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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>  implies <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V7" title="CONMETR:attr.7">satisfying_OSCH</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:10"/><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"> <font color="Maroon" title="c1">X</font> is  <a href="conmetr.html#V7" title="CONMETR:attr.7">satisfying_OSCH</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">a1</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#D7" target="_self" title="CONMETR:def.7">CONMETR:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">a2</font>, <font color="Olive" title="b2">a3</font>, <font color="Olive" title="b3">a4</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">b2</font>, <font color="Olive" title="b6">b3</font>, <font color="Olive" title="b7">b4</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="b8">M</font>, <font color="Olive" title="b9">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="Olive" title="b8">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Olive" title="b9">N</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</font> &amp; <font color="Olive" title="b2">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</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">M</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">M</font> &amp; <font color="Olive" title="b1">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; <font color="Olive" title="b3">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">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="b9">N</font> &amp; <font color="Olive" title="b7">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; not <font color="Olive" title="b3">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</font> &amp; not <font color="Olive" title="b1">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</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="b8">M</font> &amp; not <font color="Olive" title="b7">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b8">M</font> &amp; not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; not <font color="Olive" title="b2">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; not <font color="Olive" title="b4">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; not <font color="Olive" title="b6">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b9">N</font> &amp; <font color="Olive" title="b2">a3</font>,<font color="Olive" title="b1">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b3</font>,<font color="Olive" title="b5">b2</font> &amp; <font color="Olive" title="b1">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b5">b2</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Olive" title="b3">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b7">b4</font> holds <br/><font color="Olive" title="b2">a3</font>,<font color="Olive" title="b3">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Olive" title="b6">b3</font>,<font color="Olive" title="b7">b4</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c5">a4</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">b2</font>, <font color="Maroon" title="c8">b3</font>, <font color="Maroon" title="c9">b4</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="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">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">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="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">M</font> &amp; <font color="Maroon" title="c8">b3</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">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c5">a4</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="c9">b4</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="c5">a4</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="c3">a2</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="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="c9">b4</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="c2">a1</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="c4">a3</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="c6">b1</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="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</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> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</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> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> holds <br/><font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><span class="kw">let </span><font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c11">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="c10">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</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">M</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">M</font> &amp; <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">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="c11">N</font> &amp; <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</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="c10">M</font> &amp; not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font> &amp; not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font> &amp; <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</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> &amp; <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</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> &amp; <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> implies <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font> )</span><br/>



















<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:10"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
<font color="Maroon" title="c10">M</font> <a href="analmetr.html#R10" title="ANALMETR:pred.10">_|_</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E3:10"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E4:10"/><span class="lab"><font color="Green" title="E18">A4</font></span>: 
<font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E5:10"/><span class="lab"><font color="Green" title="E19">A5</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">M</font>
 <span class="kw">and </span><br/><a NAME="E6:10"/><span class="lab"><font color="Green" title="E20">A6</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">M</font>
 <span class="kw">and </span><br/><a NAME="E7:10"/><span class="lab"><font color="Green" title="E21">A7</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E8:10"/><span class="lab"><font color="Green" title="E22">A8</font></span>: 
<font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E9:10"/><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="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E10:10"/><span class="lab"><font color="Green" title="E24">A10</font></span>: 
<font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E11:10"/><span class="lab"><font color="Green" title="E25">A11</font></span>: 
not <font color="Maroon" title="c5">a4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E12:10"/><span class="lab"><font color="Green" title="E26">A12</font></span>: 
not <font color="Maroon" title="c3">a2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E13:10"/><span class="lab"><font color="Green" title="E27">A13</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="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E14:10"/><span class="lab"><font color="Green" title="E28">A14</font></span>: 
not <font color="Maroon" title="c9">b4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E15:10"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
not <font color="Maroon" title="c2">a1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E16:10"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
not <font color="Maroon" title="c4">a3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E17:10"/><span class="lab"><font color="Green" title="E31">A17</font></span>: 
not <font color="Maroon" title="c6">b1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E18:10"/>
not <font color="Maroon" title="c8">b3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E19:10"/><span class="lab"><font color="Green" title="E32">A18</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</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">and </span><br/><a NAME="E20:10"/><span class="lab"><font color="Green" title="E33">A19</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</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">and </span><br/><a NAME="E21:10"/><span class="lab"><font color="Green" title="E34">A20</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</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="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c12">M9</font> = <font color="Maroon" title="c10">M</font>, <font color="Maroon" title="c13">N9</font> = <font color="Maroon" title="c11">N</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T57" title="ANALMETR:th.57">ANALMETR:57</a></span>;<br/>
<a NAME="E23:10"/>
<font color="Maroon" title="c11">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="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E24:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A21</font></span>: 
<font color="Maroon" title="c13">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/>
<span class="kw">reconsider </span><font color="Maroon" title="c14">b49</font> = <font color="Maroon" title="c9">b4</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>, <font color="Maroon" title="c18">a19</font> = <font color="Maroon" title="c2">a1</font>, <font color="Maroon" title="c19">a29</font> = <font color="Maroon" title="c3">a2</font>, <font color="Maroon" title="c20">a39</font> = <font color="Maroon" title="c4">a3</font>, <font color="Maroon" title="c21">a49</font> = <font color="Maroon" title="c5">a4</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="E26:10"/>
<font color="Maroon" title="c10">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="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="analmetr.html#T62" title="ANALMETR:th.62">ANALMETR:62</a></span>;<br/>
<a NAME="E27:10"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A22</font></span>: 
<font color="Maroon" title="c12">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="E28:10"/>
not <font color="Maroon" title="c12">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">N9</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_1"/>
<font color="Maroon" title="c12">M9</font> <a href="aff_1.html#R4" title="AFF_1:pred.4">//</a> <font color="Maroon" title="c13">N9</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="E2:10_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">M</font> <a href="analmetr.html#R9" title="ANALMETR:pred.9">//</a> <font color="Maroon" title="c11">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T64" title="ANALMETR:th.64">ANALMETR:64</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:10_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="analmetr.html#T73" title="ANALMETR:th.73">ANALMETR:73</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E29:10"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">o9</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> st <br/>( <font color="Olive" title="b1">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M9</font> &amp; <font color="Olive" title="b1">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">N9</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T72" title="AFF_1:th.72">AFF_1:72</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c22">o</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E31:10"/><span class="lab"><font color="Green" title="E37">A23</font></span>: 
<font color="Maroon" title="c22">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">and </span><br/><a NAME="E32:10"/><span class="lab"><font color="Green" title="E38">A24</font></span>: 
<font color="Maroon" title="c22">o</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c23">o9</font> = <font color="Maroon" title="c22">o</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E39">A25</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:10_2"/><span class="lab"><font color="Green" title="E40">A26</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="c9">b4</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="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><div><span class="lab"><font color="Green" title="E41">A27</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">consider </span><font color="Maroon" title="c24">e19</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="E2:10_2_1"/><span class="lab"><font color="Green" title="E42">A28</font></span>: 
<font color="Maroon" title="c23">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c24">e19</font>
 <span class="kw">and </span><br/><a NAME="E3:10_2_1"/><span class="lab"><font color="Green" title="E43">A29</font></span>: 
<font color="Maroon" title="c24">e19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c25">e1</font> = <font color="Maroon" title="c24">e19</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="E5:10_2_1"/>
 ex <font color="Olive" title="b1">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> st <br/>( <font color="Maroon" title="c23">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">d49</font> &amp; <font color="Olive" title="b1">d49</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">N9</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></span>;<br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">d4</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="E7:10_2_1"/><span class="lab"><font color="Green" title="E44">A30</font></span>: 
<font color="Maroon" title="c26">d4</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">and </span><br/><a NAME="E8:10_2_1"/><span class="lab"><font color="Green" title="E45">A31</font></span>: 
<font color="Maroon" title="c26">d4</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c22">o</font>
 ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c27">d49</font> = <font color="Maroon" title="c26">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/><span class="kw">consider </span><font color="Maroon" title="c28">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="E11:10_2_1"/><span class="lab"><font color="Green" title="E46">A32</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c26">d4</font>,<font color="Maroon" title="c28">e2</font>
 <span class="kw">and </span><br/><a NAME="E12:10_2_1"/><span class="lab"><font color="Green" title="E47">A33</font></span>: 
<font color="Maroon" title="c28">e2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d4</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="c29">e29</font> = <font color="Maroon" title="c28">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="E14:10_2_1"/><span class="lab"><font color="Green" title="E48">A34</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E15:10_2_1"/>
not <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c24">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d49</font>,<font color="Maroon" title="c29">e29</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:10_2_1_1"/><span class="lab"><font color="Green" title="E49">A35</font></span>: 
<font color="Maroon" title="c21">a49</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c19">a29</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_2_1_1_1"/>
<font color="Maroon" title="c21">a49</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c19">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="E2:10_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:10"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E3:10_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</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="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E20:10"><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="E4:10_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E5:10_2_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</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="E6:10_2_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">b49</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/>
<a NAME="E7:10_2_1_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">b49</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/>
<span class="kw">hence </span><a NAME="E8:10_2_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:10"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E17:10"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:10_2"><span class="lab"><font color="Green" title="E40">A26</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="E2:10_2_1_1"/><span class="lab"><font color="Green" title="E50">A36</font></span>: 
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">a3</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_2_1_1_2"/>
<font color="Maroon" title="c2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">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="E2:10_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</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="txt" href="#E20:10"><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="E3:10_2_1_1_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="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E19:10"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E4:10_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E5:10_2_1_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="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="E6:10_2_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E7:10_2_1_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b19</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/>
<span class="kw">hence </span><a NAME="E8:10_2_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E14:10_2_1"><span class="lab"><font color="Green" title="E48">A34</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">assume </span><a NAME="E3:10_2_1_1"/>
<font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c24">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c27">d49</font>,<font color="Maroon" title="c29">e29</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="E4:10_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d4</font>,<font color="Maroon" title="c28">e2</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="E5:10_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A37</font></span>: 
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:10_2_1"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="txt" href="#E12:10_2_1"><span class="lab"><font color="Green" title="E47">A33</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E6:10_2_1_1"/>
<font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c24">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">a19</font>,<font color="Maroon" title="c20">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E31:10"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E3:10_2_1"><span class="lab"><font color="Green" title="E43">A29</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="E7:10_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">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="E8:10_2_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A38</font></span>: 
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_2_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="txt" href="#E5:10_2_1_1"><span class="lab"><font color="Green" title="E51">A37</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E9:10_2_1_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/>
<a NAME="E10:10_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:10_2_1_1"><span class="lab"><font color="Green" title="E52">A38</font></span></a>, <a class="txt" href="#E2:10_2_1_1"><span class="lab"><font color="Green" title="E50">A36</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E11:10_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c2">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="E12:10_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">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="E13:10_2_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">a49</font>,<font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c18">a19</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="E14:10_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:10_2_1_1"><span class="lab"><font color="Green" title="E49">A35</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c30">d19</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="E17:10_2_1"/><span class="lab"><font color="Green" title="E49">A39</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c24">e19</font>,<font color="Maroon" title="c30">d19</font>
 <span class="kw">and </span><br/><a NAME="E18:10_2_1"/><span class="lab"><font color="Green" title="E50">A40</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c27">d49</font>,<font color="Maroon" title="c29">e29</font>,<font color="Maroon" title="c30">d19</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="c31">d1</font> = <font color="Maroon" title="c30">d19</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/><span class="kw">consider </span><font color="Maroon" title="c32">e19</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="E21:10_2_1"/><span class="lab"><font color="Green" title="E51">A41</font></span>: 
<font color="Maroon" title="c23">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c32">e19</font>
 <span class="kw">and </span><br/><a NAME="E22:10_2_1"/><span class="lab"><font color="Green" title="E52">A42</font></span>: 
<font color="Maroon" title="c32">e19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">N9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></span>;<br/><a NAME="E23:10_2_1"/><span class="lab"><font color="Green" title="E53">A43</font></span>: 
<font color="Maroon" title="c31">d1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E31:10"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E2:10_2_1"><span class="lab"><font color="Green" title="E42">A28</font></span></a>, <a class="txt" href="#E3:10_2_1"><span class="lab"><font color="Green" title="E43">A29</font></span></a>, <a class="txt" href="#E17:10_2_1"><span class="lab"><font color="Green" title="E49">A39</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E24:10_2_1"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c26">d4</font>,<font color="Maroon" title="c28">e2</font>,<font color="Maroon" title="c31">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:10_2_1"><span class="lab"><font color="Green" title="E50">A40</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E25:10_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c26">d4</font>,<font color="Maroon" title="c28">e2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d4</font>,<font color="Maroon" title="c31">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E26:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A44</font></span>: 
<font color="Maroon" title="c31">d1</font>,<font color="Maroon" title="c26">d4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">d4</font>,<font color="Maroon" title="c28">e2</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="E27:10_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c31">d1</font>,<font color="Maroon" title="c26">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:10_2_1"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="txt" href="#E12:10_2_1"><span class="lab"><font color="Green" title="E47">A33</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E28:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A45</font></span>: 
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c31">d1</font>,<font color="Maroon" title="c26">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E11:10"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E21:10"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c33">e1</font> = <font color="Maroon" title="c32">e19</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/><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="E31:10_2_1"/><span class="lab"><font color="Green" title="E56">A46</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c31">d1</font>,<font color="Maroon" title="c34">e2</font>
 <span class="kw">and </span><br/><a NAME="E32:10_2_1"/><span class="lab"><font color="Green" title="E57">A47</font></span>: 
<font color="Maroon" title="c34">e2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c31">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="c35">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="E34:10_2_1"/>
not <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c32">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c35">e29</font>,<font color="Maroon" title="c30">d19</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1_2"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:10_2_1_2"/><span class="lab"><font color="Green" title="E58">A48</font></span>: 
<font color="Maroon" title="c18">a19</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c20">a39</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_2_1_2_1"/>
<font color="Maroon" title="c18">a19</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c20">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="E2:10_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</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="txt" href="#E20:10"><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="E3:10_2_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E19:10"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E4:10_2_1_2_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#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E5:10_2_1_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="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="E6:10_2_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c17">b39</font>,<font color="Maroon" title="c15">b19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E7:10_2_1_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b19</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/>
<span class="kw">hence </span><a NAME="E8:10_2_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E14:10_2_1"><span class="lab"><font color="Green" title="E48">A34</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="E2:10_2_1_2"/>
<font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c32">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c21">a49</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E32:10"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E22:10_2_1"><span class="lab"><font color="Green" title="E52">A42</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="E3:10_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A49</font></span>: 
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c33">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</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="E4:10_2_1_2"/><span class="lab"><font color="Green" title="E60">A50</font></span>: 
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">a4</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_2_1_2_2"/>
<font color="Maroon" title="c3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">a4</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="E2:10_2_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:10"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E3:10_2_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</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="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E20:10"><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="E4:10_2_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E5:10_2_1_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</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="E6:10_2_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">b49</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/>
<a NAME="E7:10_2_1_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">b49</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/>
<span class="kw">hence </span><a NAME="E8:10_2_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:10"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E17:10"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:10_2"><span class="lab"><font color="Green" title="E40">A26</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="E5:10_2_1_2"/>
<font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c32">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c35">e29</font>,<font color="Maroon" title="c30">d19</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="E6:10_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A51</font></span>: 
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c33">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c34">e2</font>,<font color="Maroon" title="c31">d1</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="E7:10_2_1_2"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c34">e2</font>,<font color="Maroon" title="c31">d1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:10_2_1"><span class="lab"><font color="Green" title="E56">A46</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E8:10_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c33">e1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:10_2_1"><span class="lab"><font color="Green" title="E57">A47</font></span></a>, <a class="txt" href="#E6:10_2_1_2"><span class="lab"><font color="Green" title="E61">A51</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E9:10_2_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A52</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:10_2_1"><span class="lab"><font color="Green" title="E51">A41</font></span></a>, <a class="txt" href="#E3:10_2_1_2"><span class="lab"><font color="Green" title="E59">A49</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E10:10_2_1_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/>
<a NAME="E11:10_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:10_2_1_2"><span class="lab"><font color="Green" title="E62">A52</font></span></a>, <a class="txt" href="#E4:10_2_1_2"><span class="lab"><font color="Green" title="E60">A50</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E12:10_2_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</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="E13:10_2_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">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="E14:10_2_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">a19</font>,<font color="Maroon" title="c20">a39</font>,<font color="Maroon" title="c19">a29</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:10_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E1:10_2_1_2"><span class="lab"><font color="Green" title="E58">A48</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c36">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="E36:10_2_1"/><span class="lab"><font color="Green" title="E58">A53</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c32">e19</font>,<font color="Maroon" title="c36">d29</font>
 <span class="kw">and </span><br/><a NAME="E37:10_2_1"/><span class="lab"><font color="Green" title="E59">A54</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c35">e29</font>,<font color="Maroon" title="c30">d19</font>,<font color="Maroon" title="c36">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="c37">d2</font> = <font color="Maroon" title="c36">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="E39:10_2_1"/><span class="lab"><font color="Green" title="E60">A55</font></span>: 
<font color="Maroon" title="c37">d2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E32:10"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E21:10_2_1"><span class="lab"><font color="Green" title="E51">A41</font></span></a>, <a class="txt" href="#E22:10_2_1"><span class="lab"><font color="Green" title="E52">A42</font></span></a>, <a class="txt" href="#E36:10_2_1"><span class="lab"><font color="Green" title="E58">A53</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E40:10_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c30">d19</font>,<font color="Maroon" title="c36">d29</font>,<font color="Maroon" title="c35">e29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E37:10_2_1"><span class="lab"><font color="Green" title="E59">A54</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E41:10_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c31">d1</font>,<font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c34">e2</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="E42:10_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c31">d1</font>,<font color="Maroon" title="c37">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c31">d1</font>,<font color="Maroon" title="c34">e2</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="E43:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A56</font></span>: 
<font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c31">d1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c34">e2</font>,<font color="Maroon" title="c31">d1</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="E44:10_2_1"/><span class="lab"><font color="Green" title="E62">A57</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c34">e2</font>,<font color="Maroon" title="c31">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:10_2_1"><span class="lab"><font color="Green" title="E56">A46</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E45:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A58</font></span>: 
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c31">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:10_2_1"><span class="lab"><font color="Green" title="E57">A47</font></span></a>, <a class="txt" href="#E43:10_2_1"><span class="lab"><font color="Green" title="E61">A56</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><span class="kw">consider </span><font color="Maroon" title="c38">e19</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="E47:10_2_1"/><span class="lab"><font color="Green" title="E64">A59</font></span>: 
<font color="Maroon" title="c23">o9</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c38">e19</font>
 <span class="kw">and </span><br/><a NAME="E48:10_2_1"/><span class="lab"><font color="Green" title="E65">A60</font></span>: 
<font color="Maroon" title="c38">e19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c12">M9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="ref" href="aff_1.html#T32" title="AFF_1:th.32">AFF_1:32</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c39">e1</font> = <font color="Maroon" title="c38">e19</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/><span class="kw">consider </span><font color="Maroon" title="c40">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="E51:10_2_1"/><span class="lab"><font color="Green" title="E66">A61</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c40">e2</font>
 <span class="kw">and </span><br/><a NAME="E52:10_2_1"/><span class="lab"><font color="Green" title="E67">A62</font></span>: 
<font color="Maroon" title="c40">e2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c37">d2</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="c41">e29</font> = <font color="Maroon" title="c40">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="E54:10_2_1"/>
not <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c38">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c41">e29</font>,<font color="Maroon" title="c36">d29</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1_3"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:10_2_1_3"/><span class="lab"><font color="Green" title="E68">A63</font></span>: 
<font color="Maroon" title="c19">a29</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c21">a49</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_2_1_3_1"/>
<font color="Maroon" title="c19">a29</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c21">a49</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="E2:10_2_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:10"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E3:10_2_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</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="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E20:10"><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="E4:10_2_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E5:10_2_1_3_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c9">b4</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="E6:10_2_1_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c15">b19</font>,<font color="Maroon" title="c14">b49</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/>
<a NAME="E7:10_2_1_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">b29</font>,<font color="Maroon" title="c14">b49</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/>
<span class="kw">hence </span><a NAME="E8:10_2_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:10"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E17:10"><span class="lab"><font color="Green" title="E31">A17</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:10_2"><span class="lab"><font color="Green" title="E40">A26</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="E2:10_2_1_3"/>
<font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c38">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c41">e29</font>,<font color="Maroon" title="c36">d29</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="E3:10_2_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c39">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c40">e2</font>,<font color="Maroon" title="c37">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="E4:10_2_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c39">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c40">e2</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="E5:10_2_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A64</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c39">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:10_2_1"><span class="lab"><font color="Green" title="E66">A61</font></span></a>, <a class="txt" href="#E52:10_2_1"><span class="lab"><font color="Green" title="E67">A62</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E6:10_2_1_3"/>
<font color="Maroon" title="c22">o</font>,<font color="Maroon" title="c39">e1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E31:10"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E48:10_2_1"><span class="lab"><font color="Green" title="E65">A60</font></span></a>, <a class="ref" href="analmetr.html#T78" title="ANALMETR:th.78">ANALMETR:78</a></span>;<br/>
<a NAME="E7:10_2_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E47:10_2_1"><span class="lab"><font color="Green" title="E64">A59</font></span></a>, <a class="txt" href="#E5:10_2_1_3"><span class="lab"><font color="Green" title="E69">A64</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E8:10_2_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></span>;<br/>
<a NAME="E9:10_2_1_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c5">a4</font>,<font color="Maroon" title="c4">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="E10:10_2_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c21">a49</font>,<font color="Maroon" title="c20">a39</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E11:10_2_1_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E16:10"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E1:10_2_1_3"><span class="lab"><font color="Green" title="E68">A63</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c42">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="E56:10_2_1"/><span class="lab"><font color="Green" title="E68">A65</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c38">e19</font>,<font color="Maroon" title="c42">d39</font>
 <span class="kw">and </span><br/><a NAME="E57:10_2_1"/><span class="lab"><font color="Green" title="E69">A66</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c41">e29</font>,<font color="Maroon" title="c36">d29</font>,<font color="Maroon" title="c42">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="c43">d3</font> = <font color="Maroon" title="c42">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="E59:10_2_1"/><span class="lab"><font color="Green" title="E70">A67</font></span>: 
<font color="Maroon" title="c43">d3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c10">M</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E31:10"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E47:10_2_1"><span class="lab"><font color="Green" title="E64">A59</font></span></a>, <a class="txt" href="#E48:10_2_1"><span class="lab"><font color="Green" title="E65">A60</font></span></a>, <a class="txt" href="#E56:10_2_1"><span class="lab"><font color="Green" title="E68">A65</font></span></a>, <a class="ref" href="aff_1.html#T39" title="AFF_1:th.39">AFF_1:39</a></span>;<br/><a NAME="E60:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A68</font></span>: 
<font color="Maroon" title="c43">d3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c26">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E31:10"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E32:10"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="txt" href="#E7:10_2_1"><span class="lab"><font color="Green" title="E44">A30</font></span></a>, <a class="txt" href="#E8:10_2_1"><span class="lab"><font color="Green" title="E45">A31</font></span></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</a></span>;<br/><a NAME="E61:10_2_1"/>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c2">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c31">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:10_2_1"><span class="lab"><font color="Green" title="E57">A47</font></span></a>, <a class="txt" href="#E43:10_2_1"><span class="lab"><font color="Green" title="E61">A56</font></span></a>, <a class="txt" href="#E44:10_2_1"><span class="lab"><font color="Green" title="E62">A57</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E62:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A69</font></span>: 
<font color="Maroon" title="c7">b2</font>,<font color="Maroon" title="c6">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c31">d1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E20:10"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E63:10_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c36">d29</font>,<font color="Maroon" title="c42">d39</font>,<font color="Maroon" title="c41">e29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:10_2_1"><span class="lab"><font color="Green" title="E69">A66</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E64:10_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c43">d3</font>,<font color="Maroon" title="c40">e2</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="E65:10_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c43">d3</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c40">e2</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="E66:10_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c43">d3</font>,<font color="Maroon" title="c37">d2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c37">d2</font>,<font color="Maroon" title="c40">e2</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="E67:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A70</font></span>: 
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c3">a2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c43">d3</font>,<font color="Maroon" title="c37">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:10_2_1"><span class="lab"><font color="Green" title="E66">A61</font></span></a>, <a class="txt" href="#E52:10_2_1"><span class="lab"><font color="Green" title="E67">A62</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E68:10_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c7">b2</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c43">d3</font>,<font color="Maroon" title="c37">d2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E19:10"><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="E69:10_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A71</font></span>: 
<font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c43">d3</font>,<font color="Maroon" title="c26">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E6:10"><span class="lab"><font color="Green" title="E20">A6</font></span></a>, <a class="txt" href="#E9:10"><span class="lab"><font color="Green" title="E23">A9</font></span></a>, <a class="txt" href="#E10:10"><span class="lab"><font color="Green" title="E24">A10</font></span></a>, <a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E14:10"><span class="lab"><font color="Green" title="E28">A14</font></span></a>, <a class="txt" href="#E7:10_2_1"><span class="lab"><font color="Green" title="E44">A30</font></span></a>, <a class="txt" href="#E23:10_2_1"><span class="lab"><font color="Green" title="E53">A43</font></span></a>, <a class="txt" href="#E39:10_2_1"><span class="lab"><font color="Green" title="E60">A55</font></span></a>, <a class="txt" href="#E59:10_2_1"><span class="lab"><font color="Green" title="E70">A67</font></span></a>, <a class="txt" href="#E28:10_2_1"><span class="lab"><font color="Green" title="E55">A45</font></span></a>, <a class="txt" href="#E62:10_2_1"><span class="lab"><font color="Green" title="E72">A69</font></span></a>, <a class="ref" href="conmetr.html#D3" target="_self" title="CONMETR:def.3">Def3</a></span>;<br/><a NAME="E70:10_2_1"/>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c31">d1</font>,<font color="Maroon" title="c26">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:10_2_1"><span class="lab"><font color="Green" title="E46">A32</font></span></a>, <a class="txt" href="#E12:10_2_1"><span class="lab"><font color="Green" title="E47">A33</font></span></a>, <a class="txt" href="#E26:10_2_1"><span class="lab"><font color="Green" title="E54">A44</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E71:10_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c43">d3</font>,<font color="Maroon" title="c26">d4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E2:10"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E11:10"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E7:10_2_1"><span class="lab"><font color="Green" title="E44">A30</font></span></a>, <a class="txt" href="#E23:10_2_1"><span class="lab"><font color="Green" title="E53">A43</font></span></a>, <a class="txt" href="#E39:10_2_1"><span class="lab"><font color="Green" title="E60">A55</font></span></a>, <a class="txt" href="#E45:10_2_1"><span class="lab"><font color="Green" title="E63">A58</font></span></a>, <a class="txt" href="#E67:10_2_1"><span class="lab"><font color="Green" title="E73">A70</font></span></a>, <a class="txt" href="#E59:10_2_1"><span class="lab"><font color="Green" title="E70">A67</font></span></a>, <a class="ref" href="conmetr.html#D3" target="_self" title="CONMETR:def.3">Def3</a></span>;<br/><span class="kw">hence </span><a NAME="E72:10_2_1"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E60:10_2_1"><span class="lab"><font color="Green" title="E71">A68</font></span></a>, <a class="txt" href="#E69:10_2_1"><span class="lab"><font color="Green" title="E74">A71</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_2"><span class="kw">now </span></a><div class="add"><a NAME="E1:10_2_2"/><span class="lab"><font color="Green" title="E42">A72</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c18">a19</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_2_2_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c18">a19</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:10_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c19">a29</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c18">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="E3:10_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E12:10"><span class="lab"><font color="Green" title="E26">A12</font></span></a>, <a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E31:10"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E32:10"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="ref" href="aff_1.html#T62" title="AFF_1:th.62">AFF_1:62</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="E2:10_2_2"/><span class="lab"><font color="Green" title="E43">A73</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c18">a19</font>,<font color="Maroon" title="c20">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E4:10"><span class="lab"><font color="Green" title="E18">A4</font></span></a>, <a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E31:10"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><span class="kw">assume </span><a NAME="E3:10_2_2"/><span class="lab"><font color="Green" title="E44">A74</font></span>: 
<font color="Maroon" title="c6">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">b3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E4:10_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c3">a2</font>,<font color="Maroon" title="c4">a3</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="txt" href="#E19:10"><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="E5:10_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A75</font></span>: 
<font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c20">a39</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="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E6:10_2_2"/>
<font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c18">a19</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="#E20:10"><span class="lab"><font color="Green" title="E33">A19</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E7:10_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c18">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">a29</font>,<font color="Maroon" title="c20">a39</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E5:10_2_2"><span class="lab"><font color="Green" title="E45">A75</font></span></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></span>;<br/><span class="kw">hence </span><a NAME="E8:10_2_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:10"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E3:10_2_2"><span class="lab"><font color="Green" title="E44">A74</font></span></a>, <a class="txt" href="#E1:10_2_2"><span class="lab"><font color="Green" title="E42">A72</font></span></a>, <a class="txt" href="#E2:10_2_2"><span class="lab"><font color="Green" title="E43">A73</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E4:10_2"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:10_2"><span class="lab"><font color="Green" title="E41">A27</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3"><span class="kw">now </span></a><div class="add"><a NAME="E1:10_3"/><span class="lab"><font color="Green" title="E40">A76</font></span>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c18">a19</font>,<font color="Maroon" title="c21">a49</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="10_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:10_3_1"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c18">a19</font>,<font color="Maroon" title="c21">a49</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="E2:10_3_1"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">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> st <br/>( <font color="Olive" title="b1">A9</font> is  <a href="aff_1.html#V1" title="AFF_1:attr.1">being_line</a>  &amp; <font color="Maroon" title="c23">o9</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A9</font> &amp; <font color="Maroon" title="c18">a19</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">A9</font> &amp; <font color="Maroon" title="c21">a49</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">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">hence </span><a NAME="E3:10_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:10"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="txt" href="#E11:10"><span class="lab"><font color="Green" title="E25">A11</font></span></a>, <a class="txt" href="#E15:10"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E27:10"><span class="lab"><font color="Green" title="E36">A22</font></span></a>, <a class="txt" href="#E31:10"><span class="lab"><font color="Green" title="E37">A23</font></span></a>, <a class="txt" href="#E32:10"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="ref" href="aff_1.html#T30" title="AFF_1:th.30">AFF_1:30</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="E2:10_3"/><span class="lab"><font color="Green" title="E41">A77</font></span>: 
<font color="Maroon" title="c7">b2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">b4</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="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font></span><br/><a NAME="E3:10_3"/>
<font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c7">b2</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:10"><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="E4:10_3"/><span class="kw">then </span>
<font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a1</font>,<font color="Maroon" title="c3">a2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:10"><span class="lab"><font color="Green" title="E19">A5</font></span></a>, <a class="txt" href="#E13:10"><span class="lab"><font color="Green" title="E27">A13</font></span></a>, <a class="txt" href="#E21:10"><span class="lab"><font color="Green" title="E34">A20</font></span></a>, <a class="txt" href="#E2:10_3"><span class="lab"><font color="Green" title="E41">A77</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/><a NAME="E5:10_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A78</font></span>: 
<font color="Maroon" title="c18">a19</font>,<font color="Maroon" title="c21">a49</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">a19</font>,<font color="Maroon" title="c19">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E6:10_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c23">o9</font>,<font color="Maroon" title="c21">a49</font>,<font color="Maroon" title="c19">a29</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:10"><span class="lab"><font color="Green" title="E21">A7</font></span></a>, <a class="txt" href="#E8:10"><span class="lab"><font color="Green" title="E22">A8</font></span></a>, <a class="txt" href="#E24:10"><span class="lab"><font color="Green" title="E35">A21</font></span></a>, <a class="txt" href="#E32:10"><span class="lab"><font color="Green" title="E38">A24</font></span></a>, <a class="ref" href="aff_1.html#T33" title="AFF_1:th.33">AFF_1:33</a></span>;<br/><span class="kw">hence </span><a NAME="E7:10_3"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:10"><span class="lab"><font color="Green" title="E32">A18</font></span></a>, <a class="txt" href="#E2:10_3"><span class="lab"><font color="Green" title="E41">A77</font></span></a>, <a class="txt" href="#E5:10_3"><span class="lab"><font color="Green" title="E42">A78</font></span></a>, <a class="txt" href="#E1:10_3"><span class="lab"><font color="Green" title="E40">A76</font></span></a>, <a class="ref" href="aff_1.html#T23" title="AFF_1:th.23">AFF_1:23</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E36:10"/>
<font color="Maroon" title="c4">a3</font>,<font color="Maroon" title="c5">a4</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">b3</font>,<font color="Maroon" title="c9">b4</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:10"><span class="lab"><font color="Green" title="E39">A25</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>
