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<span class="kw">let </span><font color="Maroon" title="c1">MS</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a>  iff  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a>  )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">AS</font> =  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font>;<br/>
<div><span class="lab"><font color="Green" title="E21">A1</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:22_1"/><span class="lab"><font color="Green" title="E22">A2</font></span>: 
<font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> </span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">P</font>, <font color="Maroon" title="c5">C</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">MS</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">a9</font>, <font color="Olive" title="b5">b9</font>, <font color="Olive" title="b6">c9</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font></span>)</span>  st <font color="Maroon" title="c3">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b4">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b2">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b5">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b3">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Olive" title="b6">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c3">A</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c4">P</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c5">C</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b5">b9</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">a9</font>,<font color="Olive" title="b6">c9</font> holds <br/><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b9</font>,<font color="Olive" title="b6">c9</font></span><br/><span class="kw">let </span><font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c9">a9</font>, <font color="Maroon" title="c10">b9</font>, <font color="Maroon" title="c11">c9</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">MS</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c9">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c10">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c11">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c3">A</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c4">P</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c5">C</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">C</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">b9</font> &amp; <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">c9</font> implies <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b9</font>,<font color="Maroon" title="c11">c9</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:22_1_1"/><span class="lab"><font color="Green" title="E23">A3</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c4">P</font>
 <span class="kw">and </span><br/><a NAME="E2:22_1_1"/><span class="lab"><font color="Green" title="E24">A4</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c5">C</font>
 <span class="kw">and </span><br/><a NAME="E3:22_1_1"/><span class="lab"><font color="Green" title="E25">A5</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E4:22_1_1"/><span class="lab"><font color="Green" title="E26">A6</font></span>: 
<font color="Maroon" title="c9">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 <span class="kw">and </span><br/><a NAME="E5:22_1_1"/><span class="lab"><font color="Green" title="E27">A7</font></span>: 
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font>
 <span class="kw">and </span><br/><a NAME="E6:22_1_1"/><span class="lab"><font color="Green" title="E28">A8</font></span>: 
<font color="Maroon" title="c10">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font>
 <span class="kw">and </span><br/><a NAME="E7:22_1_1"/><span class="lab"><font color="Green" title="E29">A9</font></span>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font>
 <span class="kw">and </span><br/><a NAME="E8:22_1_1"/><span class="lab"><font color="Green" title="E30">A10</font></span>: 
<font color="Maroon" title="c11">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font>
 <span class="kw">and </span><br/><a NAME="E9:22_1_1"/><span class="lab"><font color="Green" title="E31">A11</font></span>: 
<font color="Maroon" title="c3">A</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E10:22_1_1"/><span class="lab"><font color="Green" title="E32">A12</font></span>: 
<font color="Maroon" title="c4">P</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E11:22_1_1"/><span class="lab"><font color="Green" title="E33">A13</font></span>: 
<font color="Maroon" title="c5">C</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E12:22_1_1"/><span class="lab"><font color="Green" title="E34">A14</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">P</font>
 <span class="kw">and </span><br/><a NAME="E13:22_1_1"/><span class="lab"><font color="Green" title="E35">A15</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">C</font>
 <span class="kw">and </span><br/><a NAME="E14:22_1_1"/><span class="lab"><font color="Green" title="E36">A16</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">b9</font>
 <span class="kw">and </span><br/><a NAME="E15:22_1_1"/><span class="lab"><font color="Green" title="E37">A17</font></span>: 
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">c9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b9</font>,<font color="Maroon" title="c11">c9</font></span><br/><a NAME="E16:22_1_1"/><span class="lab"><font color="Green" title="E38">A18</font></span>: 
 not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E3:22_1_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E13:22_1_1"><span class="lab"><font color="Green" title="E35">A15</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><div><span class="lab"><font color="Green" title="E39">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">reconsider </span><font color="Maroon" title="c12">aa</font> = <font color="Maroon" title="c6">a</font>, <font color="Maroon" title="c13">a1</font> = <font color="Maroon" title="c9">a9</font>, <font color="Maroon" title="c14">bb</font> = <font color="Maroon" title="c7">b</font>, <font color="Maroon" title="c15">b1</font> = <font color="Maroon" title="c10">b9</font>, <font color="Maroon" title="c16">cc</font> = <font color="Maroon" title="c8">c</font>, <font color="Maroon" title="c17">c1</font> = <font color="Maroon" title="c11">c9</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E2:22_1_1_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E3:22_1_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E4:22_1_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E5:22_1_1"><span class="lab"><font color="Green" title="E27">A7</font></span></a>, <a class="txt" href="#E6:22_1_1"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E3:22_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A20</font></span>: 
<font color="Maroon" title="c12">aa</font>,<font color="Maroon" title="c13">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">bb</font>,<font color="Maroon" title="c15">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E4:22_1_1_1"/>
<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c9">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E3:22_1_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E4:22_1_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E7:22_1_1"><span class="lab"><font color="Green" title="E29">A9</font></span></a>, <a class="txt" href="#E8:22_1_1"><span class="lab"><font color="Green" title="E30">A10</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E5:22_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A21</font></span>: 
<font color="Maroon" title="c12">aa</font>,<font color="Maroon" title="c13">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">cc</font>,<font color="Maroon" title="c17">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><span class="kw">assume </span><a NAME="E6:22_1_1_1"/><span class="lab"><font color="Green" title="E42">A22</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c9">a9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b9</font>,<font color="Maroon" title="c11">c9</font></span><br/><a NAME="E7:22_1_1_1"/><span class="lab"><font color="Green" title="E43">A23</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">aa</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c14">bb</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:22_1_1_1_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">aa</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c14">bb</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:22_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="c6">a</font>,<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c7">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:22_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_1_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E4:22_1_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E9:22_1_1"><span class="lab"><font color="Green" title="E31">A11</font></span></a>, <a class="txt" href="#E6:22_1_1_1"><span class="lab"><font color="Green" title="E42">A22</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:22_1_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E5:22_1_1"><span class="lab"><font color="Green" title="E27">A7</font></span></a>, <a class="txt" href="#E12:22_1_1"><span class="lab"><font color="Green" title="E34">A14</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E8:22_1_1_1"/><span class="lab"><font color="Green" title="E44">A24</font></span>: 
 not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">aa</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c16">cc</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:22_1_1_1_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">aa</font>,<font color="Maroon" title="c13">a1</font>,<font color="Maroon" title="c16">cc</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:22_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="c6">a</font>,<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c8">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T40" title="ANALMETR:th.40">ANALMETR:40</a></span>;<br/>
<a NAME="E3:22_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_1_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E4:22_1_1"><span class="lab"><font color="Green" title="E26">A6</font></span></a>, <a class="txt" href="#E9:22_1_1"><span class="lab"><font color="Green" title="E31">A11</font></span></a>, <a class="txt" href="#E6:22_1_1_1"><span class="lab"><font color="Green" title="E42">A22</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:22_1_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_1_1"><span class="lab"><font color="Green" title="E24">A4</font></span></a>, <a class="txt" href="#E7:22_1_1"><span class="lab"><font color="Green" title="E29">A9</font></span></a>, <a class="txt" href="#E13:22_1_1"><span class="lab"><font color="Green" title="E35">A15</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E9:22_1_1_1"/>
( <font color="Maroon" title="c12">aa</font>,<font color="Maroon" title="c14">bb</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> &amp; <font color="Maroon" title="c12">aa</font>,<font color="Maroon" title="c16">cc</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="#E14:22_1_1"><span class="lab"><font color="Green" title="E36">A16</font></span></a>, <a class="txt" href="#E15:22_1_1"><span class="lab"><font color="Green" title="E37">A17</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E10:22_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">bb</font>,<font color="Maroon" title="c16">cc</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="#E1:22_1"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="txt" href="#E7:22_1_1_1"><span class="lab"><font color="Green" title="E43">A23</font></span></a>, <a class="txt" href="#E8:22_1_1_1"><span class="lab"><font color="Green" title="E44">A24</font></span></a>, <a class="txt" href="#E3:22_1_1_1"><span class="lab"><font color="Green" title="E40">A20</font></span></a>, <a class="txt" href="#E5:22_1_1_1"><span class="lab"><font color="Green" title="E41">A21</font></span></a>, <a class="ref" href="conmetr.html#D8" title="CONMETR:def.8">CONMETR:def 8</a></span>;<br/><span class="kw">hence </span><a NAME="E11:22_1_1_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b9</font>,<font color="Maroon" title="c11">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><a NAME="E18:22_1_1"/><span class="lab"><font color="Green" title="E40">A25</font></span>: 
 not <font color="Maroon" title="c6">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_1_1"><span class="lab"><font color="Green" title="E23">A3</font></span></a>, <a class="txt" href="#E3:22_1_1"><span class="lab"><font color="Green" title="E25">A5</font></span></a>, <a class="txt" href="#E12:22_1_1"><span class="lab"><font color="Green" title="E34">A14</font></span></a>, <a class="ref" href="aff_1.html#T45" title="AFF_1:th.45">AFF_1:45</a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:22_1_1_2"/><span class="lab"><font color="Green" title="E41">A26</font></span>: 
<font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a9</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b9</font>,<font color="Maroon" title="c11">c9</font></span><br/><a NAME="E2:22_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="c6">a</font>,<font color="Maroon" title="c8">c</font>,<font color="Maroon" title="c11">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:22_1_1"><span class="lab"><font color="Green" title="E37">A17</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="E3:22_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="c8">c</font>,<font color="Maroon" title="c11">c9</font>,<font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E4:22_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A27</font></span>: 
<font color="Maroon" title="c8">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:22_1_1"><span class="lab"><font color="Green" title="E29">A9</font></span></a>, <a class="txt" href="#E8:22_1_1"><span class="lab"><font color="Green" title="E30">A10</font></span></a>, <a class="txt" href="#E11:22_1_1"><span class="lab"><font color="Green" title="E33">A13</font></span></a>, <a class="txt" href="#E16:22_1_1"><span class="lab"><font color="Green" title="E38">A18</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/><a NAME="E5:22_1_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c10">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22_1_1"><span class="lab"><font color="Green" title="E36">A16</font></span></a>, <a class="txt" href="#E1:22_1_1_2"><span class="lab"><font color="Green" title="E41">A26</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="E6:22_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="c7">b</font>,<font color="Maroon" title="c10">b9</font>,<font color="Maroon" title="c6">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T6" title="AFF_1:th.6">AFF_1:6</a></span>;<br/><a NAME="E7:22_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:22_1_1"><span class="lab"><font color="Green" title="E27">A7</font></span></a>, <a class="txt" href="#E6:22_1_1"><span class="lab"><font color="Green" title="E28">A8</font></span></a>, <a class="txt" href="#E10:22_1_1"><span class="lab"><font color="Green" title="E32">A12</font></span></a>, <a class="txt" href="#E18:22_1_1"><span class="lab"><font color="Green" title="E40">A25</font></span></a>, <a class="ref" href="aff_1.html#T25" title="AFF_1:th.25">AFF_1:25</a></span>;<br/><span class="kw">hence </span><a NAME="E8:22_1_1_2"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b9</font>,<font color="Maroon" title="c11">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_1_1_2"><span class="lab"><font color="Green" title="E42">A27</font></span></a>, <a class="ref" href="aff_1.html#T2" title="AFF_1:th.2">AFF_1:2</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E20:22_1_1"/>
<font color="Maroon" title="c7">b</font>,<font color="Maroon" title="c8">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">b9</font>,<font color="Maroon" title="c11">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:22_1_1"><span class="lab"><font color="Green" title="E39">A19</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:22_1"/>
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_2.html#D11" title="AFF_2:def.11">AFF_2:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:22_2"/><span class="lab"><font color="Green" title="E22">A28</font></span>: 
 <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a> </span><br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">c1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">MS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c5">b</font> &amp;  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c7">c</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> implies <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:22_2_1"/><span class="lab"><font color="Green" title="E23">A29</font></span>: 
(  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c5">b</font> &amp;  not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c7">c</font> )
 <span class="kw">and </span><br/><a NAME="E2:22_2_1"/><span class="lab"><font color="Green" title="E24">A30</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E3:22_2_1"/><span class="lab"><font color="Green" title="E25">A31</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">and </span><br/><a NAME="E4:22_2_1"/><span class="lab"><font color="Green" title="E26">A32</font></span>: 
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c9">a9</font> = <font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c10">a19</font> = <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c11">b9</font> = <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c12">b19</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c13">c9</font> = <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c14">c19</font> = <font color="Maroon" title="c8">c1</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T35" title="ANALMETR:th.35">ANALMETR:35</a></span>;<br/><a NAME="E6:22_2_1"/><span class="lab"><font color="Green" title="E27">A33</font></span>: 
<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c12">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:22_2_1"><span class="lab"><font color="Green" title="E24">A30</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E7:22_2_1"/><span class="lab"><font color="Green" title="E28">A34</font></span>: 
( <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c12">b19</font> &amp; <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c13">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a19</font>,<font color="Maroon" title="c14">c19</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:22_2_1"><span class="lab"><font color="Green" title="E26">A32</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><a NAME="E8:22_2_1"/><span class="lab"><font color="Green" title="E29">A35</font></span>: 
<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c14">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:22_2_1"><span class="lab"><font color="Green" title="E25">A31</font></span></a>, <a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c15">A</font> =  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>);<br/><a NAME="E9:22_2_1"/><span class="lab"><font color="Green" title="E30">A36</font></span>: 
(  not <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font> &amp;  not <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c13">c9</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:22_2_1_1"/>
( <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c11">b9</font> or <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c13">c9</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:22_2_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> or <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:22_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_2_1"><span class="lab"><font color="Green" title="E23">A29</font></span></a>, <a class="ref" href="analmetr.html#D10" title="ANALMETR:def.10">ANALMETR:def 10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E10:22_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A37</font></span>: 
<font color="Maroon" title="c9">a9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T3" title="AFF_1:th.3">AFF_1:3</a></span>;<br/><a NAME="E11:22_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A38</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>) is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D3" title="AFF_1:def.3">AFF_1:def 3</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">C</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E13:22_2_1"/><span class="lab"><font color="Green" title="E33">A39</font></span>: 
<font color="Maroon" title="c13">c9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">C</font>
 <span class="kw">and </span><br/><a NAME="E14:22_2_1"/><span class="lab"><font color="Green" title="E34">A40</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c16">C</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>;<br/><a NAME="E15:22_2_1"/><span class="lab"><font color="Green" title="E35">A41</font></span>: 
<font color="Maroon" title="c16">C</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22_2_1"><span class="lab"><font color="Green" title="E34">A40</font></span></a>, <a class="ref" href="aff_1.html#T36" title="AFF_1:th.36">AFF_1:36</a></span>;<br/><a NAME="E16:22_2_1"/><span class="lab"><font color="Green" title="E36">A42</font></span>: 
( <font color="Maroon" title="c9">a9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>) &amp; <font color="Maroon" title="c10">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E17:22_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A43</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:22_2_1"><span class="lab"><font color="Green" title="E30">A36</font></span></a>, <a class="txt" href="#E11:22_2_1"><span class="lab"><font color="Green" title="E32">A38</font></span></a>, <a class="txt" href="#E13:22_2_1"><span class="lab"><font color="Green" title="E33">A39</font></span></a>, <a class="ref" href="aff_1.html#T51" title="AFF_1:th.51">AFF_1:51</a></span>;<br/><a NAME="E18:22_2_1"/><span class="lab"><font color="Green" title="E38">A44</font></span>: 
<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:22_2_1"><span class="lab"><font color="Green" title="E32">A38</font></span></a>, <a class="txt" href="#E16:22_2_1"><span class="lab"><font color="Green" title="E36">A42</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>;<br/><a NAME="E19:22_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c16">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:22_2_1"><span class="lab"><font color="Green" title="E34">A40</font></span></a>, <a class="ref" href="aff_1.html#T43" title="AFF_1:th.43">AFF_1:43</a></span>;<br/><a NAME="E20:22_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c13">c9</font>,<font color="Maroon" title="c14">c19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c16">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:22_2_1"><span class="lab"><font color="Green" title="E29">A35</font></span></a>, <a class="txt" href="#E10:22_2_1"><span class="lab"><font color="Green" title="E31">A37</font></span></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></span>;<br/><a NAME="E21:22_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A45</font></span>: 
<font color="Maroon" title="c14">c19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c16">C</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:22_2_1"><span class="lab"><font color="Green" title="E33">A39</font></span></a>, <a class="txt" href="#E15:22_2_1"><span class="lab"><font color="Green" title="E35">A41</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">consider </span><font color="Maroon" title="c17">P</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E23:22_2_1"/><span class="lab"><font color="Green" title="E40">A46</font></span>: 
<font color="Maroon" title="c11">b9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">P</font>
 <span class="kw">and </span><br/><a NAME="E24:22_2_1"/><span class="lab"><font color="Green" title="E41">A47</font></span>: 
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>) <a href="aff_1.html#R5" title="AFF_1:pred.5">//</a> <font color="Maroon" title="c17">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:22_2_1"><span class="lab"><font color="Green" title="E32">A38</font></span></a>, <a class="ref" href="aff_1.html#T49" title="AFF_1:th.49">AFF_1:49</a></span>;<br/><a NAME="E25:22_2_1"/><span class="lab"><font color="Green" title="E42">A48</font></span>: 
<font color="Maroon" title="c17">P</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:22_2_1"><span class="lab"><font color="Green" title="E41">A47</font></span></a>, <a class="ref" href="aff_1.html#T36" title="AFF_1:th.36">AFF_1:36</a></span>;<br/><a NAME="E26:22_2_1"/>
<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c17">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:22_2_1"><span class="lab"><font color="Green" title="E38">A44</font></span></a>, <a class="txt" href="#E24:22_2_1"><span class="lab"><font color="Green" title="E41">A47</font></span></a>, <a class="ref" href="aff_1.html#T43" title="AFF_1:th.43">AFF_1:43</a></span>;<br/><a NAME="E27:22_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c12">b19</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c17">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:22_2_1"><span class="lab"><font color="Green" title="E27">A33</font></span></a>, <a class="txt" href="#E10:22_2_1"><span class="lab"><font color="Green" title="E31">A37</font></span></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></span>;<br/><a NAME="E28:22_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A49</font></span>: 
<font color="Maroon" title="c12">b19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c17">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:22_2_1"><span class="lab"><font color="Green" title="E40">A46</font></span></a>, <a class="txt" href="#E25:22_2_1"><span class="lab"><font color="Green" title="E42">A48</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>;<br/><a NAME="E29:22_2_1"/>
 <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> (<font color="Maroon" title="c9">a9</font>,<font color="Maroon" title="c10">a19</font>) <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">P</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:22_2_1"><span class="lab"><font color="Green" title="E30">A36</font></span></a>, <a class="txt" href="#E11:22_2_1"><span class="lab"><font color="Green" title="E32">A38</font></span></a>, <a class="txt" href="#E16:22_2_1"><span class="lab"><font color="Green" title="E36">A42</font></span></a>, <a class="txt" href="#E23:22_2_1"><span class="lab"><font color="Green" title="E40">A46</font></span></a>, <a class="ref" href="aff_1.html#T51" title="AFF_1:th.51">AFF_1:51</a></span>;<br/><a NAME="E30:22_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">b9</font>,<font color="Maroon" title="c13">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b19</font>,<font color="Maroon" title="c14">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22_2"><span class="lab"><font color="Green" title="E22">A28</font></span></a>, <a class="txt" href="#E7:22_2_1"><span class="lab"><font color="Green" title="E28">A34</font></span></a>, <a class="txt" href="#E11:22_2_1"><span class="lab"><font color="Green" title="E32">A38</font></span></a>, <a class="txt" href="#E16:22_2_1"><span class="lab"><font color="Green" title="E36">A42</font></span></a>, <a class="txt" href="#E23:22_2_1"><span class="lab"><font color="Green" title="E40">A46</font></span></a>, <a class="txt" href="#E24:22_2_1"><span class="lab"><font color="Green" title="E41">A47</font></span></a>, <a class="txt" href="#E13:22_2_1"><span class="lab"><font color="Green" title="E33">A39</font></span></a>, <a class="txt" href="#E14:22_2_1"><span class="lab"><font color="Green" title="E34">A40</font></span></a>, <a class="txt" href="#E25:22_2_1"><span class="lab"><font color="Green" title="E42">A48</font></span></a>, <a class="txt" href="#E15:22_2_1"><span class="lab"><font color="Green" title="E35">A41</font></span></a>, <a class="txt" href="#E28:22_2_1"><span class="lab"><font color="Green" title="E43">A49</font></span></a>, <a class="txt" href="#E21:22_2_1"><span class="lab"><font color="Green" title="E39">A45</font></span></a>, <a class="txt" href="#E17:22_2_1"><span class="lab"><font color="Green" title="E37">A43</font></span></a>, <a class="ref" href="aff_2.html#D11" title="AFF_2:def.11">AFF_2:def 11</a></span>;<br/><span class="kw">hence </span><a NAME="E31:22_2_1"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T36" title="ANALMETR:th.36">ANALMETR:36</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:22_2"/>
<font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="conmetr.html#D8" title="CONMETR:def.8">CONMETR:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:22"/>
( <font color="Maroon" title="c1">MS</font> is  <a href="conmetr.html#V8" title="CONMETR:attr.8">satisfying_des</a>  iff  <a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">MS</font> is  <a href="aff_2.html#V11" title="AFF_2:attr.11">translational</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:22"><span class="lab"><font color="Green" title="E21">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
