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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="conaffm.html#V3" title="CONAFFM:attr.3">satisfying_3H</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V1" title="CONMETR:attr.1">satisfying_OPAP</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:16"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V3" title="CONAFFM:attr.3">satisfying_3H</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#V1" title="CONMETR:attr.1">satisfying_OPAP</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="conmetr.html#D1" target="_self" title="CONMETR:def.1">CONMETR:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b7">M</font>, <font color="Olive" title="b8">N</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; <font color="Olive" title="b1">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; <font color="Olive" title="b2">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; <font color="Olive" title="b3">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; <font color="Olive" title="b4">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; <font color="Olive" title="b5">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; <font color="Olive" title="b6">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; not <font color="Olive" title="b5">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b7">M</font> &amp; not <font color="Olive" title="b3">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">N</font> &amp; <font color="Olive" title="b7">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b8">N</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">a2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">a3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b6">b3</font> &amp; <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b3">a3</font>,<font color="Olive" title="b6">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b1">a1</font>,<font color="Olive" title="b4">b1</font> holds <br/><font color="Olive" title="b1">a1</font>,<font color="Olive" title="b5">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b2">a2</font>,<font color="Olive" title="b6">b3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">M</font>, <font color="Olive" title="b2">N</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Olive" title="b1">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> holds <br/><font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><span class="kw">let </span><font color="Maroon" title="c9">M</font>, <font color="Maroon" title="c10">N</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font> &amp; not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c9">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font> &amp; <font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> implies <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font> )</span><br/>

















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:16"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">and </span><br/><a NAME="E3:16"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">and </span><br/><a NAME="E4:16"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">and </span><br/><a NAME="E5:16"/><span class="lab"><font color="Green" title="E19">A5</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">and </span><br/><a NAME="E6:16"/><span class="lab"><font color="Green" title="E20">A6</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">and </span><br/><a NAME="E7:16"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">and </span><br/><a NAME="E8:16"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">and </span><br/><a NAME="E9:16"/><span class="lab"><font color="Green" title="E23">A9</font></span>: 
<font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">and </span><br/><a NAME="E10:16"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
not <font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c9">M</font>
 <span class="kw">and </span><br/><a NAME="E11:16"/><span class="lab"><font color="Green" title="E25">A11</font></span>: 
not <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">and </span><br/><a NAME="E12:16"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
<font color="Maroon" title="c9">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">and </span><br/><a NAME="E13:16"/><span class="lab"><font color="Green" title="E27">A13</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font>
 <span class="kw">and </span><br/><a NAME="E14:16"/><span class="lab"><font color="Green" title="E28">A14</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font>
 <span class="kw">and </span><br/><a NAME="E15:16"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 <span class="kw">and </span><br/><a NAME="E16:16"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E17:16"/>
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">b2</font>
 <span class="kw">and </span><br/><a NAME="E18:16"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
<font color="Maroon" title="c2">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 <span class="kw">and </span><br/><a NAME="E19:16"/><span class="lab"><font color="Green" title="E31">A17</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E20:16"/><span class="lab"><font color="Green" title="E32">A18</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c11">o9</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c12">a19</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c13">a29</font> = <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c14">a39</font> = <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c15">b19</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c16">b29</font> = <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c17">b39</font> = <font color="Maroon" title="c8">b3</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c18">M9</font> = <font color="Maroon" title="c9">M</font>, <font color="Maroon" title="c19">N9</font> = <font color="Maroon" title="c10">N</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/>
<a NAME="E23:16"/>
<font color="Maroon" title="c10">N</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E24:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A19</font></span>: 
<font color="Maroon" title="c19">N9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></span>;<br/>
<a NAME="E25:16"/>
<font color="Maroon" title="c9">M</font> is  <a href="analmetr.html#V4" title="ANALMETR:attr.4">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E26:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A20</font></span>: 
<font color="Maroon" title="c18">M9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T58" title="ANALMETR:th.58">ANALMETR:58</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E35">A21</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:16_1"/><span class="lab"><font color="Green" title="E36">A22</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_1_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</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="E2:16_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A23</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:16_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</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="E4:16_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E16:16"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:16_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E13:16"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E2:16_1_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:16_1"/><span class="lab"><font color="Green" title="E37">A24</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E3:16_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</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="E4:16_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A25</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E5:16_1"/><span class="lab"><font color="Green" title="E39">A26</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E6:16_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:16"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E7:16_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E2:16_1"><span class="lab"><font color="Green" title="E37">A24</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E8:16_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c13">a29</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="E9:16_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_1"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E4:16_1"><span class="lab"><font color="Green" title="E38">A25</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>;<br/><a NAME="E10:16_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:16_1"><span class="lab"><font color="Green" title="E39">A26</font></span></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></span>;<br/><span class="kw">hence </span><a NAME="E11:16_1"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <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="E28:16"/><span class="lab"><font color="Green" title="E36">A27</font></span>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> holds <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b1">a</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c20">a</font>, <font color="Maroon" title="c21">b</font>, <font color="Maroon" title="c22">c</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c22">c</font> implies (  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c21">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c22">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c20">a</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c21">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c20">a</font> ) )</span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c23">a9</font> = <font color="Maroon" title="c20">a</font>, <font color="Maroon" title="c24">b9</font> = <font color="Maroon" title="c21">b</font>, <font color="Maroon" title="c25">c9</font> = <font color="Maroon" title="c22">c</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/>
<span class="kw">assume </span><a NAME="E2:16_2"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c22">c</font>
 ; <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#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c21">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c22">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c20">a</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c21">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c20">a</font> )</span><br/>

<a NAME="E3:16_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A28</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">a9</font>,<font color="Maroon" title="c24">b9</font>,<font color="Maroon" title="c25">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:16_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A29</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">b9</font>,<font color="Maroon" title="c23">a9</font>,<font color="Maroon" title="c25">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E5:16_2"/><span class="lab"><font color="Green" title="E39">A30</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c9</font>,<font color="Maroon" title="c23">a9</font>,<font color="Maroon" title="c24">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16_2"><span class="lab"><font color="Green" title="E37">A28</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:16_2"/><span class="lab"><font color="Green" title="E40">A31</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">b9</font>,<font color="Maroon" title="c25">c9</font>,<font color="Maroon" title="c23">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16_2"><span class="lab"><font color="Green" title="E37">A28</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E7:16_2"/><span class="lab"><font color="Green" title="E41">A32</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c25">c9</font>,<font color="Maroon" title="c24">b9</font>,<font color="Maroon" title="c23">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16_2"><span class="lab"><font color="Green" title="E37">A28</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E8:16_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">a9</font>,<font color="Maroon" title="c25">c9</font>,<font color="Maroon" title="c24">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16_2"><span class="lab"><font color="Green" title="E37">A28</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="E9:16_2"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c21">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c22">c</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c20">a</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c20">a</font>,<font color="Maroon" title="c21">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c22">c</font>,<font color="Maroon" title="c21">b</font>,<font color="Maroon" title="c20">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:16_2"><span class="lab"><font color="Green" title="E38">A29</font></span></a>, <a class="txt" href="#E6:16_2"><span class="lab"><font color="Green" title="E40">A31</font></span></a>, <a class="txt" href="#E5:16_2"><span class="lab"><font color="Green" title="E39">A30</font></span></a>, <a class="txt" href="#E7:16_2"><span class="lab"><font color="Green" title="E41">A32</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E37">A33</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:16_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</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="E2:16_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">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="E3:16_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A34</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E4:16_3"/>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</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="E5:16_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E6:16_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A35</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E7:16_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E8:16_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E9:16_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A36</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</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">assume </span><span class="kw">that </span><br/><a NAME="E10:16_3"/><span class="lab"><font color="Green" title="E41">A37</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 <span class="kw">and </span><br/><a NAME="E11:16_3"/><span class="lab"><font color="Green" title="E42">A38</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E12:16_3"/><span class="lab"><font color="Green" title="E43">A39</font></span>: 
( not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> &amp; not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_1"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> or  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:16_3_1"/><span class="kw">then </span>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b29</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:16_3_1"/><span class="kw">then </span>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b29</font> or  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:16_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E10:16_3"><span class="lab"><font color="Green" title="E41">A37</font></span></a>, <a class="txt" href="#E11:16_3"><span class="lab"><font color="Green" title="E42">A38</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="E13:16_3"/>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c15">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E14:16_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">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="E15:16_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A40</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c6">b1</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/><div><span class="lab"><font color="Green" title="E45">A41</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:16_3_2"/><span class="lab"><font color="Green" title="E46">A42</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E2:16_3_2"/>
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_1"/><span class="lab"><font color="Green" title="E47">A43</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_2_1_1"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:16_3_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:16_3_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a></span>;<br/>
<a NAME="E4:16_3_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A44</font></span>: 
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E5:16_3_2_1_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a>, <a class="txt" href="#E15:16_3"><span class="lab"><font color="Green" title="E44">A40</font></span></a></span>;<br/>
<a NAME="E6:16_3_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E7:16_3_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_3_2"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="txt" href="#E4:16_3_2_1_1"><span class="lab"><font color="Green" title="E48">A44</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:16_3_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16_3"><span class="lab"><font color="Green" title="E43">A39</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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>
<a NAME="E2:16_3_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a>, <a class="txt" href="#E3:16_3"><span class="lab"><font color="Green" title="E38">A34</font></span></a></span>;<br/>
<a NAME="E3:16_3_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A45</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c2">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="E4:16_3_2_1"/><span class="lab"><font color="Green" title="E49">A46</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_2_1_2"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a1</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="E2:16_3_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="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:16_3_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16_3"><span class="lab"><font color="Green" title="E43">A39</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E5:16_3_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E6:16_3_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a></span>;<br/>
<a NAME="E7:16_3_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A47</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E8:16_3_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a>, <a class="txt" href="#E6:16_3"><span class="lab"><font color="Green" title="E39">A35</font></span></a></span>;<br/>
<a NAME="E9:16_3_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E10:16_3_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:16_3_2_1"><span class="lab"><font color="Green" title="E50">A47</font></span></a>, <a class="txt" href="#E1:16_3_2_1"><span class="lab"><font color="Green" title="E47">A43</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E11:16_3_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:16_3_2_1"><span class="lab"><font color="Green" title="E49">A46</font></span></a>, <a class="txt" href="#E3:16_3_2_1"><span class="lab"><font color="Green" title="E48">A45</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E12:16_3_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E13:16_3_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A48</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c11">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="E14:16_3_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a>, <a class="txt" href="#E9:16_3"><span class="lab"><font color="Green" title="E40">A36</font></span></a></span>;<br/>
<a NAME="E15:16_3_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A49</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">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="E16:16_3_2_1"/>
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16_3"><span class="lab"><font color="Green" title="E43">A39</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:16_3_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:16"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E13:16_3_2_1"><span class="lab"><font color="Green" title="E51">A48</font></span></a>, <a class="txt" href="#E15:16_3_2_1"><span class="lab"><font color="Green" title="E52">A49</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c20">c1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E4:16_3_2"/><span class="lab"><font color="Green" title="E47">A50</font></span>: 
<font color="Maroon" title="c20">c1</font>,<font color="Maroon" title="c4">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">and </span><br/><a NAME="E5:16_3_2"/><span class="lab"><font color="Green" title="E48">A51</font></span>: 
<font color="Maroon" title="c20">c1</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">and </span><br/><a NAME="E6:16_3_2"/><span class="lab"><font color="Green" title="E49">A52</font></span>: 
<font color="Maroon" title="c20">c1</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="conaffm.html#D3" title="CONAFFM:def.3">CONAFFM:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c21">c19</font> = <font color="Maroon" title="c20">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">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><div><span class="lab"><font color="Green" title="E50">A53</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:16_3_2_2"/><span class="lab"><font color="Green" title="E51">A54</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_1"/><span class="lab"><font color="Green" title="E52">A55</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_2_2_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:16_3_2_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:16_3_2_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E16:16"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_3_2_2_1"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:16_3_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E4:16_3_2_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A56</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</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="E5:16_3_2_2_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E6:16_3_2_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</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="E7:16_3_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_3_2"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="txt" href="#E1:16_3_2_2_1"><span class="lab"><font color="Green" title="E52">A55</font></span></a>, <a class="txt" href="#E4:16_3_2_2_1"><span class="lab"><font color="Green" title="E53">A56</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:16_3_2_2"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/><a NAME="E3:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c1</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16_3_2"><span class="lab"><font color="Green" title="E49">A52</font></span></a>, <a class="txt" href="#E1:16_3_2_2"><span class="lab"><font color="Green" title="E51">A54</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E4:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c20">c1</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="E5:16_3_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c20">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="E6:16_3_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c21">c19</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="E7:16_3_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A57</font></span>: 
<font color="Maroon" title="c20">c1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E11:16_3"><span class="lab"><font color="Green" title="E42">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E8:16_3_2_2"/><span class="lab"><font color="Green" title="E53">A58</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c21">c19</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_2"/><span class="lab"><font color="Green" title="E54">A59</font></span>: 
<font color="Maroon" title="c11">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">c19</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_2_2_2_1"/><span class="lab"><font color="Green" title="E55">A60</font></span>: 
<font color="Maroon" title="c11">o9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">c19</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="E2:16_3_2_2_2_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/>
<a NAME="E3:16_3_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:16"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E4:16_3_2"><span class="lab"><font color="Green" title="E47">A50</font></span></a>, <a class="txt" href="#E1:16_3_2_2_2_1"><span class="lab"><font color="Green" title="E55">A60</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:16_3_2_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</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="E5:16_3_2_2_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E6:16_3_2_2_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:16_3_2_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E11:16_3"><span class="lab"><font color="Green" title="E42">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:16_3_2_2_2"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/>
<a NAME="E3:16_3_2_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A61</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:16_3_2_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c21">c19</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="E5:16_3_2_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c21">c19</font>,<font color="Maroon" title="c13">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:16_3_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c13">a29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E7:16_3_2_2"><span class="lab"><font color="Green" title="E52">A57</font></span></a>, <a class="txt" href="#E1:16_3_2_2_2"><span class="lab"><font color="Green" title="E54">A59</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:16_3_2_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E14:16"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E3:16_3_2_2_2"><span class="lab"><font color="Green" title="E55">A61</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E9:16_3_2_2"/><span class="lab"><font color="Green" title="E54">A62</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_3"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_3_2_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A63</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:16_3_2_2_3"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:16_3_2_2_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E13:16"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:16_3_2_2_3"><span class="lab"><font color="Green" title="E55">A63</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="E10:16_3_2_2"/><span class="lab"><font color="Green" title="E55">A64</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">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="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E11:16_3_2_2"/><span class="lab"><font color="Green" title="E56">A65</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_4"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_4"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a>, <a class="txt" href="#E6:16_3"><span class="lab"><font color="Green" title="E39">A35</font></span></a></span>;<br/>
<a NAME="E2:16_3_2_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:16_3_2_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A66</font></span>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:16_3_2_2_4"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:16_3_2_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E10:16_3_2_2"><span class="lab"><font color="Green" title="E55">A64</font></span></a>, <a class="txt" href="#E3:16_3_2_2_4"><span class="lab"><font color="Green" title="E57">A66</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:16_3_2_2_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16_3"><span class="lab"><font color="Green" title="E43">A39</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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><a NAME="E12:16_3_2_2"/>
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_2_2_5"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:16_3_2_2_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a></span>;<br/>
<a NAME="E3:16_3_2_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c4">a2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E4:16_3_2_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E5:16_3_2_2_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A67</font></span>: 
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:16"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E11:16_3_2_2"><span class="lab"><font color="Green" title="E56">A65</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E6:16_3_2_2_5"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_5_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_5_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_3_2_2_5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A68</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:16_3_2_2_5_1"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:16_3_2_2_5_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E14:16"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:16_3_2_2_5_1"><span class="lab"><font color="Green" title="E58">A68</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="E7:16_3_2_2_5"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E5:16_3_2_2_5"><span class="lab"><font color="Green" title="E57">A67</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E8:16_3_2_2_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:16_3_2_2_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a>, <a class="txt" href="#E12:16_3"><span class="lab"><font color="Green" title="E43">A39</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">then </span><span class="kw">consider </span><font color="Maroon" title="c22">c2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E14:16_3_2_2"/><span class="lab"><font color="Green" title="E57">A69</font></span>: 
<font color="Maroon" title="c22">c2</font>,<font color="Maroon" title="c4">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E15:16_3_2_2"/><span class="lab"><font color="Green" title="E58">A70</font></span>: 
<font color="Maroon" title="c22">c2</font>,<font color="Maroon" title="c3">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E16:16_3_2_2"/><span class="lab"><font color="Green" title="E59">A71</font></span>: 
<font color="Maroon" title="c22">c2</font>,<font color="Maroon" title="c6">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="conaffm.html#D3" title="CONAFFM:def.3">CONAFFM:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c23">c29</font> = <font color="Maroon" title="c22">c2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E18:16_3_2_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c20">c1</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E20:16"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E4:16_3_2"><span class="lab"><font color="Green" title="E47">A50</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E19:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">c2</font>,<font color="Maroon" title="c4">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c1</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:16_3_2_2"><span class="lab"><font color="Green" title="E57">A69</font></span></a>, <a class="txt" href="#E9:16_3_2_2"><span class="lab"><font color="Green" title="E54">A62</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E20:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c20">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c22">c2</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="E21:16_3_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A72</font></span>: 
<font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c21">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c23">c29</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="E22:16_3_2_2"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/><a NAME="E23:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">c2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:16_3_2_2"><span class="lab"><font color="Green" title="E55">A64</font></span></a>, <a class="txt" href="#E16:16_3_2_2"><span class="lab"><font color="Green" title="E59">A71</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E24:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c22">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E25:16_3_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c22">c2</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="E26:16_3_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c23">c29</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="E27:16_3_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A73</font></span>: 
<font color="Maroon" title="c23">c29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E1:16_3_2"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E28:16_3_2_2"/><span class="lab"><font color="Green" title="E62">A74</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c23">c29</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_6"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_6"/><span class="lab"><font color="Green" title="E63">A75</font></span>: 
<font color="Maroon" title="c11">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">c29</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_6_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_6_1"/><span class="lab"><font color="Green" title="E64">A76</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_6_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_6_1_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_3_2_2_6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A77</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:16_3_2_2_6_1_1"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:16_3_2_2_6_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E14:16"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:16_3_2_2_6_1_1"><span class="lab"><font color="Green" title="E65">A77</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="E2:16_3_2_2_6_1"/>
<font color="Maroon" title="c11">o9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">c29</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="E3:16_3_2_2_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A78</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E15:16_3_2_2"><span class="lab"><font color="Green" title="E58">A70</font></span></a>, <a class="txt" href="#E1:16_3_2_2_6_1"><span class="lab"><font color="Green" title="E64">A76</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E4:16_3_2_2_6_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/>
<a NAME="E5:16_3_2_2_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:16"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E3:16_3_2_2_6_1"><span class="lab"><font color="Green" title="E65">A78</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E6:16_3_2_2_6_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</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="E7:16_3_2_2_6_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E8:16_3_2_2_6_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:16_3_2_2_6_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E11:16_3"><span class="lab"><font color="Green" title="E42">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:16_3_2_2_6"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/>
<a NAME="E3:16_3_2_2_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A79</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:16_3_2_2_6"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c23">c29</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="E5:16_3_2_2_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c23">c29</font>,<font color="Maroon" title="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:16_3_2_2_6"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E27:16_3_2_2"><span class="lab"><font color="Green" title="E61">A73</font></span></a>, <a class="txt" href="#E1:16_3_2_2_6"><span class="lab"><font color="Green" title="E63">A75</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:16_3_2_2_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E13:16"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E3:16_3_2_2_6"><span class="lab"><font color="Green" title="E64">A79</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="E29:16_3_2_2"/>
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_2_2_7"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:16_3_2_2_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:16_3_2_2_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E10:16_3"><span class="lab"><font color="Green" title="E41">A37</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c24">c3</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E31:16_3_2_2"/><span class="lab"><font color="Green" title="E63">A80</font></span>: 
<font color="Maroon" title="c24">c3</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">and </span><br/><a NAME="E32:16_3_2_2"/><span class="lab"><font color="Green" title="E64">A81</font></span>: 
<font color="Maroon" title="c24">c3</font>,<font color="Maroon" title="c3">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font>
 <span class="kw">and </span><br/><a NAME="E33:16_3_2_2"/><span class="lab"><font color="Green" title="E65">A82</font></span>: 
<font color="Maroon" title="c24">c3</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="conaffm.html#D3" title="CONAFFM:def.3">CONAFFM:def 3</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c25">c39</font> = <font color="Maroon" title="c24">c3</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E35:16_3_2_2"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_8"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_8"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_3_2_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A83</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:16_3_2_2_8"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:16_3_2_2_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E14:16"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:16_3_2_2_8"><span class="lab"><font color="Green" title="E66">A83</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="E36:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c22">c2</font>,<font color="Maroon" title="c3">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E15:16_3_2_2"><span class="lab"><font color="Green" title="E58">A70</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E37:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">c2</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">c3</font>,<font color="Maroon" title="c3">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E32:16_3_2_2"><span class="lab"><font color="Green" title="E64">A81</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E38:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c22">c2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c24">c3</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="E39:16_3_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A84</font></span>: 
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c23">c29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c25">c39</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="E40:16_3_2_2"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c3">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/><a NAME="E41:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">c2</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:16_3_2_2"><span class="lab"><font color="Green" title="E55">A64</font></span></a>, <a class="txt" href="#E16:16_3_2_2"><span class="lab"><font color="Green" title="E59">A71</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E42:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c22">c2</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="E43:16_3_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c22">c2</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="E44:16_3_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c23">c29</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="E45:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">c2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E1:16_3_2"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E46:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c21">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c23">c29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E7:16_3_2_2"><span class="lab"><font color="Green" title="E52">A57</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="E47:16_3_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c21">c19</font>,<font color="Maroon" title="c23">c29</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="E48:16_3_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A85</font></span>: 
<font color="Maroon" title="c20">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">c2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16_3_2_2"><span class="lab"><font color="Green" title="E53">A58</font></span></a>, <a class="txt" href="#E21:16_3_2_2"><span class="lab"><font color="Green" title="E60">A72</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>;<br/><a NAME="E49:16_3_2_2"/><span class="lab"><font color="Green" title="E68">A86</font></span>: 
<font color="Maroon" title="c20">c1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_9"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_9"/><span class="lab"><font color="Green" title="E69">A87</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_9_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_2_9_1"/><span class="lab"><font color="Green" title="E70">A88</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_2_9_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_2_2_9_1_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:16_3_2_2_9_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:16_3_2_2_9_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E16:16"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_3_2_2_9_1"/>
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:16_3_2_2_9_1"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E4:16_3_2_2_9_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A89</font></span>: 
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</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="E5:16_3_2_2_9_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E6:16_3_2_2_9_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</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="E7:16_3_2_2_9_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16_3_2"><span class="lab"><font color="Green" title="E46">A42</font></span></a>, <a class="txt" href="#E1:16_3_2_2_9_1"><span class="lab"><font color="Green" title="E70">A88</font></span></a>, <a class="txt" href="#E4:16_3_2_2_9_1"><span class="lab"><font color="Green" title="E71">A89</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E2:16_3_2_2_9"/><span class="lab"><font color="Green" title="E70">A90</font></span>: 
<font color="Maroon" title="c20">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E3:16_3_2_2_9"/>
<font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:16"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/>
<a NAME="E4:16_3_2_2_9"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16_3_2"><span class="lab"><font color="Green" title="E49">A52</font></span></a>, <a class="txt" href="#E2:16_3_2_2_9"><span class="lab"><font color="Green" title="E70">A90</font></span></a>, <a class="txt" href="#E1:16_3_2_2_9"><span class="lab"><font color="Green" title="E69">A87</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E5:16_3_2_2_9"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E6:16_3_2_2_9"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E7:16_3_2_2_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:16_3_2_2_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E11:16_3"><span class="lab"><font color="Green" title="E42">A38</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="E50:16_3_2_2"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E12:16"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/><a NAME="E51:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c24">c3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:16_3"><span class="lab"><font color="Green" title="E41">A37</font></span></a>, <a class="txt" href="#E33:16_3_2_2"><span class="lab"><font color="Green" title="E65">A82</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E52:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c24">c3</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="E53:16_3_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c24">c3</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="E54:16_3_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c25">c39</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="E55:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c25">c39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c19">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E11:16_3"><span class="lab"><font color="Green" title="E42">A38</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E56:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c23">c29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c25">c39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E27:16_3_2_2"><span class="lab"><font color="Green" title="E61">A73</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="E57:16_3_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c23">c29</font>,<font color="Maroon" title="c25">c39</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="E58:16_3_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">c2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c24">c3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16_3_2_2"><span class="lab"><font color="Green" title="E62">A74</font></span></a>, <a class="txt" href="#E39:16_3_2_2"><span class="lab"><font color="Green" title="E66">A84</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="E59:16_3_2_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:16_3_2"><span class="lab"><font color="Green" title="E48">A51</font></span></a>, <a class="txt" href="#E48:16_3_2_2"><span class="lab"><font color="Green" title="E67">A85</font></span></a>, <a class="txt" href="#E31:16_3_2_2"><span class="lab"><font color="Green" title="E63">A80</font></span></a>, <a class="txt" href="#E49:16_3_2_2"><span class="lab"><font color="Green" title="E68">A86</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</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="16_3_2_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:16_3_2_3"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_3_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A91</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E3:16_3_2_3"/><span class="lab"><font color="Green" title="E52">A92</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">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="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E4:16_3_2_3"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_2_3_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_3_2_3_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_3_2_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A93</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:16_3_2_3_1"/>
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<span class="kw">hence </span><a NAME="E4:16_3_2_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E13:16"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:16_3_2_3_1"><span class="lab"><font color="Green" title="E53">A93</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="E5:16_3_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E20:16"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E3:16_3_2_3"><span class="lab"><font color="Green" title="E52">A92</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E6:16_3_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E7:16_3_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:16"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E11:16"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:16_3_2_3"><span class="lab"><font color="Green" title="E51">A91</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E8:16_3_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">a29</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16_3_2_3"><span class="lab"><font color="Green" title="E52">A92</font></span></a>, <a class="ref" href="aff_1.html#T11" title="AFF_1:th.11">AFF_1:11</a></span>;<br/><span class="kw">hence </span><a NAME="E9:16_3_2_3"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <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="E10:16_3_2"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:16_3_2"><span class="lab"><font color="Green" title="E50">A53</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="16_3_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:16_3_3"/><span class="lab"><font color="Green" title="E46">A94</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</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="E2:16_3_3_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:16_3_3_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a></span>;<br/>
<a NAME="E4:16_3_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A95</font></span>: 
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E5:16_3_3_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a>, <a class="txt" href="#E9:16_3"><span class="lab"><font color="Green" title="E40">A36</font></span></a></span>;<br/>
<a NAME="E6:16_3_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E7:16_3_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E4:16_3_3_1"><span class="lab"><font color="Green" title="E47">A95</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:16_3_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16_3"><span class="lab"><font color="Green" title="E43">A39</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 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><a NAME="E2:16_3_3"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a>, <a class="txt" href="#E3:16_3"><span class="lab"><font color="Green" title="E38">A34</font></span></a></span>;<br/><a NAME="E3:16_3_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A96</font></span>: 
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c2">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="E4:16_3_3"/><span class="lab"><font color="Green" title="E48">A97</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_3_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:16_3_3_2"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a1</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="E2:16_3_3_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:16_3_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:16_3"><span class="lab"><font color="Green" title="E43">A39</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</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="E5:16_3_3"/>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c3">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16_3"><span class="lab"><font color="Green" title="E39">A35</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E6:16_3_3"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16_3_3"><span class="lab"><font color="Green" title="E47">A96</font></span></a>, <a class="txt" href="#E4:16_3_3"><span class="lab"><font color="Green" title="E48">A97</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E7:16_3_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E8:16_3_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:16"><span class="lab"><font color="Green" title="E36">A27</font></span></a></span>;<br/><a NAME="E9:16_3_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A98</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c14">a39</font>,<font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">assume </span><a NAME="E10:16_3_3"/><span class="lab"><font color="Green" title="E50">A99</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E11:16_3_3"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E12:16_3_3"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c13">a29</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="E13:16_3_3"/><span class="kw">then </span>
<font color="Maroon" title="c14">a39</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:16_3_3"><span class="lab"><font color="Green" title="E49">A98</font></span></a>, <a class="txt" href="#E1:16_3_3"><span class="lab"><font color="Green" title="E46">A94</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="E14:16_3_3"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:16"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E10:16_3_3"><span class="lab"><font color="Green" title="E50">A99</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</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="E18:16_3"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:16_3"><span class="lab"><font color="Green" title="E45">A41</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="16_4"><span class="kw">now </span></a><div class="add"><a NAME="E1:16_4"/><span class="lab"><font color="Green" title="E38">A100</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c15">b19</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_4_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:16_4_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:16"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</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="E2:16_4_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A101</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:16_4_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c15">b19</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E4:16_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">b19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c18">M9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E13:16"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:16_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E10:16"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E16:16"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E26:16"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:16_4_1"><span class="lab"><font color="Green" title="E39">A101</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E2:16_4"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:16"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:16"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E9:16"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E24:16"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="aff_1.html#T53" title="AFF_1:th.53">AFF_1:53</a>, <a class="ref" href="aff_1.html#T55" title="AFF_1:th.55">AFF_1:55</a></span>;<br/><a NAME="E3:16_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A102</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><span class="kw">assume </span><a NAME="E4:16_4"/><span class="lab"><font color="Green" title="E40">A103</font></span>: 
<font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font></span><br/><a NAME="E5:16_4"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c6">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:16"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E6:16_4"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><span class="kw">hence </span><a NAME="E7:16_4"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:16"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E4:16_4"><span class="lab"><font color="Green" title="E40">A103</font></span></a>, <a class="txt" href="#E1:16_4"><span class="lab"><font color="Green" title="E38">A100</font></span></a>, <a class="txt" href="#E3:16_4"><span class="lab"><font color="Green" title="E39">A102</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E31:16"/>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a2</font>,<font color="Maroon" title="c8">b3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:16"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E29:16"><span class="lab"><font color="Green" title="E37">A33</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>
