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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V3" title="CONMETR:attr.3">satisfying_MH1</a>  &amp; <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V4" title="CONMETR:attr.4">satisfying_MH2</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="E1:15"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V3" title="CONMETR:attr.3">satisfying_MH1</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V4" title="CONMETR:attr.4">satisfying_MH2</a>  or <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="E2:15"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V4" title="CONMETR:attr.4">satisfying_MH2</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="E3:15"/><span class="lab"><font color="Green" title="E17">A3</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="E4:15"/><span class="lab"><font color="Green" title="E18">A4</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="E5:15"/><span class="lab"><font color="Green" title="E19">A5</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="E6:15"/><span class="lab"><font color="Green" title="E20">A6</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="E7:15"/><span class="lab"><font color="Green" title="E21">A7</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="E8:15"/><span class="lab"><font color="Green" title="E22">A8</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="E9:15"/><span class="lab"><font color="Green" title="E23">A9</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="E10:15"/><span class="lab"><font color="Green" title="E24">A10</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="E11:15"/><span class="lab"><font color="Green" title="E25">A11</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="E12:15"/><span class="lab"><font color="Green" title="E26">A12</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="E13:15"/><span class="lab"><font color="Green" title="E27">A13</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="E14:15"/><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="c3">a1</font>
 <span class="kw">and </span><br/><a NAME="E15:15"/><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="c4">a2</font>
 <span class="kw">and </span><br/><a NAME="E16:15"/>
<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="E17:15"/><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="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E18:15"/>
<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="E19:15"/><span class="lab"><font color="Green" title="E31">A17</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="E20:15"/><span class="lab"><font color="Green" title="E32">A18</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="E21:15"/><span class="lab"><font color="Green" title="E33">A19</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="E24:15"/>
<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="#E13:15"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E25:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A20</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="E26:15"/>
<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="#E13:15"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E27:15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A21</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="E36">A22</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c20">e1</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="E2:15_1"/><span class="lab"><font color="Green" title="E37">A23</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">e1</font>
 <span class="kw">and </span><br/><a NAME="E3:15_1"/><span class="lab"><font color="Green" title="E38">A24</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="c20">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c21">d1</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="E5:15_1"/><span class="lab"><font color="Green" title="E39">A25</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">and </span><br/><a NAME="E6:15_1"/><span class="lab"><font color="Green" title="E40">A26</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="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c22">d19</font> = <font color="Maroon" title="c21">d1</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">consider </span><font color="Maroon" title="c23">e2</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="E9:15_1"/><span class="lab"><font color="Green" title="E41">A27</font></span>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c23">e2</font>
 <span class="kw">and </span><br/><a NAME="E10:15_1"/><span class="lab"><font color="Green" title="E42">A28</font></span>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">e19</font> = <font color="Maroon" title="c20">e1</font>, <font color="Maroon" title="c25">e29</font> = <font color="Maroon" title="c23">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <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><span class="kw">that </span><br/><a NAME="E12:15_1"/><span class="lab"><font color="Green" title="E43">A29</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="c4">a2</font>
 <span class="kw">and </span><br/><a NAME="E13:15_1"/>
<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>
 <span class="kw">and </span><br/><a NAME="E14:15_1"/><span class="lab"><font color="Green" title="E44">A30</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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">d4</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <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="E15:15_1"/><span class="lab"><font color="Green" title="E45">A31</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:15_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E16:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A32</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="c17">b39</font>,<font color="Maroon" title="c22">d19</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="E17:15_1"/>
<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="#E13:15"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E18:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A33</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="E19:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A34</font></span>: 
<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="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:15"><span class="lab"><font color="Green" title="E24">A10</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="E20:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</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>;<br/><a NAME="E21:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A35</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#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E22:15_1"/><span class="lab"><font color="Green" title="E50">A36</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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_1"/><span class="lab"><font color="Green" title="E51">A37</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="c13">a29</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_1_1"/>
<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="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E27:15"><span class="lab"><font color="Green" title="E35">A21</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="E2:15_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A38</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="E3:15_1_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="c13">a29</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="E4:15_1_1_1"/><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="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E17:15"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E25:15"><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="E5:15_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E15:15"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E25:15"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:15_1_1_1"><span class="lab"><font color="Green" title="E52">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>
<span class="kw">assume </span><a NAME="E2:15_1_1"/>
<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"> contradiction</span><br/>

<a NAME="E3:15_1_1"/><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="txt" href="#E6:15"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E11:15"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E20:15"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E21:15"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E4:15_1_1"/><span class="kw">then </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="c6">b1</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/>
<a NAME="E5:15_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A39</font></span>: 
<font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c13">a29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E6:15_1_1"/>
<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="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E27:15"><span class="lab"><font color="Green" title="E35">A21</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="E7:15_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="c13">a29</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/>
<span class="kw">hence </span><a NAME="E8:15_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:15_1"><span class="lab"><font color="Green" title="E43">A29</font></span></a>, <a class="txt" href="#E1:15_1_1"><span class="lab"><font color="Green" title="E51">A37</font></span></a>, <a class="txt" href="#E5:15_1_1"><span class="lab"><font color="Green" title="E52">A39</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="E23:15_1"/><span class="lab"><font color="Green" title="E51">A40</font></span>: 
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="15_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_2"/>
 <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="E2:15_1_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="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="E3:15_1_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="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="E4:15_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:15"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E22:15_1"><span class="lab"><font color="Green" title="E50">A36</font></span></a>, <a class="txt" href="#E18:15_1"><span class="lab"><font color="Green" title="E47">A33</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="E24:15_1"/><span class="lab"><font color="Green" title="E52">A41</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="c8">b3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_3"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:15_1_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="c14">a39</font>,<font color="Maroon" title="c17">b39</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="E3:15_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E25:15_1"/>
<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="#E8:15"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:15"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E18:15_1"><span class="lab"><font color="Green" title="E47">A33</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="E26:15_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="c6">b1</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="E27:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A42</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#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E28:15_1"/>
<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="#E13:15"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/><a NAME="E29:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A43</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/><a NAME="E30:15_1"/><span class="kw">then </span>
<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="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E20">A6</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="E31:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A44</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</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="E32:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A45</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#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E33:15_1"/><span class="lab"><font color="Green" title="E57">A46</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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_4"/>
 <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="E2:15_1_4"/><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="E3:15_1_4"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E11:15"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E14:15_1"><span class="lab"><font color="Green" title="E44">A30</font></span></a>, <a class="txt" href="#E29:15_1"><span class="lab"><font color="Green" title="E54">A43</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="E34:15_1"/><span class="lab"><font color="Green" title="E58">A47</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="c7">b2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_5"/>
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:15_1_5"/><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="E3:15_1_5"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E35:15_1"/><span class="lab"><font color="Green" title="E59">A48</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <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="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E10:15"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E13:15"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/><a NAME="E36:15_1"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c23">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c26">e19</font> = <font color="Maroon" title="c20">e1</font>, <font color="Maroon" title="c27">e29</font> = <font color="Maroon" title="c23">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <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="E2:15_1_6"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c23">e2</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="E3:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c27">e29</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="E4:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c27">e29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c26">e19</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="E5:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c23">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E6:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">e1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="#E9:15_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="txt" href="#E10:15_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E7:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</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="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E3:15_1"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E8:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</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="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E35:15_1"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E9:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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/>
<a NAME="E10:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E11:15_1_6"/><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="c11">o9</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="E12:15_1_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="c17">b39</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="E13:15_1_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A49</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E14:15_1_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="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E15:15_1_6"/><span class="kw">then </span>
<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="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E16:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E17:15_1_6"/><span class="kw">then </span>
<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="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E13:15_1_6"><span class="lab"><font color="Green" title="E60">A49</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E18:15_1_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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:15_1_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E20:15_1_6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A50</font></span>: 
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E21:15_1_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="c14">a39</font>,<font color="Maroon" title="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E22:15_1_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</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/>
<a NAME="E23:15_1_6"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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/>
<a NAME="E24:15_1_6"/><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="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:15"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E20:15_1_6"><span class="lab"><font color="Green" title="E61">A50</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E25:15_1_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</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="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E26:15_1_6"/><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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:15_1_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E37:15_1"/><span class="kw">then </span>
not <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c24">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c25">e29</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">then </span><span class="kw">consider </span><font color="Maroon" title="c26">d29</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E39:15_1"/><span class="lab"><font color="Green" title="E60">A51</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="c24">e19</font>,<font color="Maroon" title="c26">d29</font>
 <span class="kw">and </span><br/><a NAME="E40:15_1"/><span class="lab"><font color="Green" title="E61">A52</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c25">e29</font>,<font color="Maroon" title="c26">d29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c27">d2</font> = <font color="Maroon" title="c26">d29</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E42:15_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c23">e2</font>,<font color="Maroon" title="c27">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:15_1"><span class="lab"><font color="Green" title="E61">A52</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E43:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A53</font></span>: 
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c23">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</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="E44:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A54</font></span>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:15_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="txt" href="#E10:15_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E45:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E64">A55</font></span>: 
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c3">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E46:15_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">e1</font>,<font color="Maroon" title="c27">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:15_1"><span class="lab"><font color="Green" title="E60">A51</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E47:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c20">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</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="E48:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E65">A56</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:15_1"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E3:15_1"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E49:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A57</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="c27">d2</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="E50:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A58</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="c26">d29</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">consider </span><font color="Maroon" title="c28">e1</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="E52:15_1"/><span class="lab"><font color="Green" title="E68">A59</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font>
 <span class="kw">and </span><br/><a NAME="E53:15_1"/><span class="lab"><font color="Green" title="E69">A60</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="c28">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c29">e2</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="E55:15_1"/><span class="lab"><font color="Green" title="E70">A61</font></span>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font>
 <span class="kw">and </span><br/><a NAME="E56:15_1"/><span class="lab"><font color="Green" title="E71">A62</font></span>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c29">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">e19</font> = <font color="Maroon" title="c28">e1</font>, <font color="Maroon" title="c31">e29</font> = <font color="Maroon" title="c29">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <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="E58:15_1"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c32">e19</font> = <font color="Maroon" title="c28">e1</font>, <font color="Maroon" title="c33">e29</font> = <font color="Maroon" title="c29">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <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="E2:15_1_7"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</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="E3:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c32">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c33">e29</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="E4:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c33">e29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c32">e19</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="E5:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E6:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="txt" href="#E55:15_1"><span class="lab"><font color="Green" title="E70">A61</font></span></a>, <a class="txt" href="#E56:15_1"><span class="lab"><font color="Green" title="E71">A62</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E7:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="txt" href="#E52:15_1"><span class="lab"><font color="Green" title="E68">A59</font></span></a>, <a class="txt" href="#E53:15_1"><span class="lab"><font color="Green" title="E69">A60</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E8:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E35:15_1"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E9:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</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="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E10:15_1_7"/><span class="kw">then </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="E11:15_1_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="c17">b39</font>,<font color="Maroon" title="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:15_1_7"/><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="c11">o9</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/>
<a NAME="E13:15_1_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A63</font></span>: 
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E14:15_1_7"/>
 <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="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E15:15_1_7"/><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="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E16:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</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/>
<a NAME="E17:15_1_7"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E13:15_1_7"><span class="lab"><font color="Green" title="E72">A63</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E18:15_1_7"/><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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:15_1_7"/><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="c14">a39</font>,<font color="Maroon" title="c17">b39</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="E20:15_1_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E59:15_1"/><span class="kw">then </span>
not <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c30">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c31">e29</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">then </span><span class="kw">consider </span><font color="Maroon" title="c32">d39</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E61:15_1"/><span class="lab"><font color="Green" title="E72">A64</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="c30">e19</font>,<font color="Maroon" title="c32">d39</font>
 <span class="kw">and </span><br/><a NAME="E62:15_1"/><span class="lab"><font color="Green" title="E73">A65</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c31">e29</font>,<font color="Maroon" title="c32">d39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c33">d3</font> = <font color="Maroon" title="c32">d39</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E64:15_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font>,<font color="Maroon" title="c33">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E62:15_1"><span class="lab"><font color="Green" title="E73">A65</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E65:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A66</font></span>: 
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c29">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</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="E66:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A67</font></span>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:15_1"><span class="lab"><font color="Green" title="E70">A61</font></span></a>, <a class="txt" href="#E56:15_1"><span class="lab"><font color="Green" title="E71">A62</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E67:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</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">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E68:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A68</font></span>: 
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</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">by</span> <span class="lab"><a class="txt" href="#E21:15"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E24:15_1"><span class="lab"><font color="Green" title="E52">A41</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E69:15_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font>,<font color="Maroon" title="c33">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:15_1"><span class="lab"><font color="Green" title="E72">A64</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E70:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c28">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c33">d3</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="E71:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E77">A69</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c33">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:15_1"><span class="lab"><font color="Green" title="E68">A59</font></span></a>, <a class="txt" href="#E53:15_1"><span class="lab"><font color="Green" title="E69">A60</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E72:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A70</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c33">d3</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="E73:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A71</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="c17">b39</font>,<font color="Maroon" title="c32">d39</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">consider </span><font color="Maroon" title="c34">e2</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="E75:15_1"/><span class="lab"><font color="Green" title="E80">A72</font></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="c33">d3</font>,<font color="Maroon" title="c34">e2</font>
 <span class="kw">and </span><br/><a NAME="E76:15_1"/><span class="lab"><font color="Green" title="E81">A73</font></span>: 
<font color="Maroon" title="c33">d3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c34">e2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c35">e1</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="E78:15_1"/><span class="lab"><font color="Green" title="E82">A74</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">e1</font>
 <span class="kw">and </span><br/><a NAME="E79:15_1"/><span class="lab"><font color="Green" title="E83">A75</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="c35">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c36">e19</font> = <font color="Maroon" title="c35">e1</font>, <font color="Maroon" title="c37">e29</font> = <font color="Maroon" title="c34">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <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="E81:15_1"/>
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c34">e2</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">reconsider </span><font color="Maroon" title="c38">e19</font> = <font color="Maroon" title="c35">e1</font>, <font color="Maroon" title="c39">e29</font> = <font color="Maroon" title="c34">e2</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <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="E2:15_1_8"/>
 <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="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:15_1_8"/><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="c11">o9</font>,<font color="Maroon" title="c17">b39</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="E4:15_1_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A76</font></span>: 
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="E5:15_1_8"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c34">e2</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="E6:15_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c38">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">d39</font>,<font color="Maroon" title="c39">e29</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="E7:15_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c32">d39</font>,<font color="Maroon" title="c39">e29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c38">e19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E8:15_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c34">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">e1</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="E9:15_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">e1</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="#E75:15_1"><span class="lab"><font color="Green" title="E80">A72</font></span></a>, <a class="txt" href="#E76:15_1"><span class="lab"><font color="Green" title="E81">A73</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E10:15_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</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="#E78:15_1"><span class="lab"><font color="Green" title="E82">A74</font></span></a>, <a class="txt" href="#E79:15_1"><span class="lab"><font color="Green" title="E83">A75</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E11:15_1_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E85">A77</font></span>: 
<font color="Maroon" title="c2">o</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="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E35:15_1"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E12:15_1_8"/>
 <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="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E13:15_1_8"/><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="c17">b39</font>,<font color="Maroon" title="c16">b29</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="E14:15_1_8"/><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="c8">b3</font>,<font color="Maroon" title="c7">b2</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="E15:15_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</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/>
<a NAME="E16:15_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</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="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E11:15_1_8"><span class="lab"><font color="Green" title="E85">A77</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E17:15_1_8"/><span class="kw">then </span>
<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="c14">a39</font>,<font color="Maroon" title="c16">b29</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="E18:15_1_8"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E19:15_1_8"/><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="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E11:15"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E4:15_1_8"><span class="lab"><font color="Green" title="E84">A76</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E20:15_1_8"/><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="c14">a39</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">hence </span><a NAME="E21:15_1_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E82:15_1"/><span class="kw">then </span>
not <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c36">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c32">d39</font>,<font color="Maroon" title="c37">e29</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">then </span><span class="kw">consider </span><font color="Maroon" title="c38">d49</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E84:15_1"/><span class="lab"><font color="Green" title="E84">A78</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="c36">e19</font>,<font color="Maroon" title="c38">d49</font>
 <span class="kw">and </span><br/><a NAME="E85:15_1"/><span class="lab"><font color="Green" title="E85">A79</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c32">d39</font>,<font color="Maroon" title="c37">e29</font>,<font color="Maroon" title="c38">d49</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c39">d4</font> = <font color="Maroon" title="c38">d49</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E87:15_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c34">e2</font>,<font color="Maroon" title="c39">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E85:15_1"><span class="lab"><font color="Green" title="E85">A79</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E88:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A80</font></span>: 
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c34">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c39">d4</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="E89:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A81</font></span>: 
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c39">d4</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="#E75:15_1"><span class="lab"><font color="Green" title="E80">A72</font></span></a>, <a class="txt" href="#E76:15_1"><span class="lab"><font color="Green" title="E81">A73</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E90:15_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">e1</font>,<font color="Maroon" title="c39">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E84:15_1"><span class="lab"><font color="Green" title="E84">A78</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E91:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c35">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c39">d4</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="E92:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A82</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c39">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E78:15_1"><span class="lab"><font color="Green" title="E82">A74</font></span></a>, <a class="txt" href="#E79:15_1"><span class="lab"><font color="Green" title="E83">A75</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E93:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E89">A83</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="c39">d4</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="E94:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A84</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="c38">d49</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="E95:15_1"/><span class="lab"><font color="Green" title="E91">A85</font></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="c33">d3</font>,<font color="Maroon" title="c39">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E75:15_1"><span class="lab"><font color="Green" title="E80">A72</font></span></a>, <a class="txt" href="#E76:15_1"><span class="lab"><font color="Green" title="E81">A73</font></span></a>, <a class="txt" href="#E88:15_1"><span class="lab"><font color="Green" title="E86">A80</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E96:15_1"/><span class="kw">then </span>
( <font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c39">d4</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> or <font color="Maroon" title="c5">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">b2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:15"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E97:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E92">A86</font></span>: 
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c39">d4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="#E34:15_1"><span class="lab"><font color="Green" title="E58">A47</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E98:15_1"/><span class="lab"><font color="Green" title="E93">A87</font></span>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">o</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_9"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_9"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c21">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E35:15_1"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="txt" href="#E5:15_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E2:15_1_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E94">A88</font></span>: 
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:15_1_9"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</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="E4:15_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="#E9:15_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="txt" href="#E10:15_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="txt" href="#E43:15_1"><span class="lab"><font color="Green" title="E62">A53</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E5:15_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</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="#E6:15_1"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E2:15_1_9"><span class="lab"><font color="Green" title="E94">A88</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E6:15_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E31:15_1"><span class="lab"><font color="Green" title="E55">A44</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E7:15_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c17">b39</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="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E8:15_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</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="E9:15_1_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</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="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:15_1_9"/><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="c17">b39</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="E11:15_1_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E95">A89</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E12:15_1_9"/>
 <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="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E13:15_1_9"/><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="c17">b39</font>,<font color="Maroon" title="c16">b29</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="E14:15_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E15:15_1_9"/><span class="kw">then </span>
<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="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E11:15_1_9"><span class="lab"><font color="Green" title="E95">A89</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E16:15_1_9"/><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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E17:15_1_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E18:15_1_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A90</font></span>: 
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:15_1_9"/>
 <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="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E20:15_1_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</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/>
<a NAME="E21:15_1_9"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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/>
<a NAME="E22:15_1_9"/><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="c12">a19</font>,<font color="Maroon" title="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:15"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E18:15_1_9"><span class="lab"><font color="Green" title="E96">A90</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E23:15_1_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</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="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E24:15_1_9"/><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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:15_1_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E99:15_1"/><span class="lab"><font color="Green" title="E94">A91</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_10"/><span class="lab"><font color="Green" title="E95">A92</font></span>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_10_1"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">d3</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="E2:15_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c26">d29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E71:15_1"><span class="lab"><font color="Green" title="E77">A69</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E3:15_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c26">d29</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="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E4:15_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</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>;<br/>
<a NAME="E5:15_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="#E48:15_1"><span class="lab"><font color="Green" title="E65">A56</font></span></a>, <a class="txt" href="#E98:15_1"><span class="lab"><font color="Green" title="E93">A87</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E6:15_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E7:15_1_10_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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:15_1_10_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="c11">o9</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/>
<a NAME="E9:15_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:15_1_10_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A93</font></span>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</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#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E11:15_1_10_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="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E12:15_1_10_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="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E13:15_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</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/>
<a NAME="E14:15_1_10_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 
<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="E15:15_1_10_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="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E10:15_1_10_1"><span class="lab"><font color="Green" title="E96">A93</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E16:15_1_10_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="E17:15_1_10_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/>
<a NAME="E18:15_1_10_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="c14">a39</font>,<font color="Maroon" title="c17">b39</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="E19:15_1_10_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E2:15_1_10"/><span class="lab"><font color="Green" title="E96">A94</font></span>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_10_2"/>
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">d2</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="E2:15_1_10_2"/><span class="kw">then </span>
<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="c22">d19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:15_1"><span class="lab"><font color="Green" title="E65">A56</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E3:15_1_10_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">d19</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="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E4:15_1_10_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c21">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</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="E5:15_1_10_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="#E5:15_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E6:15_1_10_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E7:15_1_10_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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:15_1_10_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="c11">o9</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/>
<a NAME="E9:15_1_10_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:15_1_10_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A95</font></span>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</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#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E11:15_1_10_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="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E12:15_1_10_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="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E13:15_1_10_2"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</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/>
<a NAME="E14:15_1_10_2"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 
<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="E15:15_1_10_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="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E10:15_1_10_2"><span class="lab"><font color="Green" title="E97">A95</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E16:15_1_10_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="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="E17:15_1_10_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="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/>
<a NAME="E18:15_1_10_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="c14">a39</font>,<font color="Maroon" title="c17">b39</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="E19:15_1_10_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E3:15_1_10"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</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="E4:15_1_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c32">d39</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="E5:15_1_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</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="E6:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c22">d19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c32">d39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E7:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c26">d29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c32">d39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E8:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</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="E9:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="#E44:15_1"><span class="lab"><font color="Green" title="E63">A54</font></span></a>, <a class="txt" href="#E2:15_1_10"><span class="lab"><font color="Green" title="E96">A94</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E10:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c8">b3</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="txt" href="#E66:15_1"><span class="lab"><font color="Green" title="E75">A67</font></span></a>, <a class="txt" href="#E1:15_1_10"><span class="lab"><font color="Green" title="E95">A92</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E11:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E12:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E13:15_1_10"/><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="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/>
<a NAME="E14:15_1_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</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="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E15:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</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="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E16:15_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E97">A96</font></span>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</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="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E17:15_1_10"/><span class="lab"><font color="Green" title="E98">A97</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_10_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_10_3"/>
<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"> contradiction</span><br/>

<a NAME="E2:15_1_10_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="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="E3:15_1_10_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E18:15_1_10"/>
 <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="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E19:15_1_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E20:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E21:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E22:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</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="#E17:15_1_10"><span class="lab"><font color="Green" title="E98">A97</font></span></a>, <a class="txt" href="#E16:15_1_10"><span class="lab"><font color="Green" title="E97">A96</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E23:15_1_10"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</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="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E24:15_1_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</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="E25:15_1_10"/><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="c17">b39</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="E26:15_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E99">A98</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E27:15_1_10"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="#E19:15_1"><span class="lab"><font color="Green" title="E48">A34</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E28:15_1_10"/><span class="kw">then </span>
<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="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E26:15_1_10"><span class="lab"><font color="Green" title="E99">A98</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E29:15_1_10"/><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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E30:15_1_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E31:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E32:15_1_10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E100">A99</font></span>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</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="E33:15_1_10"/>
 <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="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E34:15_1_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</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/>
<a NAME="E35:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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/>
<a NAME="E36:15_1_10"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</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#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E37:15_1_10"/><span class="kw">then </span>
<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="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:15"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E32:15_1_10"><span class="lab"><font color="Green" title="E100">A99</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E38:15_1_10"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</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="E39:15_1_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</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/>
<a NAME="E40:15_1_10"/><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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E41:15_1_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E100:15_1"/><span class="lab"><font color="Green" title="E95">A100</font></span>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c39">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_11"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_11"/><span class="lab"><font color="Green" title="E96">A101</font></span>: 
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_11_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_11_1"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">d3</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="E2:15_1_11_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c32">d39</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="E3:15_1_11_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E99:15_1"><span class="lab"><font color="Green" title="E94">A91</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="E2:15_1_11"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c39">d4</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="E3:15_1_11"/><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="c27">d2</font>,<font color="Maroon" title="c33">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E95:15_1"><span class="lab"><font color="Green" title="E91">A85</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E4:15_1_11"/><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="c8">b3</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E66:15_1"><span class="lab"><font color="Green" title="E75">A67</font></span></a>, <a class="txt" href="#E1:15_1_11"><span class="lab"><font color="Green" title="E96">A101</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E5:15_1_11"/><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="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E6:15_1_11"/><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="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="E7:15_1_11"/><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="c16">b29</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="E8:15_1_11"/><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="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:15_1_11"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:15"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E25:15"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E22:15_1"><span class="lab"><font color="Green" title="E50">A36</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="E101:15_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="c17">b39</font>,<font color="Maroon" title="c17">b39</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/><a NAME="E102:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E96">A102</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</font>,<font color="Maroon" title="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E16:15_1"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="txt" href="#E73:15_1"><span class="lab"><font color="Green" title="E79">A71</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c40">A9</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E104:15_1"/><span class="lab"><font color="Green" title="E97">A103</font></span>: 
<font color="Maroon" title="c40">A9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E105:15_1"/><span class="lab"><font color="Green" title="E98">A104</font></span>: 
<font color="Maroon" title="c22">d19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c40">A9</font>
 <span class="kw">and </span><br/><a NAME="E106:15_1"/><span class="lab"><font color="Green" title="E99">A105</font></span>: 
<font color="Maroon" title="c32">d39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c40">A9</font>
 <span class="kw">and </span><br/><a NAME="E107:15_1"/><span class="lab"><font color="Green" title="E100">A106</font></span>: 
<font color="Maroon" title="c17">b39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c40">A9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c41">A</font> = <font color="Maroon" title="c40">A9</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/><a NAME="E109:15_1"/><span class="lab"><font color="Green" title="E101">A107</font></span>: 
<font color="Maroon" title="c22">d19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c32">d39</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_12"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_12"/>
<font color="Maroon" title="c22">d19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c32">d39</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="E2:15_1_12"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c32">d39</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="E3:15_1_12"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E99:15_1"><span class="lab"><font color="Green" title="E94">A91</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="E110:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c40">A9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E104:15_1"><span class="lab"><font color="Green" title="E97">A103</font></span></a>, <a class="txt" href="#E105:15_1"><span class="lab"><font color="Green" title="E98">A104</font></span></a>, <a class="txt" href="#E106:15_1"><span class="lab"><font color="Green" title="E99">A105</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/><a NAME="E111:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A108</font></span>: 
<font color="Maroon" title="c41">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></span>;<br/><a NAME="E112:15_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="c17">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E113:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A109</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="c17">b39</font>,<font color="Maroon" title="c16">b29</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="E114:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E104">A110</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E16:15_1"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="txt" href="#E73:15_1"><span class="lab"><font color="Green" title="E79">A71</font></span></a>, <a class="txt" href="#E104:15_1"><span class="lab"><font color="Green" title="E97">A103</font></span></a>, <a class="txt" href="#E105:15_1"><span class="lab"><font color="Green" title="E98">A104</font></span></a>, <a class="txt" href="#E106:15_1"><span class="lab"><font color="Green" title="E99">A105</font></span></a>, <a class="txt" href="#E109:15_1"><span class="lab"><font color="Green" title="E101">A107</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E115:15_1"/><span class="lab"><font color="Green" title="E105">A111</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="c33">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_13"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_13"/>
<font color="Maroon" title="c33">d3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</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="E2:15_1_13"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A112</font></span>: 
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="txt" href="#E55:15_1"><span class="lab"><font color="Green" title="E70">A61</font></span></a>, <a class="txt" href="#E56:15_1"><span class="lab"><font color="Green" title="E71">A62</font></span></a>, <a class="txt" href="#E65:15_1"><span class="lab"><font color="Green" title="E74">A66</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E3:15_1_13"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E35:15_1"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="txt" href="#E48:15_1"><span class="lab"><font color="Green" title="E65">A56</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E4:15_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E5:15_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</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="txt" href="#E98:15_1"><span class="lab"><font color="Green" title="E93">A87</font></span></a>, <a class="txt" href="#E2:15_1_13"><span class="lab"><font color="Green" title="E106">A112</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E6:15_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E7:15_1_13"/><span class="kw">then </span><span class="lab"><font color="Green" title="E107">A113</font></span>: 
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E8:15_1_13"/>
 <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="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E9:15_1_13"/><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="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E10:15_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</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/>
<a NAME="E11:15_1_13"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E7:15_1_13"><span class="lab"><font color="Green" title="E107">A113</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E12:15_1_13"/><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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:15_1_13"/><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="c14">a39</font>,<font color="Maroon" title="c17">b39</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="E14:15_1_13"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E116:15_1"/><span class="lab"><font color="Green" title="E106">A114</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="c39">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_14"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_14"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c33">d3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E35:15_1"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="txt" href="#E71:15_1"><span class="lab"><font color="Green" title="E77">A69</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E2:15_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E107">A115</font></span>: 
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c2">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:15_1_14"/>
<font color="Maroon" title="c39">d4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">o</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="E4:15_1_14"/><span class="kw">then </span>
<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c2">o</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="#E75:15_1"><span class="lab"><font color="Green" title="E80">A72</font></span></a>, <a class="txt" href="#E76:15_1"><span class="lab"><font color="Green" title="E81">A73</font></span></a>, <a class="txt" href="#E88:15_1"><span class="lab"><font color="Green" title="E86">A80</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E5:15_1_14"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</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="#E115:15_1"><span class="lab"><font color="Green" title="E105">A111</font></span></a>, <a class="txt" href="#E2:15_1_14"><span class="lab"><font color="Green" title="E107">A115</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E6:15_1_14"/><span class="kw">then </span>
<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="c14">a39</font>,<font color="Maroon" title="c16">b29</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="E7:15_1_14"/><span class="kw">then </span><span class="lab"><font color="Green" title="E108">A116</font></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="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="E8:15_1_14"/>
 <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="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E9:15_1_14"/><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="c11">o9</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="E10:15_1_14"/><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="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="E11:15_1_14"/><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="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E7:15_1_14"><span class="lab"><font color="Green" title="E108">A116</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E12:15_1_14"/><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="c16">b29</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="E13:15_1_14"/><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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E14:15_1_14"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E117:15_1"/><span class="lab"><font color="Green" title="E107">A117</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c39">d4</font>,<font color="Maroon" title="c33">d3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_15"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_15"/><span class="lab"><font color="Green" title="E108">A118</font></span>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c33">d3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_15_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_15_1"/><span class="lab"><font color="Green" title="E109">A119</font></span>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">d2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_15_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_15_1_1"/>
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c27">d2</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="E2:15_1_15_1_1"/><span class="kw">then </span>
<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="c22">d19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:15_1"><span class="lab"><font color="Green" title="E65">A56</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E3:15_1_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">d19</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="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E4:15_1_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c21">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</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="E5:15_1_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="#E5:15_1"><span class="lab"><font color="Green" title="E39">A25</font></span></a>, <a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E6:15_1_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E7:15_1_15_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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E8:15_1_15_1_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="c11">o9</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/>
<a NAME="E9:15_1_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:15_1_15_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A120</font></span>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</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#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E11:15_1_15_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="c16">b29</font>,<font color="Maroon" title="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E12:15_1_15_1_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="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E13:15_1_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</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/>
<a NAME="E14:15_1_15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font>
 
<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="E15:15_1_15_1_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="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E10:15_1_15_1_1"><span class="lab"><font color="Green" title="E110">A120</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E16:15_1_15_1_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="E17:15_1_15_1_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/>
<a NAME="E18:15_1_15_1_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="c14">a39</font>,<font color="Maroon" title="c17">b39</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="E19:15_1_15_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E2:15_1_15_1"/>
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c33">d3</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="E3:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</font>,<font color="Maroon" title="c8">b3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E66:15_1"><span class="lab"><font color="Green" title="E75">A67</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E4:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</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="c8">b3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E44:15_1"><span class="lab"><font color="Green" title="E63">A54</font></span></a>, <a class="txt" href="#E1:15_1_15_1"><span class="lab"><font color="Green" title="E109">A119</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E5:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</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="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="E6:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c12">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E7:15_1_15_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="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/>
<a NAME="E8:15_1_15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</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="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E9:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</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="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:15_1_15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A121</font></span>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</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="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E11:15_1_15_1"/><span class="lab"><font color="Green" title="E111">A122</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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_15_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_15_1_2"/>
<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"> contradiction</span><br/>

<a NAME="E2:15_1_15_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="E3:15_1_15_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E12:15_1_15_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="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E13:15_1_15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E14:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c14">a39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E15:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E16:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</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="#E11:15_1_15_1"><span class="lab"><font color="Green" title="E111">A122</font></span></a>, <a class="txt" href="#E10:15_1_15_1"><span class="lab"><font color="Green" title="E110">A121</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E17:15_1_15_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</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="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E18:15_1_15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</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="E19:15_1_15_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="c17">b39</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="E20:15_1_15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A123</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E21:15_1_15_1"/>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</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="#E19:15_1"><span class="lab"><font color="Green" title="E48">A34</font></span></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E22:15_1_15_1"/><span class="kw">then </span>
<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="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E20:15_1_15_1"><span class="lab"><font color="Green" title="E112">A123</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E23:15_1_15_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="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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E24:15_1_15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c16">b29</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="E25:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E26:15_1_15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A124</font></span>: 
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c7">b2</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="E27:15_1_15_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="c12">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E28:15_1_15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</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/>
<a NAME="E29:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">a19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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/>
<a NAME="E30:15_1_15_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a1</font>,<font color="Maroon" title="c2">o</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#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E31:15_1_15_1"/><span class="kw">then </span>
<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="c3">a1</font>,<font color="Maroon" title="c5">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:15"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E26:15_1_15_1"><span class="lab"><font color="Green" title="E113">A124</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E32:15_1_15_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a1</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="E33:15_1_15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c12">a19</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/>
<a NAME="E34:15_1_15_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>
 
<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="E35:15_1_15_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E2:15_1_15"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c39">d4</font>,<font color="Maroon" title="c33">d3</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="E3:15_1_15"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c38">d49</font>,<font color="Maroon" title="c32">d39</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="E4:15_1_15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E109">A125</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</font>,<font color="Maroon" title="c38">d49</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="E5:15_1_15"/><span class="lab"><font color="Green" title="E110">A126</font></span>: 
<font color="Maroon" title="c16">b29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c17">b39</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_15_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_15_2"/>
<font color="Maroon" title="c16">b29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">b39</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="E2:15_1_15_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="c14">a39</font>,<font color="Maroon" title="c17">b39</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="E3:15_1_15_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E6:15_1_15"/>
 <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="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E7:15_1_15"/><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="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E8:15_1_15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E111">A127</font></span>: 
<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="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:15_1_15"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E16:15_1"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="txt" href="#E73:15_1"><span class="lab"><font color="Green" title="E79">A71</font></span></a>, <a class="txt" href="#E113:15_1"><span class="lab"><font color="Green" title="E103">A109</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></span>;<br/>
<a NAME="E10:15_1_15"/><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="c38">d49</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E102:15_1"><span class="lab"><font color="Green" title="E96">A102</font></span></a>, <a class="txt" href="#E1:15_1_15"><span class="lab"><font color="Green" title="E108">A118</font></span></a>, <a class="txt" href="#E4:15_1_15"><span class="lab"><font color="Green" title="E109">A125</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></span>;<br/>
<a NAME="E11:15_1_15"/><span class="kw">then </span>
<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="c38">d49</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="E12:15_1_15"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c38">d49</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:15_1_15"><span class="lab"><font color="Green" title="E111">A127</font></span></a>, <a class="txt" href="#E5:15_1_15"><span class="lab"><font color="Green" title="E110">A126</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E13:15_1_15"/><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="c11">o9</font>,<font color="Maroon" title="c38">d49</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="E14:15_1_15"/><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="c38">d49</font>,<font color="Maroon" title="c16">b29</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="E15:15_1_15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A128</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c38">d49</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="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E16:15_1_15"/>
<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="c38">d49</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E92:15_1"><span class="lab"><font color="Green" title="E88">A82</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E17:15_1_15"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c38">d49</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="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E18:15_1_15"/><span class="kw">then </span>
<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="c14">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E116:15_1"><span class="lab"><font color="Green" title="E106">A114</font></span></a>, <a class="txt" href="#E15:15_1_15"><span class="lab"><font color="Green" title="E112">A128</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E19:15_1_15"/><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="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/>
<a NAME="E20:15_1_15"/><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="c11">o9</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/>
<a NAME="E21:15_1_15"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A129</font></span>: 
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E22:15_1_15"/>
 <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="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E23:15_1_15"/><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="c11">o9</font>,<font color="Maroon" title="c17">b39</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="E24:15_1_15"/><span class="kw">then </span>
<font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="E25:15_1_15"/><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="c17">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E11:15"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E21:15_1_15"><span class="lab"><font color="Green" title="E113">A129</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E26:15_1_15"/><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="c14">a39</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">hence </span><a NAME="E27:15_1_15"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E118:15_1"/><span class="lab"><font color="Green" title="E108">A130</font></span>: 
not <font color="Maroon" title="c39">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_16"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_16"/>
<font color="Maroon" title="c39">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">A</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="E2:15_1_16"/><span class="kw">then </span>
<font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c38">d49</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E104:15_1"><span class="lab"><font color="Green" title="E97">A103</font></span></a>, <a class="txt" href="#E105:15_1"><span class="lab"><font color="Green" title="E98">A104</font></span></a>, <a class="txt" href="#E106:15_1"><span class="lab"><font color="Green" title="E99">A105</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="E3:15_1_16"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c38">d49</font>,<font color="Maroon" title="c32">d39</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="E4:15_1_16"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E117:15_1"><span class="lab"><font color="Green" title="E107">A117</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="E119:15_1"/><span class="lab"><font color="Green" title="E109">A131</font></span>: 
<font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="txt" href="#E55:15_1"><span class="lab"><font color="Green" title="E70">A61</font></span></a>, <a class="txt" href="#E56:15_1"><span class="lab"><font color="Green" title="E71">A62</font></span></a>, <a class="txt" href="#E65:15_1"><span class="lab"><font color="Green" title="E74">A66</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><span class="kw">take </span><font color="Maroon" title="c42">d4</font> = <font color="Maroon" title="c39">d4</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="E120:15_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="c17">b39</font>,<font color="Maroon" title="c22">d19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:15_1"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E121:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E110">A132</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">d19</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="E122:15_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="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E123:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E111">A133</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c38">d49</font>,<font color="Maroon" title="c12">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E50:15_1"><span class="lab"><font color="Green" title="E67">A58</font></span></a>, <a class="txt" href="#E94:15_1"><span class="lab"><font color="Green" title="E90">A84</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c43">K9</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E125:15_1"/><span class="lab"><font color="Green" title="E112">A134</font></span>: 
<font color="Maroon" title="c43">K9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E126:15_1"/><span class="lab"><font color="Green" title="E113">A135</font></span>: 
<font color="Maroon" title="c26">d29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c43">K9</font>
 <span class="kw">and </span><br/><a NAME="E127:15_1"/><span class="lab"><font color="Green" title="E114">A136</font></span>: 
<font color="Maroon" title="c38">d49</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c43">K9</font>
 <span class="kw">and </span><br/><a NAME="E128:15_1"/><span class="lab"><font color="Green" title="E115">A137</font></span>: 
<font color="Maroon" title="c12">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c43">K9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c44">K</font> = <font color="Maroon" title="c43">K9</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/><a NAME="E130:15_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="c14">a39</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/><a NAME="E131:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E116">A138</font></span>: 
<font color="Maroon" title="c5">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c44">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E50:15_1"><span class="lab"><font color="Green" title="E67">A58</font></span></a>, <a class="txt" href="#E94:15_1"><span class="lab"><font color="Green" title="E90">A84</font></span></a>, <a class="txt" href="#E100:15_1"><span class="lab"><font color="Green" title="E95">A100</font></span></a>, <a class="txt" href="#E125:15_1"><span class="lab"><font color="Green" title="E112">A134</font></span></a>, <a class="txt" href="#E126:15_1"><span class="lab"><font color="Green" title="E113">A135</font></span></a>, <a class="txt" href="#E127:15_1"><span class="lab"><font color="Green" title="E114">A136</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E132:15_1"/>
<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="#E4:15"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E5:15"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E29:15_1"><span class="lab"><font color="Green" title="E54">A43</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="E133:15_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="c4">a2</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="E134:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E117">A139</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#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E135:15_1"/><span class="lab"><font color="Green" title="E118">A140</font></span>: 
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c8">b3</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c42">d4</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c42">d4</font>,<font color="Maroon" title="c4">a2</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_17"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_17"/><span class="lab"><font color="Green" title="E119">A141</font></span>: 
<font color="Maroon" title="c17">b39</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c16">b29</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_17_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_17_1"/>
<font color="Maroon" title="c17">b39</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">b29</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="E2:15_1_17_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="c14">a39</font>,<font color="Maroon" title="c17">b39</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="E3:15_1_17_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:15_1"><span class="lab"><font color="Green" title="E51">A40</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="E2:15_1_17"/>
 <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="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:15_1_17"/><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="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E4:15_1_17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E120">A142</font></span>: 
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:15_1_17"/>
 <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="txt" href="#E27:15_1"><span class="lab"><font color="Green" title="E53">A42</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E6:15_1_17"/><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="c15">b19</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="E7:15_1_17"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <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="E8:15_1_17"/><span class="kw">then </span>
<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:15_1_17"><span class="lab"><font color="Green" title="E120">A142</font></span></a>, <a class="txt" href="#E1:15_1_17"><span class="lab"><font color="Green" title="E119">A141</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E9:15_1_17"/><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="c15">b19</font>,<font color="Maroon" title="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E10:15_1_17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E121">A143</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="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#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E11:15_1_17"/><span class="lab"><font color="Green" title="E122">A144</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="c17">b39</font>,<font color="Maroon" title="c32">d39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E72:15_1"><span class="lab"><font color="Green" title="E78">A70</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E12:15_1_17"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c22">d19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:15_1"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E13:15_1_17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E123">A145</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</font>,<font color="Maroon" title="c15">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E10:15_1_17"><span class="lab"><font color="Green" title="E121">A143</font></span></a>, <a class="txt" href="#E11:15_1_17"><span class="lab"><font color="Green" title="E122">A144</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c45">o9</font> = <font color="Maroon" title="c2">o</font>, <font color="Maroon" title="c46">a19</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c47">a29</font> = <font color="Maroon" title="c4">a2</font>, <font color="Maroon" title="c48">a39</font> = <font color="Maroon" title="c5">a3</font>, <font color="Maroon" title="c49">d29</font> = <font color="Maroon" title="c27">d2</font>, <font color="Maroon" title="c50">d49</font> = <font color="Maroon" title="c42">d4</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="E15:15_1_17"/><span class="lab"><font color="Green" title="E124">A146</font></span>: 
<font color="Maroon" title="c48">a39</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c46">a19</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_17_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_17_2"/>
<font color="Maroon" title="c46">a19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c48">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="E2:15_1_17_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c46">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="E3:15_1_17_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E16:15_1_17"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">o9</font>,<font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c46">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E17:15_1_17"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c46">a19</font>,<font color="Maroon" title="c45">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E18:15_1_17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E125">A147</font></span>: 
<font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c46">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c45">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E19:15_1_17"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c46">a19</font>,<font color="Maroon" title="c47">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E134:15_1"><span class="lab"><font color="Green" title="E117">A139</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E20:15_1_17"/><span class="kw">then </span>
<font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c46">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c47">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="E21:15_1_17"/><span class="kw">then </span>
<font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c47">a29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c45">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:15_1_17"><span class="lab"><font color="Green" title="E125">A147</font></span></a>, <a class="txt" href="#E15:15_1_17"><span class="lab"><font color="Green" title="E124">A146</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E22:15_1_17"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c47">a29</font>,<font color="Maroon" title="c45">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E23:15_1_17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E126">A148</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">o9</font>,<font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c47">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="E24:15_1_17"/><span class="lab"><font color="Green" title="E127">A149</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">o9</font>,<font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c50">d49</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E93:15_1"><span class="lab"><font color="Green" title="E89">A83</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E25:15_1_17"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">o9</font>,<font color="Maroon" title="c48">a39</font>,<font color="Maroon" title="c49">d29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:15_1"><span class="lab"><font color="Green" title="E66">A57</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E26:15_1_17"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c49">d29</font>,<font color="Maroon" title="c50">d49</font>,<font color="Maroon" title="c47">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E23:15_1_17"><span class="lab"><font color="Green" title="E126">A148</font></span></a>, <a class="txt" href="#E24:15_1_17"><span class="lab"><font color="Green" title="E127">A149</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E27:15_1_17"/>
(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c8">b3</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font>,<font color="Maroon" title="c6">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c42">d4</font>,<font color="Maroon" title="c3">a1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c42">d4</font>,<font color="Maroon" title="c4">a2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E102:15_1"><span class="lab"><font color="Green" title="E96">A102</font></span></a>, <a class="txt" href="#E123:15_1"><span class="lab"><font color="Green" title="E111">A133</font></span></a>, <a class="txt" href="#E13:15_1_17"><span class="lab"><font color="Green" title="E123">A145</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="E136:15_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="c17">b39</font>,<font color="Maroon" title="c32">d39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E72:15_1"><span class="lab"><font color="Green" title="E78">A70</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E137:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c17">b39</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c32">d39</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="E138:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">d19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c32">d39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E121:15_1"><span class="lab"><font color="Green" title="E110">A132</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><a NAME="E139:15_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="c22">d19</font>,<font color="Maroon" title="c32">d39</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="E140:15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c32">d39</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="E141:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</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="E142:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c22">d19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</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="E143:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E119">A150</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c21">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</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="E144:15_1"/>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c21">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E121:15_1"><span class="lab"><font color="Green" title="E110">A132</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E145:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c21">d1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <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="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E35:15_1"><span class="lab"><font color="Green" title="E59">A48</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E146:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E120">A151</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:15_1"><span class="lab"><font color="Green" title="E40">A26</font></span></a>, <a class="txt" href="#E143:15_1"><span class="lab"><font color="Green" title="E119">A150</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E147:15_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="c26">d29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E49:15_1"><span class="lab"><font color="Green" title="E66">A57</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E148:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E121">A152</font></span>: 
<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="c26">d29</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="E149:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</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="E150:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E122">A153</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E146:15_1"><span class="lab"><font color="Green" title="E120">A151</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E151:15_1"/><span class="lab"><font color="Green" title="E123">A154</font></span>: 
not <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_18"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_18"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c41">A</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="E2:15_1_18"/><span class="kw">then </span>
<font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c26">d29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c32">d39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E104:15_1"><span class="lab"><font color="Green" title="E97">A103</font></span></a>, <a class="txt" href="#E105:15_1"><span class="lab"><font color="Green" title="E98">A104</font></span></a>, <a class="txt" href="#E106:15_1"><span class="lab"><font color="Green" title="E99">A105</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="E3:15_1_18"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">d19</font>,<font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c32">d39</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="E4:15_1_18"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E99:15_1"><span class="lab"><font color="Green" title="E94">A91</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="E152:15_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="c38">d49</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E93:15_1"><span class="lab"><font color="Green" title="E89">A83</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E153:15_1"/><span class="kw">then </span>
<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="c38">d49</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="E154:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c26">d29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c38">d49</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E148:15_1"><span class="lab"><font color="Green" title="E121">A152</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/><a NAME="E155:15_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="c26">d29</font>,<font color="Maroon" title="c38">d49</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="E156:15_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c38">d49</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="E157:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c11">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c38">d49</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="E158:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c26">d29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c38">d49</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="E159:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c42">d4</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="E160:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E124">A155</font></span>: 
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c42">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E98:15_1"><span class="lab"><font color="Green" title="E93">A87</font></span></a>, <a class="txt" href="#E150:15_1"><span class="lab"><font color="Green" title="E122">A153</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E161:15_1"/>
<font color="Maroon" title="c43">K9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c26">d29</font>,<font color="Maroon" title="c38">d49</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E100:15_1"><span class="lab"><font color="Green" title="E95">A100</font></span></a>, <a class="txt" href="#E125:15_1"><span class="lab"><font color="Green" title="E112">A134</font></span></a>, <a class="txt" href="#E126:15_1"><span class="lab"><font color="Green" title="E113">A135</font></span></a>, <a class="txt" href="#E127:15_1"><span class="lab"><font color="Green" title="E114">A136</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/><a NAME="E162:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c44">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c42">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></span>;<br/><a NAME="E163:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E125">A156</font></span>: 
<font color="Maroon" title="c41">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c44">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E160:15_1"><span class="lab"><font color="Green" title="E124">A155</font></span></a>, <a class="txt" href="#E100:15_1"><span class="lab"><font color="Green" title="E95">A100</font></span></a>, <a class="txt" href="#E109:15_1"><span class="lab"><font color="Green" title="E101">A107</font></span></a>, <a class="txt" href="#E111:15_1"><span class="lab"><font color="Green" title="E102">A108</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c45">d19</font> = <font color="Maroon" title="c21">d1</font>, <font color="Maroon" title="c46">d29</font> = <font color="Maroon" title="c27">d2</font>, <font color="Maroon" title="c47">d39</font> = <font color="Maroon" title="c33">d3</font>, <font color="Maroon" title="c48">d49</font> = <font color="Maroon" title="c42">d4</font>, <font color="Maroon" title="c49">b39</font> = <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c50">a19</font> = <font color="Maroon" title="c3">a1</font>, <font color="Maroon" title="c51">b19</font> = <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c52">a29</font> = <font color="Maroon" title="c4">a2</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="E165:15_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">d19</font>,<font color="Maroon" title="c47">d39</font>,<font color="Maroon" title="c49">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E135:15_1"><span class="lab"><font color="Green" title="E118">A140</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c53">A9</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E167:15_1"/><span class="lab"><font color="Green" title="E126">A157</font></span>: 
<font color="Maroon" title="c53">A9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E168:15_1"/><span class="lab"><font color="Green" title="E127">A158</font></span>: 
<font color="Maroon" title="c45">d19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c53">A9</font>
 <span class="kw">and </span><br/><a NAME="E169:15_1"/><span class="lab"><font color="Green" title="E128">A159</font></span>: 
<font color="Maroon" title="c47">d39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c53">A9</font>
 <span class="kw">and </span><br/><a NAME="E170:15_1"/><span class="lab"><font color="Green" title="E129">A160</font></span>: 
<font color="Maroon" title="c49">b39</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c53">A9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><a NAME="E171:15_1"/><span class="lab"><font color="Green" title="E130">A161</font></span>: 
<font color="Maroon" title="c45">d19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c47">d39</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_19"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_19"/>
<font color="Maroon" title="c45">d19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c47">d39</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="E2:15_1_19"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">d19</font>,<font color="Maroon" title="c46">d29</font>,<font color="Maroon" title="c47">d39</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="E3:15_1_19"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E99:15_1"><span class="lab"><font color="Green" title="E94">A91</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">reconsider </span><font color="Maroon" title="c54">A</font> = <font color="Maroon" title="c53">A9</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/><a NAME="E173:15_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c45">d19</font>,<font color="Maroon" title="c47">d39</font>,<font color="Maroon" title="c51">b19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E135:15_1"><span class="lab"><font color="Green" title="E118">A140</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E174:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E131">A162</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E167:15_1"><span class="lab"><font color="Green" title="E126">A157</font></span></a>, <a class="txt" href="#E168:15_1"><span class="lab"><font color="Green" title="E127">A158</font></span></a>, <a class="txt" href="#E169:15_1"><span class="lab"><font color="Green" title="E128">A159</font></span></a>, <a class="txt" href="#E171:15_1"><span class="lab"><font color="Green" title="E130">A161</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E175:15_1"/><span class="lab"><font color="Green" title="E132">A163</font></span>: 
not <font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_20"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_20"/>
<font color="Maroon" title="c27">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</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="E2:15_1_20"/><span class="kw">then </span>
<font color="Maroon" title="c45">d19</font>,<font color="Maroon" title="c46">d29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c45">d19</font>,<font color="Maroon" title="c47">d39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E167:15_1"><span class="lab"><font color="Green" title="E126">A157</font></span></a>, <a class="txt" href="#E168:15_1"><span class="lab"><font color="Green" title="E127">A158</font></span></a>, <a class="txt" href="#E169:15_1"><span class="lab"><font color="Green" title="E128">A159</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="E3:15_1_20"/><span class="kw">then </span>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</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="E4:15_1_20"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E99:15_1"><span class="lab"><font color="Green" title="E94">A91</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="E176:15_1"/><span class="lab"><font color="Green" title="E133">A164</font></span>: 
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c42">d4</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_21"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_1_21"/>
 <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="c48">d49</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E93:15_1"><span class="lab"><font color="Green" title="E89">A83</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E2:15_1_21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E134">A165</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="c48">d49</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/>
<a NAME="E3:15_1_21"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c48">d49</font>,<font color="Maroon" title="c11">o9</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/>
<a NAME="E4:15_1_21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E135">A166</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c48">d49</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="#E2:15_1_21"><span class="lab"><font color="Green" title="E134">A165</font></span></a>, <a class="ref" href="aff_1.html#T19" title="AFF_1:th.19">AFF_1:19</a></span>;<br/>
<a NAME="E5:15_1_21"/><span class="lab"><font color="Green" title="E136">A167</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="c49">b39</font>,<font color="Maroon" title="c11">o9</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/>
<a NAME="E6:15_1_21"/>
 <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="c49">b39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:15_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E7:15_1_21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E137">A168</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="c49">b39</font>,<font color="Maroon" title="c16">b29</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="E8:15_1_21"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c49">b39</font>,<font color="Maroon" title="c45">d19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:15_1"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E9:15_1_21"/><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="c45">d19</font>,<font color="Maroon" title="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:15"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E5:15_1_21"><span class="lab"><font color="Green" title="E136">A167</font></span></a>, <a class="txt" href="#E7:15_1_21"><span class="lab"><font color="Green" title="E137">A168</font></span></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></span>;<br/>
<a NAME="E10:15_1_21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E138">A169</font></span>: 
<font color="Maroon" title="c11">o9</font>,<font color="Maroon" title="c45">d19</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="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="E11:15_1_21"/>
<font color="Maroon" title="c21">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c42">d4</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="E12:15_1_21"/><span class="kw">then </span>
<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="c16">b29</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E116:15_1"><span class="lab"><font color="Green" title="E106">A114</font></span></a>, <a class="txt" href="#E10:15_1_21"><span class="lab"><font color="Green" title="E138">A169</font></span></a>, <a class="txt" href="#E4:15_1_21"><span class="lab"><font color="Green" title="E135">A166</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E13:15_1_21"/><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="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/>
<a NAME="E14:15_1_21"/><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="c16">b29</font>,<font color="Maroon" title="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E15:15_1_21"/><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="c11">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E16:15_1_21"/><span class="kw">then </span><span class="lab"><font color="Green" title="E139">A170</font></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="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="E17:15_1_21"/>
 <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="c50">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:15_1"><span class="lab"><font color="Green" title="E56">A45</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E18:15_1_21"/><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="c11">o9</font>,<font color="Maroon" title="c50">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="E19:15_1_21"/><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="c50">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="E20:15_1_21"/><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="c50">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E16:15_1_21"><span class="lab"><font color="Green" title="E139">A170</font></span></a>, <a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></span>;<br/>
<a NAME="E21:15_1_21"/><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="c16">b29</font>,<font color="Maroon" title="c50">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="E22:15_1_21"/><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="c50">a19</font>,<font color="Maroon" title="c16">b29</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="E23:15_1_21"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:15_1"><span class="lab"><font color="Green" title="E57">A46</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="E177:15_1"/><span class="lab"><font color="Green" title="E134">A171</font></span>: 
not <font color="Maroon" title="c42">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_22"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_1_22"/>
<font color="Maroon" title="c42">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c54">A</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="E2:15_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c45">d19</font>,<font color="Maroon" title="c48">d49</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c45">d19</font>,<font color="Maroon" title="c47">d39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E167:15_1"><span class="lab"><font color="Green" title="E126">A157</font></span></a>, <a class="txt" href="#E168:15_1"><span class="lab"><font color="Green" title="E127">A158</font></span></a>, <a class="txt" href="#E169:15_1"><span class="lab"><font color="Green" title="E128">A159</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="E3:15_1_22"/><span class="kw">then </span>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c42">d4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</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="E4:15_1_22"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E117:15_1"><span class="lab"><font color="Green" title="E107">A117</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="E178:15_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c46">d29</font>,<font color="Maroon" title="c48">d49</font>,<font color="Maroon" title="c50">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E135:15_1"><span class="lab"><font color="Green" title="E118">A140</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c55">K9</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E180:15_1"/><span class="lab"><font color="Green" title="E135">A172</font></span>: 
<font color="Maroon" title="c55">K9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a> 
 <span class="kw">and </span><br/><a NAME="E181:15_1"/><span class="lab"><font color="Green" title="E136">A173</font></span>: 
<font color="Maroon" title="c46">d29</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">K9</font>
 <span class="kw">and </span><br/><a NAME="E182:15_1"/><span class="lab"><font color="Green" title="E137">A174</font></span>: 
<font color="Maroon" title="c48">d49</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">K9</font>
 <span class="kw">and </span><br/><a NAME="E183:15_1"/><span class="lab"><font color="Green" title="E138">A175</font></span>: 
<font color="Maroon" title="c50">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c55">K9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c56">K</font> = <font color="Maroon" title="c55">K9</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/><a NAME="E185:15_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c46">d29</font>,<font color="Maroon" title="c48">d49</font>,<font color="Maroon" title="c52">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E135:15_1"><span class="lab"><font color="Green" title="E118">A140</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E186:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E139">A176</font></span>: 
<font color="Maroon" title="c4">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c56">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E100:15_1"><span class="lab"><font color="Green" title="E95">A100</font></span></a>, <a class="txt" href="#E180:15_1"><span class="lab"><font color="Green" title="E135">A172</font></span></a>, <a class="txt" href="#E181:15_1"><span class="lab"><font color="Green" title="E136">A173</font></span></a>, <a class="txt" href="#E182:15_1"><span class="lab"><font color="Green" title="E137">A174</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E187:15_1"/>
<font color="Maroon" title="c55">K9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c46">d29</font>,<font color="Maroon" title="c48">d49</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E100:15_1"><span class="lab"><font color="Green" title="E95">A100</font></span></a>, <a class="txt" href="#E180:15_1"><span class="lab"><font color="Green" title="E135">A172</font></span></a>, <a class="txt" href="#E181:15_1"><span class="lab"><font color="Green" title="E136">A173</font></span></a>, <a class="txt" href="#E182:15_1"><span class="lab"><font color="Green" title="E137">A174</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/><a NAME="E188:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E140">A177</font></span>: 
<font color="Maroon" title="c56">K</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c27">d2</font>,<font color="Maroon" title="c42">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></span>;<br/><a NAME="E189:15_1"/>
<font color="Maroon" title="c53">A9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c45">d19</font>,<font color="Maroon" title="c47">d39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E167:15_1"><span class="lab"><font color="Green" title="E126">A157</font></span></a>, <a class="txt" href="#E168:15_1"><span class="lab"><font color="Green" title="E127">A158</font></span></a>, <a class="txt" href="#E169:15_1"><span class="lab"><font color="Green" title="E128">A159</font></span></a>, <a class="txt" href="#E171:15_1"><span class="lab"><font color="Green" title="E130">A161</font></span></a>, <a class="ref" href="aff_1.html#T38" title="AFF_1:th.38">AFF_1:38</a></span>;<br/><a NAME="E190:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c54">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analmetr.html#K4" title="ANALMETR:func.4">Line</a> <font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c33">d3</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T56" title="ANALMETR:th.56">ANALMETR:56</a></span>;<br/><a NAME="E191:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c54">A</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c56">K</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E160:15_1"><span class="lab"><font color="Green" title="E124">A155</font></span></a>, <a class="txt" href="#E100:15_1"><span class="lab"><font color="Green" title="E95">A100</font></span></a>, <a class="txt" href="#E171:15_1"><span class="lab"><font color="Green" title="E130">A161</font></span></a>, <a class="txt" href="#E188:15_1"><span class="lab"><font color="Green" title="E140">A177</font></span></a>, <a class="ref" href="analmetr.html#T63" title="ANALMETR:th.63">ANALMETR:63</a></span>;<br/><a NAME="E192:15_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E141">A178</font></span>: 
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c42">d4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c4">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:15"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E68:15_1"><span class="lab"><font color="Green" title="E76">A68</font></span></a>, <a class="txt" href="#E97:15_1"><span class="lab"><font color="Green" title="E92">A86</font></span></a>, <a class="txt" href="#E45:15_1"><span class="lab"><font color="Green" title="E64">A55</font></span></a>, <a class="txt" href="#E168:15_1"><span class="lab"><font color="Green" title="E127">A158</font></span></a>, <a class="txt" href="#E169:15_1"><span class="lab"><font color="Green" title="E128">A159</font></span></a>, <a class="txt" href="#E170:15_1"><span class="lab"><font color="Green" title="E129">A160</font></span></a>, <a class="txt" href="#E181:15_1"><span class="lab"><font color="Green" title="E136">A173</font></span></a>, <a class="txt" href="#E182:15_1"><span class="lab"><font color="Green" title="E137">A174</font></span></a>, <a class="txt" href="#E183:15_1"><span class="lab"><font color="Green" title="E138">A175</font></span></a>, <a class="txt" href="#E175:15_1"><span class="lab"><font color="Green" title="E132">A163</font></span></a>, <a class="txt" href="#E177:15_1"><span class="lab"><font color="Green" title="E134">A171</font></span></a>, <a class="txt" href="#E174:15_1"><span class="lab"><font color="Green" title="E131">A162</font></span></a>, <a class="txt" href="#E186:15_1"><span class="lab"><font color="Green" title="E139">A176</font></span></a>, <a class="ref" href="conmetr.html#D3" target="_self" title="CONMETR:def.3">Def3</a></span>;<br/><a NAME="E193:15_1"/>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c27">d2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</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="#E9:15_1"><span class="lab"><font color="Green" title="E41">A27</font></span></a>, <a class="txt" href="#E10:15_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="txt" href="#E43:15_1"><span class="lab"><font color="Green" title="E62">A53</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E194:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c21">d1</font>,<font color="Maroon" title="c42">d4</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">by</span> <span class="lab"><a class="txt" href="#E2:15"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E119:15_1"><span class="lab"><font color="Green" title="E109">A131</font></span></a>, <a class="txt" href="#E89:15_1"><span class="lab"><font color="Green" title="E87">A81</font></span></a>, <a class="txt" href="#E105:15_1"><span class="lab"><font color="Green" title="E98">A104</font></span></a>, <a class="txt" href="#E106:15_1"><span class="lab"><font color="Green" title="E99">A105</font></span></a>, <a class="txt" href="#E107:15_1"><span class="lab"><font color="Green" title="E100">A106</font></span></a>, <a class="txt" href="#E126:15_1"><span class="lab"><font color="Green" title="E113">A135</font></span></a>, <a class="txt" href="#E127:15_1"><span class="lab"><font color="Green" title="E114">A136</font></span></a>, <a class="txt" href="#E128:15_1"><span class="lab"><font color="Green" title="E115">A137</font></span></a>, <a class="txt" href="#E151:15_1"><span class="lab"><font color="Green" title="E123">A154</font></span></a>, <a class="txt" href="#E118:15_1"><span class="lab"><font color="Green" title="E108">A130</font></span></a>, <a class="txt" href="#E163:15_1"><span class="lab"><font color="Green" title="E125">A156</font></span></a>, <a class="txt" href="#E114:15_1"><span class="lab"><font color="Green" title="E104">A110</font></span></a>, <a class="txt" href="#E131:15_1"><span class="lab"><font color="Green" title="E116">A138</font></span></a>, <a class="ref" href="conmetr.html#D4" target="_self" title="CONMETR:def.4">Def4</a></span>;<br/><a NAME="E195:15_1"/><span class="kw">then </span>
( <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="c8">b3</font>,<font color="Maroon" title="c4">a2</font> or <font color="Maroon" title="c21">d1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c42">d4</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E192:15_1"><span class="lab"><font color="Green" title="E141">A178</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E196:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c50">a19</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c49">b39</font>,<font color="Maroon" title="c52">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E176:15_1"><span class="lab"><font color="Green" title="E133">A164</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E197:15_1"/><span class="kw">then </span>
<font color="Maroon" title="c50">a19</font>,<font color="Maroon" title="c16">b29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c52">a29</font>,<font color="Maroon" title="c49">b39</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><span class="kw">hence </span><a NAME="E198:15_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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2"><span class="kw">now </span></a><div class="add"><div><span class="lab"><font color="Green" title="E37">A179</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_1"><span class="kw">now </span></a><div class="add"><a NAME="E1:15_2_1"/>
<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="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:15"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E25:15"><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="E2:15_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A180</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="E3:15_2_1"/><span class="lab"><font color="Green" title="E39">A181</font></span>: 
<font color="Maroon" title="c3">a1</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"> <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="E4:15_2_1"/>
<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="15_2_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:15_2_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="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:15"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E27:15"><span class="lab"><font color="Green" title="E35">A21</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="E2:15_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A182</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="E3:15_2_1_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="E4:15_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E14:15"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E25:15"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:15_2_1_1"><span class="lab"><font color="Green" title="E40">A182</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="E5:15_2_1"/><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="#E20:15"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E21:15"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E3:15_2_1"><span class="lab"><font color="Green" title="E39">A181</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E6:15_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="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="E7:15_2_1"/><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="#E3:15"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E6:15"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E11:15"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E27:15"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E2:15_2_1"><span class="lab"><font color="Green" title="E38">A180</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="E8:15_2_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="#E3:15_2_1"><span class="lab"><font color="Green" title="E39">A181</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="E9:15_2_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><div><span class="lab"><font color="Green" title="E38">A183</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:15_2_2"/><span class="lab"><font color="Green" title="E39">A184</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="15_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_2_2_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="E2:15_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="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="E3:15_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E17:15"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E25:15"><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>; <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="E2:15_2_2"/>
<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="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E10:15"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E25:15"><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="E3:15_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A185</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="E4:15_2_2"/><span class="lab"><font color="Green" title="E41">A186</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="E5:15_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</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="#E21:15"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/><a NAME="E6:15_2_2"/><span class="kw">then </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="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="E7:15_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="#E20:15"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E4:15_2_2"><span class="lab"><font color="Green" title="E41">A186</font></span></a>, <a class="txt" href="#E1:15_2_2"><span class="lab"><font color="Green" title="E39">A184</font></span></a>, <a class="txt" href="#E3:15_2_2"><span class="lab"><font color="Green" title="E40">A185</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><div><span class="lab"><font color="Green" title="E39">A187</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="15_2_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:15_2_3"/><span class="lab"><font color="Green" title="E40">A188</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="15_2_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:15_2_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="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="E2:15_2_3_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="E3:15_2_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E12:15"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E17:15"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E25:15"><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>; <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="E2:15_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="#E7:15"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:15"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E9:15"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E25:15"><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="E3:15_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E41">A189</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="E4:15_2_3"/><span class="lab"><font color="Green" title="E42">A190</font></span>: 
<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"> <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="E5:15_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c5">a3</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="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:15"><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="E6:15_2_3"/><span class="kw">then </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="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E7:15_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">a2</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="c7">b2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:15"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="txt" href="#E4:15_2_3"><span class="lab"><font color="Green" title="E42">A190</font></span></a>, <a class="txt" href="#E1:15_2_3"><span class="lab"><font color="Green" title="E40">A188</font></span></a>, <a class="txt" href="#E3:15_2_3"><span class="lab"><font color="Green" title="E41">A189</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>;<br/><span class="kw">hence </span><a NAME="E8:15_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#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">assume </span><a NAME="E4:15_2"/>
( <font color="Maroon" title="c3">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a2</font> or <font color="Maroon" title="c4">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a3</font> or <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/><span class="kw">hence </span><a NAME="E5:15_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="#E1:15_2"><span class="lab"><font color="Green" title="E37">A179</font></span></a>, <a class="txt" href="#E3:15_2"><span class="lab"><font color="Green" title="E39">A187</font></span></a>, <a class="txt" href="#E2:15_2"><span class="lab"><font color="Green" title="E38">A183</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E30:15"/>
<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="#E28:15"><span class="lab"><font color="Green" title="E36">A22</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>
