">A40</font></span></a>, <a class="txt" href="#E6:8_1_2_2"><span class="lab"><font color="Green" title="E36">A48</font></span></a>, <a class="txt" href="#E5:8_1_2_2"><span class="lab"><font color="Green" title="E35">A47</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:8_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:8_1_2"><span class="lab"><font color="Green" title="E33">A43</font></span></a>, <a class="txt" href="#E3:8_1_2"><span class="lab"><font color="Green" title="E34">A44</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:8_1_3"/>
<font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font></span><br/><a NAME="E2:8_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c14">b</font>,<font color="Maroon" title="c16">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b1</font>,<font color="Maroon" title="c17">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:8_1"><span class="lab"><font color="Green" title="E31">A41</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">hence </span><a NAME="E3:8_1_3"/>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:8_1"/>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8_1"><span class="lab"><font color="Green" title="E29">A16</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E19:8"/>
<font color="Maroon" title="c5">b9</font>,<font color="Maroon" title="c6">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b19</font>,<font color="Maroon" title="c9">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:8"><span class="lab"><font color="Green" title="E19">A6</font></span></a>, <a class="txt" href="#E13:8"><span class="lab"><font color="Green" title="E26">A13</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
