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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   <a href="analmetr.html#NM2" title="ANALMETR:NM.2">OrtAfPl</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</a>  implies <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V4" title="CONAFFM:attr.4">satisfying_ODES</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:6"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V4" title="CONAFFM:attr.4">satisfying_ODES</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">o</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="conaffm.html#D4" target="_self" title="CONAFFM:def.4">CONAFFM:def 4</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">a</font>, <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">b1</font>, <font color="Olive" title="b5">c</font>, <font color="Olive" title="b6">c1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>  st <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b2">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b5">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b6">c1</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b4">b1</font> &amp; <font color="Olive" title="b1">a</font>,<font color="Olive" title="b5">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b2">a1</font>,<font color="Olive" title="b6">c1</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">a</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b1">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Olive" title="b3">b</font> holds <br/><font color="Olive" title="b3">b</font>,<font color="Olive" title="b5">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Olive" title="b4">b1</font>,<font color="Olive" title="b6">c1</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">a1</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">b1</font>, <font color="Maroon" title="c7">c</font>, <font color="Maroon" title="c8">c1</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font> &amp; <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> &amp; not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> implies <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font> )</span><br/>













<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:6"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c4">a1</font>
 <span class="kw">and </span><br/><a NAME="E3:6"/><span class="lab"><font color="Green" title="E7">A3</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E4:6"/><span class="lab"><font color="Green" title="E8">A4</font></span>: 
<font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">and </span><br/><a NAME="E5:6"/><span class="lab"><font color="Green" title="E9">A5</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c6">b1</font>
 <span class="kw">and </span><br/><a NAME="E6:6"/><span class="lab"><font color="Green" title="E10">A6</font></span>: 
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c4">a1</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">and </span><br/><a NAME="E7:6"/><span class="lab"><font color="Green" title="E11">A7</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c7">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font>
 <span class="kw">and </span><br/><a NAME="E8:6"/><span class="lab"><font color="Green" title="E12">A8</font></span>: 
not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font></span><br/>

<a NAME="E9:6"/><span class="lab"><font color="Green" title="E13">A9</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V6" title="CONAFFM:attr.6">satisfying_LIN1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="conaffm.html#T3" target="_self" title="CONAFFM:th.3">Th3</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">o</font>, <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c11">a1</font>, <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c15">c1</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"> ( <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</a>  &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> implies <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> )</span><br/><span class="kw">assume </span><a NAME="E1:6_1"/><span class="lab"><font color="Green" title="E14">A10</font></span>: 
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</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="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> implies <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:6_1"/><span class="lab"><font color="Green" title="E15">A11</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">and </span><br/><a NAME="E3:6_1"/><span class="lab"><font color="Green" title="E16">A12</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E4:6_1"/><span class="lab"><font color="Green" title="E17">A13</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">and </span><br/><a NAME="E5:6_1"/><span class="lab"><font color="Green" title="E18">A14</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E6:6_1"/><span class="lab"><font color="Green" title="E19">A15</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">and </span><br/><a NAME="E7:6_1"/><span class="lab"><font color="Green" title="E20">A16</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">and </span><br/><a NAME="E8:6_1"/><span class="lab"><font color="Green" title="E21">A17</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> implies <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> )</span><br/><span class="kw">assume </span><a NAME="E9:6_1"/><span class="lab"><font color="Green" title="E22">A18</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</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="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c16">a9</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c17">a19</font> = <font color="Maroon" title="c11">a1</font>, <font color="Maroon" title="c18">b9</font> = <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c19">b19</font> = <font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c20">c9</font> = <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c21">c19</font> = <font color="Maroon" title="c15">c1</font>, <font color="Maroon" title="c22">o9</font> = <font color="Maroon" title="c9">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="E23">A19</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:6_1_1"/><span class="lab"><font color="Green" title="E24">A20</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E2:6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A21</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E3:6_1_1"/><span class="lab"><font color="Green" title="E26">A22</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E4:6_1_1"/>
not <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_1_1"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1_1"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_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="c18">b9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:6_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="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E5:6_1_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</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="E6:6_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A23</font></span>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_1"><span class="lab"><font color="Green" title="E25">A21</font></span></a>, <a class="txt" href="#E3:6_1_1"><span class="lab"><font color="Green" title="E26">A22</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E6:6_1_1"/><span class="lab"><font color="Green" title="E28">A24</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E1:6_1_1"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E7:6_1_1"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E8:6_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A25</font></span>: 
( <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font> or <font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">c1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1_1"><span class="lab"><font color="Green" title="E28">A24</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E9:6_1_1"/>
not <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_1_2"/>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1_1"><span class="lab"><font color="Green" title="E24">A20</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_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="c20">c9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:6_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="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E5:6_1_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</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="E6:6_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E10:6_1_1"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1_1"><span class="lab"><font color="Green" title="E27">A23</font></span></a>, <a class="txt" href="#E8:6_1_1"><span class="lab"><font color="Green" title="E29">A25</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E24">A26</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_1_2"/><span class="lab"><font color="Green" title="E25">A27</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E2:6_1_2"/><span class="lab"><font color="Green" title="E26">A28</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E3:6_1_2"/><span class="lab"><font color="Green" title="E27">A29</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><a NAME="E4:6_1_2"/><span class="lab"><font color="Green" title="E28">A30</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_2_1"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</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/>
<a NAME="E3:6_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</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="E4:6_1_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:6_1_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:6_1_2"/><span class="lab"><font color="Green" title="E29">A31</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_2_2"/><span class="lab"><font color="Green" title="E30">A32</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_2_2"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E3:6_1_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E2:6_1_2"><span class="lab"><font color="Green" title="E26">A28</font></span></a>, <a class="txt" href="#E1:6_1_2_2"><span class="lab"><font color="Green" title="E30">A32</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:6_1_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E5:6_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">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</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="E6:6_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="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E7:6_1_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:6_1_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:6_1_2"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1_2"><span class="lab"><font color="Green" title="E25">A27</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E7:6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E3:6_1_2"><span class="lab"><font color="Green" title="E27">A29</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E8:6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E4:6_1_2"><span class="lab"><font color="Green" title="E28">A30</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E9:6_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E10:6_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E11:6_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E12:6_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</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="E13:6_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A33</font></span>: 
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E14:6_1_2"/>
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E15:6_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A34</font></span>: 
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1_2"><span class="lab"><font color="Green" title="E29">A31</font></span></a>, <a class="txt" href="#E13:6_1_2"><span class="lab"><font color="Green" title="E30">A33</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E16:6_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1_2"><span class="lab"><font color="Green" title="E25">A27</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E17:6_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">b9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E18:6_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E19:6_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><span class="kw">hence </span><a NAME="E20:6_1_2"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_1_2"><span class="lab"><font color="Green" title="E27">A29</font></span></a>, <a class="txt" href="#E15:6_1_2"><span class="lab"><font color="Green" title="E31">A34</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E25">A35</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_1_3"/><span class="lab"><font color="Green" title="E26">A36</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E2:6_1_3"/>
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E3:6_1_3"/><span class="lab"><font color="Green" title="E27">A37</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E4:6_1_3"/><span class="lab"><font color="Green" title="E28">A38</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_3_1"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</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/>
<a NAME="E3:6_1_3_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E4:6_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">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:6_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="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:6_1_3_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:6_1_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:6_1_3"/><span class="lab"><font color="Green" title="E29">A39</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_3_2"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</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/>
<a NAME="E3:6_1_3_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E4:6_1_3_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:6_1_3_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:6_1_3_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:6_1_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:6_1_3"/><span class="lab"><font color="Green" title="E30">A40</font></span>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E8:6_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="txt" href="#E3:6_1_3"><span class="lab"><font color="Green" title="E27">A37</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E7:6_1_3"/>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1_3"><span class="lab"><font color="Green" title="E26">A36</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E8:6_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E5:6_1_3"><span class="lab"><font color="Green" title="E29">A39</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E9:6_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E4:6_1_3"><span class="lab"><font color="Green" title="E28">A38</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E10:6_1_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E11:6_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E12:6_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">b19</font>,<font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E13:6_1_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</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="E14:6_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A41</font></span>: 
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E15:6_1_3"/>
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c11">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E16:6_1_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A42</font></span>: 
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1_3"><span class="lab"><font color="Green" title="E30">A40</font></span></a>, <a class="txt" href="#E14:6_1_3"><span class="lab"><font color="Green" title="E31">A41</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E17:6_1_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1_3"><span class="lab"><font color="Green" title="E26">A36</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E18:6_1_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E19:6_1_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</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="E20:6_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><span class="kw">hence </span><a NAME="E21:6_1_3"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1_3"><span class="lab"><font color="Green" title="E29">A39</font></span></a>, <a class="txt" href="#E16:6_1_3"><span class="lab"><font color="Green" title="E32">A42</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="6_1_4"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_1_4"/><span class="lab"><font color="Green" title="E26">A43</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E2:6_1_4"/><span class="lab"><font color="Green" title="E27">A44</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E3:6_1_4"/><span class="lab"><font color="Green" title="E28">A45</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E4:6_1_4"/><span class="lab"><font color="Green" title="E29">A46</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_1"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</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/>
<a NAME="E3:6_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</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="E4:6_1_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:6_1_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:6_1_4"/><span class="lab"><font color="Green" title="E30">A47</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_2"/><span class="lab"><font color="Green" title="E31">A48</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_4_2"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E3:6_1_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="txt" href="#E3:6_1_4"><span class="lab"><font color="Green" title="E28">A45</font></span></a>, <a class="txt" href="#E1:6_1_4_2"><span class="lab"><font color="Green" title="E31">A48</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:6_1_4_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E5:6_1_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</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="E6:6_1_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E7:6_1_4_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:6_1_4_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:6_1_4"/><span class="lab"><font color="Green" title="E31">A49</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_3"/><span class="lab"><font color="Green" title="E32">A50</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_4_3"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E3:6_1_4_3"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E3:6_1_4"><span class="lab"><font color="Green" title="E28">A45</font></span></a>, <a class="txt" href="#E1:6_1_4_3"><span class="lab"><font color="Green" title="E32">A50</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:6_1_4_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E5:6_1_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E6:6_1_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E7:6_1_4_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:6_1_4_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E7:6_1_4"/><span class="lab"><font color="Green" title="E32">A51</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><a NAME="E8:6_1_4"/><span class="lab"><font color="Green" title="E33">A52</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><a NAME="E9:6_1_4"/><span class="lab"><font color="Green" title="E34">A53</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="txt" href="#E6:6_1_4"><span class="lab"><font color="Green" title="E31">A49</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E10:6_1_4"/><span class="lab"><font color="Green" title="E35">A54</font></span>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="txt" href="#E6:6_1_4"><span class="lab"><font color="Green" title="E31">A49</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E11:6_1_4"/>
 ex <font color="Olive" title="b1">e</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c12">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>,<font color="Olive" title="b1">e</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c23">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:6_1_4_4"/><span class="lab"><font color="Green" title="E36">A55</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font>
 <span class="kw">and </span><br/><a NAME="E3:6_1_4_4"/><span class="lab"><font color="Green" title="E37">A56</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c24">p9</font> = <font color="Maroon" title="c23">p</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="c25">p1</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="E6:6_1_4_4"/><span class="lab"><font color="Green" title="E38">A57</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c25">p1</font>
 <span class="kw">and </span><br/><a NAME="E7:6_1_4_4"/><span class="lab"><font color="Green" title="E39">A58</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">p1</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="c26">p19</font> = <font color="Maroon" title="c25">p1</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="E9:6_1_4_4"/>
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c25">p1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_4_1"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c25">p1</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="E2:6_1_4_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c25">p1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_4_4"><span class="lab"><font color="Green" title="E36">A55</font></span></a>, <a class="txt" href="#E3:6_1_4_4"><span class="lab"><font color="Green" title="E37">A56</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:6_1_4_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:6_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E6:6_1_4_4"><span class="lab"><font color="Green" title="E38">A57</font></span></a>, <a class="txt" href="#E7:6_1_4_4"><span class="lab"><font color="Green" title="E39">A58</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</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="E10:6_1_4_4"/><span class="kw">then </span>
not <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">p9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c26">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c27">e9</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="E12:6_1_4_4"/><span class="lab"><font color="Green" title="E40">A59</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">p9</font>,<font color="Maroon" title="c27">e9</font>
 <span class="kw">and </span><br/><a NAME="E13:6_1_4_4"/><span class="lab"><font color="Green" title="E41">A60</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c26">p19</font>,<font color="Maroon" title="c27">e9</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="c28">e</font> = <font color="Maroon" title="c27">e9</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="E15:6_1_4_4"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font>,<font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:6_1_4_4"><span class="lab"><font color="Green" title="E40">A59</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E16:6_1_4_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E17:6_1_4_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c28">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_4_4"><span class="lab"><font color="Green" title="E36">A55</font></span></a>, <a class="txt" href="#E3:6_1_4_4"><span class="lab"><font color="Green" title="E37">A56</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E18:6_1_4_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A61</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c28">e</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E19:6_1_4_4"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c25">p1</font>,<font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:6_1_4_4"><span class="lab"><font color="Green" title="E41">A60</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E20:6_1_4_4"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c25">p1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c28">e</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="E21:6_1_4_4"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1_4_4"><span class="lab"><font color="Green" title="E38">A57</font></span></a>, <a class="txt" href="#E7:6_1_4_4"><span class="lab"><font color="Green" title="E39">A58</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E22:6_1_4_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A62</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c28">e</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="E23:6_1_4_4"/><span class="lab"><font color="Green" title="E44">A63</font></span>: 
<font color="Maroon" title="c14">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">e</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_4_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_4_2"/>
<font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">e</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="E2:6_1_4_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:6_1_4_4"><span class="lab"><font color="Green" title="E42">A61</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:6_1_4_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:6_1_4_4_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_4"><span class="lab"><font color="Green" title="E27">A44</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E24:6_1_4_4"/>
<font color="Maroon" title="c12">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">e</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_4_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_4_3"/>
<font color="Maroon" title="c12">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">e</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="E2:6_1_4_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:6_1_4_4"><span class="lab"><font color="Green" title="E43">A62</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:6_1_4_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:6_1_4_4_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1_4"><span class="lab"><font color="Green" title="E26">A43</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E25:6_1_4_4"/>
 ex <font color="Olive" title="b1">e</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c12">b</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>,<font color="Olive" title="b1">e</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:6_1_4_4"><span class="lab"><font color="Green" title="E42">A61</font></span></a>, <a class="txt" href="#E22:6_1_4_4"><span class="lab"><font color="Green" title="E43">A62</font></span></a>, <a class="txt" href="#E23:6_1_4_4"><span class="lab"><font color="Green" title="E44">A63</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">e</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="E13:6_1_4"/><span class="lab"><font color="Green" title="E36">A64</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c12">b</font>
 <span class="kw">and </span><br/><a NAME="E14:6_1_4"/><span class="lab"><font color="Green" title="E37">A65</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</font>
 <span class="kw">and </span><br/><a NAME="E15:6_1_4"/><span class="lab"><font color="Green" title="E38">A66</font></span>: 
<font color="Maroon" title="c23">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E16:6_1_4"/><span class="lab"><font color="Green" title="E39">A67</font></span>: 
<font color="Maroon" title="c23">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">e9</font> = <font color="Maroon" title="c23">e</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="analmetr.html#K3" title="ANALMETR:func.3">Af</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></span>;<br/><a NAME="E18:6_1_4"/>
 ex <font color="Olive" title="b1">e1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Olive" title="b1">e1</font>,<font color="Maroon" title="c13">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>,<font color="Olive" title="b1">e1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c25">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:6_1_4_5"/><span class="lab"><font color="Green" title="E40">A68</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font>
 <span class="kw">and </span><br/><a NAME="E3:6_1_4_5"/><span class="lab"><font color="Green" title="E41">A69</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">p</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="c26">p9</font> = <font color="Maroon" title="c25">p</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="c27">p1</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="E6:6_1_4_5"/><span class="lab"><font color="Green" title="E42">A70</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c27">p1</font>
 <span class="kw">and </span><br/><a NAME="E7:6_1_4_5"/><span class="lab"><font color="Green" title="E43">A71</font></span>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">p1</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="c28">p19</font> = <font color="Maroon" title="c27">p1</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="E9:6_1_4_5"/><span class="lab"><font color="Green" title="E44">A72</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_5_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_5_1"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_1_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E5:6_1_4"><span class="lab"><font color="Green" title="E30">A47</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:6_1_4_5_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E9:6_1"><span class="lab"><font color="Green" title="E22">A18</font></span></a>, <a class="txt" href="#E10:6_1_4"><span class="lab"><font color="Green" title="E35">A54</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>
<a NAME="E10:6_1_4_5"/>
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c27">p1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_5_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_5_2"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c27">p1</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="E2:6_1_4_5_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c27">p1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_4_5"><span class="lab"><font color="Green" title="E40">A68</font></span></a>, <a class="txt" href="#E3:6_1_4_5"><span class="lab"><font color="Green" title="E41">A69</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:6_1_4_5_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1_4_5"><span class="lab"><font color="Green" title="E42">A70</font></span></a>, <a class="txt" href="#E7:6_1_4_5"><span class="lab"><font color="Green" title="E43">A71</font></span></a>, <a class="txt" href="#E9:6_1_4_5"><span class="lab"><font color="Green" title="E44">A72</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</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="E11:6_1_4_5"/><span class="kw">then </span>
not <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">p9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c28">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c29">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="E13:6_1_4_5"/><span class="lab"><font color="Green" title="E45">A73</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">p9</font>,<font color="Maroon" title="c29">e19</font>
 <span class="kw">and </span><br/><a NAME="E14:6_1_4_5"/><span class="lab"><font color="Green" title="E46">A74</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c28">p19</font>,<font color="Maroon" title="c29">e19</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="c30">e1</font> = <font color="Maroon" title="c29">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="E16:6_1_4_5"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:6_1_4_5"><span class="lab"><font color="Green" title="E45">A73</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E17:6_1_4_5"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E18:6_1_4_5"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c30">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1_4_5"><span class="lab"><font color="Green" title="E40">A68</font></span></a>, <a class="txt" href="#E3:6_1_4_5"><span class="lab"><font color="Green" title="E41">A69</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E19:6_1_4_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A75</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c30">e1</font>,<font color="Maroon" title="c13">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="E20:6_1_4_5"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c27">p1</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1_4_5"><span class="lab"><font color="Green" title="E46">A74</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E21:6_1_4_5"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c27">p1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E22:6_1_4_5"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1_4_5"><span class="lab"><font color="Green" title="E42">A70</font></span></a>, <a class="txt" href="#E7:6_1_4_5"><span class="lab"><font color="Green" title="E43">A71</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E23:6_1_4_5"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E24:6_1_4_5"/>
 ex <font color="Olive" title="b1">e1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Olive" title="b1">e1</font>,<font color="Maroon" title="c13">b1</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>,<font color="Olive" title="b1">e1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:6_1_4_5"><span class="lab"><font color="Green" title="E47">A75</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E20:6_1_4"/><span class="lab"><font color="Green" title="E40">A76</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E21:6_1_4"/><span class="lab"><font color="Green" title="E41">A77</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c25">e1</font>
 ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">e19</font> = <font color="Maroon" title="c25">e1</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="E23:6_1_4"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:6_1_4"><span class="lab"><font color="Green" title="E36">A64</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E24:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</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="E25:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E26:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E27:6_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A78</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E8:6_1_4"><span class="lab"><font color="Green" title="E33">A52</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E28:6_1_4"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:6_1_4"><span class="lab"><font color="Green" title="E40">A76</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E29:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c19">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="E30:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c19">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E31:6_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A79</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E32:6_1_4"/><span class="lab"><font color="Green" title="E44">A80</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">e</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_6"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">e</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="E2:6_1_4_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c22">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1_4"><span class="lab"><font color="Green" title="E37">A65</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:6_1_4_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E4:6_1_4_6"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</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="E5:6_1_4_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E33:6_1_4"/><span class="lab"><font color="Green" title="E45">A81</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_7"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">e1</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="E2:6_1_4_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c21">c19</font>,<font color="Maroon" title="c22">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:6_1_4"><span class="lab"><font color="Green" title="E41">A77</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:6_1_4_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c21">c19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E4:6_1_4_7"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:6_1_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E6:6_1_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E3:6_1_4"><span class="lab"><font color="Green" title="E28">A45</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:6_1_4_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="txt" href="#E6:6_1_4"><span class="lab"><font color="Green" title="E31">A49</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><a NAME="E34:6_1_4"/><span class="lab"><font color="Green" title="E46">A82</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1_4"><span class="lab"><font color="Green" title="E30">A47</font></span></a>, <a class="txt" href="#E27:6_1_4"><span class="lab"><font color="Green" title="E42">A78</font></span></a>, <a class="txt" href="#E31:6_1_4"><span class="lab"><font color="Green" title="E43">A79</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E35:6_1_4"/><span class="lab"><font color="Green" title="E47">A83</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c23">e</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_8"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c23">e</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="E2:6_1_4_8"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_1_4_8"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</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="E4:6_1_4_8"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E5:6_1_4_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A84</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</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="E6:6_1_4_8"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:6_1_4"><span class="lab"><font color="Green" title="E36">A64</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:6_1_4_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_1"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="txt" href="#E32:6_1_4"><span class="lab"><font color="Green" title="E44">A80</font></span></a>, <a class="txt" href="#E5:6_1_4_8"><span class="lab"><font color="Green" title="E48">A84</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E36:6_1_4"/>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c23">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1_4"><span class="lab"><font color="Green" title="E37">A65</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E37:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c24">e9</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="E38:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c16">a9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E39:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E40:6_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A85</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E9:6_1_4"><span class="lab"><font color="Green" title="E34">A53</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E41:6_1_4"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:6_1_4"><span class="lab"><font color="Green" title="E41">A77</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E42:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:6_1_4"><span class="lab"><font color="Green" title="E35">A54</font></span></a>, <a class="txt" href="#E40:6_1_4"><span class="lab"><font color="Green" title="E48">A85</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E43:6_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A86</font></span>: 
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E44:6_1_4"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_1"><span class="lab"><font color="Green" title="E18">A14</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E45:6_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A87</font></span>: 
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_1"><span class="lab"><font color="Green" title="E14">A10</font></span></a>, <a class="txt" href="#E2:6_1"><span class="lab"><font color="Green" title="E15">A11</font></span></a>, <a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E3:6_1_4"><span class="lab"><font color="Green" title="E28">A45</font></span></a>, <a class="txt" href="#E5:6_1_4"><span class="lab"><font color="Green" title="E30">A47</font></span></a>, <a class="txt" href="#E7:6_1_4"><span class="lab"><font color="Green" title="E32">A51</font></span></a>, <a class="txt" href="#E8:6_1_4"><span class="lab"><font color="Green" title="E33">A52</font></span></a>, <a class="txt" href="#E13:6_1_4"><span class="lab"><font color="Green" title="E36">A64</font></span></a>, <a class="txt" href="#E16:6_1_4"><span class="lab"><font color="Green" title="E39">A67</font></span></a>, <a class="txt" href="#E20:6_1_4"><span class="lab"><font color="Green" title="E40">A76</font></span></a>, <a class="txt" href="#E32:6_1_4"><span class="lab"><font color="Green" title="E44">A80</font></span></a>, <a class="txt" href="#E33:6_1_4"><span class="lab"><font color="Green" title="E45">A81</font></span></a>, <a class="txt" href="#E34:6_1_4"><span class="lab"><font color="Green" title="E46">A82</font></span></a>, <a class="txt" href="#E35:6_1_4"><span class="lab"><font color="Green" title="E47">A83</font></span></a>, <a class="txt" href="#E43:6_1_4"><span class="lab"><font color="Green" title="E49">A86</font></span></a>, <a class="ref" href="conaffm.html#D5" target="_self" title="CONAFFM:def.5">Def5</a></span>;<br/><a NAME="E46:6_1_4"/><span class="lab"><font color="Green" title="E51">A88</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1_4_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_1_4_9"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</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="E2:6_1_4_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:6_1_4_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c22">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E4:6_1_4_9"/><span class="kw">then </span>
<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c22">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E5:6_1_4_9"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A89</font></span>: 
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E6:6_1_4_9"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1_4"><span class="lab"><font color="Green" title="E37">A65</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E7:6_1_4_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E8:6_1_4_9"/><span class="kw">then </span>
<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E9:6_1_4_9"/><span class="kw">then </span>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E10:6_1_4_9"/><span class="kw">then </span>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:6_1_4"><span class="lab"><font color="Green" title="E38">A66</font></span></a>, <a class="txt" href="#E5:6_1_4_9"><span class="lab"><font color="Green" title="E52">A89</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E11:6_1_4_9"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E12:6_1_4_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E13:6_1_4_9"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E14:6_1_4_9"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</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="E15:6_1_4_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_1"><span class="lab"><font color="Green" title="E20">A16</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E47:6_1_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_1_4"><span class="lab"><font color="Green" title="E37">A65</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E48:6_1_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c24">e9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E49:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E50:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E51:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E52:6_1_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A90</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_1"><span class="lab"><font color="Green" title="E19">A15</font></span></a>, <a class="txt" href="#E9:6_1_4"><span class="lab"><font color="Green" title="E34">A53</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E53:6_1_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c21">c19</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:6_1_4"><span class="lab"><font color="Green" title="E41">A77</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E54:6_1_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">c19</font>,<font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E55:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c21">c19</font>,<font color="Maroon" title="c17">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c19</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E56:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c21">c19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E57:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E58:6_1_4"/><span class="kw">then </span>
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:6_1_4"><span class="lab"><font color="Green" title="E35">A54</font></span></a>, <a class="txt" href="#E52:6_1_4"><span class="lab"><font color="Green" title="E52">A90</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><span class="kw">hence </span><a NAME="E59:6_1_4"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:6"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="txt" href="#E3:6_1"><span class="lab"><font color="Green" title="E16">A12</font></span></a>, <a class="txt" href="#E4:6_1"><span class="lab"><font color="Green" title="E17">A13</font></span></a>, <a class="txt" href="#E4:6_1_4"><span class="lab"><font color="Green" title="E29">A46</font></span></a>, <a class="txt" href="#E5:6_1_4"><span class="lab"><font color="Green" title="E30">A47</font></span></a>, <a class="txt" href="#E6:6_1_4"><span class="lab"><font color="Green" title="E31">A49</font></span></a>, <a class="txt" href="#E8:6_1_4"><span class="lab"><font color="Green" title="E33">A52</font></span></a>, <a class="txt" href="#E13:6_1_4"><span class="lab"><font color="Green" title="E36">A64</font></span></a>, <a class="txt" href="#E16:6_1_4"><span class="lab"><font color="Green" title="E39">A67</font></span></a>, <a class="txt" href="#E20:6_1_4"><span class="lab"><font color="Green" title="E40">A76</font></span></a>, <a class="txt" href="#E32:6_1_4"><span class="lab"><font color="Green" title="E44">A80</font></span></a>, <a class="txt" href="#E33:6_1_4"><span class="lab"><font color="Green" title="E45">A81</font></span></a>, <a class="txt" href="#E34:6_1_4"><span class="lab"><font color="Green" title="E46">A82</font></span></a>, <a class="txt" href="#E45:6_1_4"><span class="lab"><font color="Green" title="E50">A87</font></span></a>, <a class="txt" href="#E46:6_1_4"><span class="lab"><font color="Green" title="E51">A88</font></span></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</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="E15:6_1"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:6_1"><span class="lab"><font color="Green" title="E23">A19</font></span></a>, <a class="txt" href="#E12:6_1"><span class="lab"><font color="Green" title="E24">A26</font></span></a>, <a class="txt" href="#E13:6_1"><span class="lab"><font color="Green" title="E25">A35</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E11:6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A91</font></span>: 
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">c</font> implies <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E4:6"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E5:6"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E6:6"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E7:6"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E8:6"><span class="lab"><font color="Green" title="E12">A8</font></span></a></span>;<br/>
<div><span class="lab"><font color="Green" title="E15">A92</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">o</font>, <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c11">a1</font>, <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c15">c1</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"> ( <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> implies <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_2"/><span class="lab"><font color="Green" title="E16">A93</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">and </span><br/><a NAME="E2:6_2"/><span class="lab"><font color="Green" title="E17">A94</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E3:6_2"/><span class="lab"><font color="Green" title="E18">A95</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">and </span><br/><a NAME="E4:6_2"/><span class="lab"><font color="Green" title="E19">A96</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E5:6_2"/><span class="lab"><font color="Green" title="E20">A97</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">and </span><br/><a NAME="E6:6_2"/><span class="lab"><font color="Green" title="E21">A98</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">and </span><br/><a NAME="E7:6_2"/><span class="lab"><font color="Green" title="E22">A99</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> implies <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> )</span><br/><span class="kw">assume </span><a NAME="E8:6_2"/><span class="lab"><font color="Green" title="E23">A100</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</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="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c16">a9</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c17">a19</font> = <font color="Maroon" title="c11">a1</font>, <font color="Maroon" title="c18">b9</font> = <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c19">b19</font> = <font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c20">c9</font> = <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c21">c19</font> = <font color="Maroon" title="c15">c1</font>, <font color="Maroon" title="c22">o9</font> = <font color="Maroon" title="c9">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="E24">A101</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:6_2_1"/><span class="lab"><font color="Green" title="E25">A102</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E2:6_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A103</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2"><span class="lab"><font color="Green" title="E17">A94</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E3:6_2_1"/><span class="lab"><font color="Green" title="E27">A104</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_2"><span class="lab"><font color="Green" title="E19">A96</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E4:6_2_1"/>
not <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_1_1"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2_1"><span class="lab"><font color="Green" title="E25">A102</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_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="c18">b9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:6_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="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E5:6_2_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</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="E6:6_2_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:6_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A105</font></span>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2_1"><span class="lab"><font color="Green" title="E26">A103</font></span></a>, <a class="txt" href="#E3:6_2_1"><span class="lab"><font color="Green" title="E27">A104</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E6:6_2_1"/><span class="lab"><font color="Green" title="E29">A106</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_2"><span class="lab"><font color="Green" title="E18">A95</font></span></a>, <a class="txt" href="#E1:6_2_1"><span class="lab"><font color="Green" title="E25">A102</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E7:6_2_1"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_2"><span class="lab"><font color="Green" title="E20">A97</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E8:6_2_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A107</font></span>: 
( <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font> or <font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">c1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2_1"><span class="lab"><font color="Green" title="E29">A106</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E9:6_2_1"/>
not <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_1_2"/>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2_1"><span class="lab"><font color="Green" title="E25">A102</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_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="c20">c9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:6_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="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E5:6_2_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</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="E6:6_2_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E10:6_2_1"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_2_1"><span class="lab"><font color="Green" title="E28">A105</font></span></a>, <a class="txt" href="#E8:6_2_1"><span class="lab"><font color="Green" title="E30">A107</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E25">A108</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_2_2"/><span class="lab"><font color="Green" title="E26">A109</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E2:6_2_2"/><span class="lab"><font color="Green" title="E27">A110</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E3:6_2_2"/><span class="lab"><font color="Green" title="E28">A111</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><a NAME="E4:6_2_2"/><span class="lab"><font color="Green" title="E29">A112</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_2_1"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</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/>
<a NAME="E3:6_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</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="E4:6_2_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:6_2_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:6_2_2"/><span class="lab"><font color="Green" title="E30">A113</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_2_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_2_2"/><span class="lab"><font color="Green" title="E31">A114</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_2_2"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E3:6_2_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_2"><span class="lab"><font color="Green" title="E19">A96</font></span></a>, <a class="txt" href="#E2:6_2_2"><span class="lab"><font color="Green" title="E27">A110</font></span></a>, <a class="txt" href="#E1:6_2_2_2"><span class="lab"><font color="Green" title="E31">A114</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:6_2_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E5:6_2_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</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="E6:6_2_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E7:6_2_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:6_2_2_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:6_2_2"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2_2"><span class="lab"><font color="Green" title="E26">A109</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E7:6_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2"><span class="lab"><font color="Green" title="E17">A94</font></span></a>, <a class="txt" href="#E3:6_2_2"><span class="lab"><font color="Green" title="E28">A111</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E8:6_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_2"><span class="lab"><font color="Green" title="E18">A95</font></span></a>, <a class="txt" href="#E4:6_2_2"><span class="lab"><font color="Green" title="E29">A112</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E9:6_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E10:6_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E11:6_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E12:6_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</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="E13:6_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A115</font></span>: 
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E14:6_2_2"/>
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2"><span class="lab"><font color="Green" title="E17">A94</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E15:6_2_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A116</font></span>: 
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_2_2"><span class="lab"><font color="Green" title="E30">A113</font></span></a>, <a class="txt" href="#E13:6_2_2"><span class="lab"><font color="Green" title="E31">A115</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E16:6_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2_2"><span class="lab"><font color="Green" title="E26">A109</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E17:6_2_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E18:6_2_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E19:6_2_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><span class="kw">hence </span><a NAME="E20:6_2_2"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_2_2"><span class="lab"><font color="Green" title="E28">A111</font></span></a>, <a class="txt" href="#E15:6_2_2"><span class="lab"><font color="Green" title="E32">A116</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E26">A117</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_2_3"/><span class="lab"><font color="Green" title="E27">A118</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E2:6_2_3"/>
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E3:6_2_3"/><span class="lab"><font color="Green" title="E28">A119</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E4:6_2_3"/><span class="lab"><font color="Green" title="E29">A120</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_3_1"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</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/>
<a NAME="E3:6_2_3_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E4:6_2_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:6_2_3_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:6_2_3_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:6_2_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:6_2_3"/><span class="lab"><font color="Green" title="E30">A121</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_3_2"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</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/>
<a NAME="E3:6_2_3_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E4:6_2_3_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E5:6_2_3_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E6:6_2_3_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:6_2_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:6_2_3"/><span class="lab"><font color="Green" title="E31">A122</font></span>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="txt" href="#E2:6_2"><span class="lab"><font color="Green" title="E17">A94</font></span></a>, <a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="txt" href="#E3:6_2_3"><span class="lab"><font color="Green" title="E28">A119</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E7:6_2_3"/>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2_3"><span class="lab"><font color="Green" title="E27">A118</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E8:6_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_2"><span class="lab"><font color="Green" title="E19">A96</font></span></a>, <a class="txt" href="#E5:6_2_3"><span class="lab"><font color="Green" title="E30">A121</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E9:6_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_2"><span class="lab"><font color="Green" title="E20">A97</font></span></a>, <a class="txt" href="#E4:6_2_3"><span class="lab"><font color="Green" title="E29">A120</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E10:6_2_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E11:6_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E12:6_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E13:6_2_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</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="E14:6_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A123</font></span>: 
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E15:6_2_3"/>
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c11">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_2"><span class="lab"><font color="Green" title="E19">A96</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E16:6_2_3"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A124</font></span>: 
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2_3"><span class="lab"><font color="Green" title="E31">A122</font></span></a>, <a class="txt" href="#E14:6_2_3"><span class="lab"><font color="Green" title="E32">A123</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E17:6_2_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2_3"><span class="lab"><font color="Green" title="E27">A118</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E18:6_2_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E19:6_2_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</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="E20:6_2_3"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><span class="kw">hence </span><a NAME="E21:6_2_3"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_2_3"><span class="lab"><font color="Green" title="E30">A121</font></span></a>, <a class="txt" href="#E16:6_2_3"><span class="lab"><font color="Green" title="E33">A124</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="6_2_4"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_2_4"/><span class="lab"><font color="Green" title="E27">A125</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E2:6_2_4"/><span class="lab"><font color="Green" title="E28">A126</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">and </span><br/><a NAME="E3:6_2_4"/><span class="lab"><font color="Green" title="E29">A127</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E4:6_2_4"/><span class="lab"><font color="Green" title="E30">A128</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><a NAME="E5:6_2_4"/><span class="lab"><font color="Green" title="E31">A129</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c14">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_1"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">c</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</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/>
<a NAME="E3:6_2_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</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="E4:6_2_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:6_2_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E6:6_2_4"/><span class="lab"><font color="Green" title="E32">A130</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_2"/><span class="lab"><font color="Green" title="E33">A131</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_4_2"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E3:6_2_4_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_2"><span class="lab"><font color="Green" title="E19">A96</font></span></a>, <a class="txt" href="#E3:6_2_4"><span class="lab"><font color="Green" title="E29">A127</font></span></a>, <a class="txt" href="#E1:6_2_4_2"><span class="lab"><font color="Green" title="E33">A131</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:6_2_4_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E5:6_2_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</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="E6:6_2_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E7:6_2_4_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:6_2_4_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E7:6_2_4"/><span class="lab"><font color="Green" title="E33">A132</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">c1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_3"/><span class="lab"><font color="Green" title="E34">A133</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_4_3"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E3:6_2_4_3"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_2"><span class="lab"><font color="Green" title="E20">A97</font></span></a>, <a class="txt" href="#E3:6_2_4"><span class="lab"><font color="Green" title="E29">A127</font></span></a>, <a class="txt" href="#E1:6_2_4_3"><span class="lab"><font color="Green" title="E34">A133</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:6_2_4_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E5:6_2_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E6:6_2_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E7:6_2_4_3"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:6_2_4_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E8:6_2_4"/><span class="lab"><font color="Green" title="E34">A134</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><a NAME="E9:6_2_4"/><span class="lab"><font color="Green" title="E35">A135</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><a NAME="E10:6_2_4"/><span class="lab"><font color="Green" title="E36">A136</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="txt" href="#E4:6_2_4"><span class="lab"><font color="Green" title="E30">A128</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/><a NAME="E11:6_2_4"/>
 ex <font color="Olive" title="b1">e</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>,<font color="Olive" title="b1">e</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c10">a</font> &amp; <font color="Maroon" title="c14">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">e</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">e</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c23">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:6_2_4_4"/><span class="lab"><font color="Green" title="E37">A137</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font>
 <span class="kw">and </span><br/><a NAME="E3:6_2_4_4"/><span class="lab"><font color="Green" title="E38">A138</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c24">p9</font> = <font color="Maroon" title="c23">p</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="c25">p1</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="E6:6_2_4_4"/><span class="lab"><font color="Green" title="E39">A139</font></span>: 
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c25">p1</font>
 <span class="kw">and </span><br/><a NAME="E7:6_2_4_4"/><span class="lab"><font color="Green" title="E40">A140</font></span>: 
<font color="Maroon" title="c12">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">p1</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="c26">p19</font> = <font color="Maroon" title="c25">p1</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="E9:6_2_4_4"/>
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c25">p1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_4_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_4_1"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c25">p1</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="E2:6_2_4_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c25">p1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2_4_4"><span class="lab"><font color="Green" title="E37">A137</font></span></a>, <a class="txt" href="#E3:6_2_4_4"><span class="lab"><font color="Green" title="E38">A138</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E3:6_2_4_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2_4_4"><span class="lab"><font color="Green" title="E39">A139</font></span></a>, <a class="txt" href="#E7:6_2_4_4"><span class="lab"><font color="Green" title="E40">A140</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E4:6_2_4_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</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="E5:6_2_4_4_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:6_2_4_4_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_2"><span class="lab"><font color="Green" title="E23">A100</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E10:6_2_4_4"/><span class="kw">then </span>
not <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">p9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c26">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c27">e9</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="E12:6_2_4_4"/><span class="lab"><font color="Green" title="E41">A141</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">p9</font>,<font color="Maroon" title="c27">e9</font>
 <span class="kw">and </span><br/><a NAME="E13:6_2_4_4"/><span class="lab"><font color="Green" title="E42">A142</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c26">p19</font>,<font color="Maroon" title="c27">e9</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="c28">e</font> = <font color="Maroon" title="c27">e9</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="E15:6_2_4_4"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font>,<font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:6_2_4_4"><span class="lab"><font color="Green" title="E41">A141</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E16:6_2_4_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A143</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E17:6_2_4_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c28">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2_4_4"><span class="lab"><font color="Green" title="E37">A137</font></span></a>, <a class="txt" href="#E3:6_2_4_4"><span class="lab"><font color="Green" title="E38">A138</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E18:6_2_4_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A144</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c28">e</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E19:6_2_4_4"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c25">p1</font>,<font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:6_2_4_4"><span class="lab"><font color="Green" title="E42">A142</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E20:6_2_4_4"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c25">p1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c28">e</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="E21:6_2_4_4"/><span class="kw">then </span>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2_4_4"><span class="lab"><font color="Green" title="E39">A139</font></span></a>, <a class="txt" href="#E7:6_2_4_4"><span class="lab"><font color="Green" title="E40">A140</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E22:6_2_4_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A145</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c28">e</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="E23:6_2_4_4"/><span class="lab"><font color="Green" title="E46">A146</font></span>: 
<font color="Maroon" title="c14">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="txt" href="#E2:6_2_4_4"><span class="lab"><font color="Green" title="E37">A137</font></span></a>, <a class="txt" href="#E3:6_2_4_4"><span class="lab"><font color="Green" title="E38">A138</font></span></a>, <a class="txt" href="#E16:6_2_4_4"><span class="lab"><font color="Green" title="E43">A143</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E24:6_2_4_4"/><span class="lab"><font color="Green" title="E47">A147</font></span>: 
<font color="Maroon" title="c12">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">e</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_4_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_4_2"/>
<font color="Maroon" title="c12">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">e</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="E2:6_2_4_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:6_2_4_4"><span class="lab"><font color="Green" title="E44">A144</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:6_2_4_4_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E4:6_2_4_4_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</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="E5:6_2_4_4_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E25:6_2_4_4"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c28">e</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_4_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_4_3"/>
<font color="Maroon" title="c10">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">e</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="E2:6_2_4_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:6_2_4_4"><span class="lab"><font color="Green" title="E45">A145</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:6_2_4_4_3"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:6_2_4_4_3"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2_4"><span class="lab"><font color="Green" title="E27">A125</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E26:6_2_4_4"/>
 ex <font color="Olive" title="b1">e</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>,<font color="Olive" title="b1">e</font> &amp;  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Olive" title="b1">e</font>,<font color="Maroon" title="c10">a</font> &amp; <font color="Maroon" title="c14">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">e</font> &amp; <font color="Olive" title="b1">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">e</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:6_2_4_4"><span class="lab"><font color="Green" title="E44">A144</font></span></a>, <a class="txt" href="#E22:6_2_4_4"><span class="lab"><font color="Green" title="E45">A145</font></span></a>, <a class="txt" href="#E23:6_2_4_4"><span class="lab"><font color="Green" title="E46">A146</font></span></a>, <a class="txt" href="#E24:6_2_4_4"><span class="lab"><font color="Green" title="E47">A147</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c23">e</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="E13:6_2_4"/><span class="lab"><font color="Green" title="E37">A148</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</font>
 <span class="kw">and </span><br/><a NAME="E14:6_2_4"/><span class="lab"><font color="Green" title="E38">A149</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">and </span><br/><a NAME="E15:6_2_4"/><span class="lab"><font color="Green" title="E39">A150</font></span>: 
<font color="Maroon" title="c23">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <span class="kw">and </span><br/><a NAME="E16:6_2_4"/><span class="lab"><font color="Green" title="E40">A151</font></span>: 
<font color="Maroon" title="c14">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">e</font>
 <span class="kw">and </span><br/><a NAME="E17:6_2_4"/><span class="lab"><font color="Green" title="E41">A152</font></span>: 
<font color="Maroon" title="c10">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">e</font>
 ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c24">e9</font> = <font color="Maroon" title="c23">e</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="E19:6_2_4"/>
 ex <font color="Olive" title="b1">e1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Olive" title="b1">e1</font>,<font color="Maroon" title="c11">a1</font> &amp; <font color="Maroon" title="c23">e</font>,<font color="Olive" title="b1">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">consider </span><font color="Maroon" title="c25">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E2:6_2_4_5"/><span class="lab"><font color="Green" title="E42">A153</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font>
 <span class="kw">and </span><br/><a NAME="E3:6_2_4_5"/><span class="lab"><font color="Green" title="E43">A154</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">p</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="c26">p9</font> = <font color="Maroon" title="c25">p</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="c27">p1</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="E6:6_2_4_5"/><span class="lab"><font color="Green" title="E44">A155</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c27">p1</font>
 <span class="kw">and </span><br/><a NAME="E7:6_2_4_5"/><span class="lab"><font color="Green" title="E45">A156</font></span>: 
<font color="Maroon" title="c23">e</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c27">p1</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="c28">p19</font> = <font color="Maroon" title="c27">p1</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="E9:6_2_4_5"/>
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c27">p1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_5_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_5_1"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c27">p1</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="E2:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c27">p1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2_4_5"><span class="lab"><font color="Green" title="E42">A153</font></span></a>, <a class="txt" href="#E3:6_2_4_5"><span class="lab"><font color="Green" title="E43">A154</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E3:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c28">p19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E4:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c28">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E5:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c27">p1</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="E6:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c27">p1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="txt" href="#E3:6_2_4"><span class="lab"><font color="Green" title="E29">A127</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E7:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2_4_5"><span class="lab"><font color="Green" title="E44">A155</font></span></a>, <a class="txt" href="#E7:6_2_4_5"><span class="lab"><font color="Green" title="E45">A156</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E8:6_2_4_5_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A157</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E9:6_2_4_5_1"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E10:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_2_4"><span class="lab"><font color="Green" title="E34">A134</font></span></a>, <a class="txt" href="#E8:6_2_4_5_1"><span class="lab"><font color="Green" title="E46">A157</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E11:6_2_4_5_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E12:6_2_4_5_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E13:6_2_4_5_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E14:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E15:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E16:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E17:6_2_4_5_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_2_4"><span class="lab"><font color="Green" title="E34">A134</font></span></a>, <a class="txt" href="#E8:6_2_4_5_1"><span class="lab"><font color="Green" title="E46">A157</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E18:6_2_4_5_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:6_2_4"><span class="lab"><font color="Green" title="E36">A136</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</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="E10:6_2_4_5"/><span class="kw">then </span>
not <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">p9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c28">p19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c29">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="E12:6_2_4_5"/><span class="lab"><font color="Green" title="E46">A158</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">p9</font>,<font color="Maroon" title="c29">e19</font>
 <span class="kw">and </span><br/><a NAME="E13:6_2_4_5"/><span class="lab"><font color="Green" title="E47">A159</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c28">p19</font>,<font color="Maroon" title="c29">e19</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="c30">e1</font> = <font color="Maroon" title="c29">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="E15:6_2_4_5"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:6_2_4_5"><span class="lab"><font color="Green" title="E46">A158</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E16:6_2_4_5"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E17:6_2_4_5"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c30">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2_4_5"><span class="lab"><font color="Green" title="E42">A153</font></span></a>, <a class="txt" href="#E3:6_2_4_5"><span class="lab"><font color="Green" title="E43">A154</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E18:6_2_4_5"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A160</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c30">e1</font>,<font color="Maroon" title="c11">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="E19:6_2_4_5"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c27">p1</font>,<font color="Maroon" title="c30">e1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:6_2_4_5"><span class="lab"><font color="Green" title="E47">A159</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E20:6_2_4_5"/><span class="kw">then </span>
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c27">p1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c30">e1</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="E21:6_2_4_5"/><span class="kw">then </span>
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c30">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2_4_5"><span class="lab"><font color="Green" title="E44">A155</font></span></a>, <a class="txt" href="#E7:6_2_4_5"><span class="lab"><font color="Green" title="E45">A156</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<span class="kw">hence </span><a NAME="E22:6_2_4_5"/>
 ex <font color="Olive" title="b1">e1</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> st <br/>(  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Olive" title="b1">e1</font>,<font color="Maroon" title="c11">a1</font> &amp; <font color="Maroon" title="c23">e</font>,<font color="Olive" title="b1">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:6_2_4_5"><span class="lab"><font color="Green" title="E48">A160</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c25">e1</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E21:6_2_4"/><span class="lab"><font color="Green" title="E42">A161</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">and </span><br/><a NAME="E22:6_2_4"/><span class="lab"><font color="Green" title="E43">A162</font></span>: 
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c26">e19</font> = <font color="Maroon" title="c25">e1</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="E24:6_2_4"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_2_4"><span class="lab"><font color="Green" title="E38">A149</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E25:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</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="E26:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E27:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</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="E28:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A163</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="txt" href="#E8:6_2_4"><span class="lab"><font color="Green" title="E34">A134</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E29:6_2_4"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:6_2_4"><span class="lab"><font color="Green" title="E42">A161</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E30:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E31:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E32:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A164</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E33:6_2_4"/><span class="lab"><font color="Green" title="E46">A165</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c23">e</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_6"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c23">e</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="E2:6_2_4_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c22">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:6_2_4"><span class="lab"><font color="Green" title="E37">A148</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E3:6_2_4_6"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:6_2_4_6"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2_4"><span class="lab"><font color="Green" title="E28">A126</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E34:6_2_4"/><span class="lab"><font color="Green" title="E47">A166</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c25">e1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_7"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_7"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c25">e1</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="E2:6_2_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c22">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:6_2_4"><span class="lab"><font color="Green" title="E43">A162</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E3:6_2_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E4:6_2_4_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A167</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E5:6_2_4_7"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_2_4"><span class="lab"><font color="Green" title="E38">A149</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E6:6_2_4_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A168</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:6_2_4"><span class="lab"><font color="Green" title="E46">A165</font></span></a>, <a class="txt" href="#E4:6_2_4_7"><span class="lab"><font color="Green" title="E48">A167</font></span></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></span>;<br/>
<a NAME="E7:6_2_4_7"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A169</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="txt" href="#E8:6_2_4"><span class="lab"><font color="Green" title="E34">A134</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<a NAME="E8:6_2_4_7"/>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2_4_7"><span class="lab"><font color="Green" title="E49">A168</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E9:6_2_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E10:6_2_4_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E11:6_2_4_7"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E12:6_2_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c22">o9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a19</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/>
<a NAME="E13:6_2_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">a19</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<a NAME="E14:6_2_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/>
<a NAME="E15:6_2_4_7"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_2_4"><span class="lab"><font color="Green" title="E29">A127</font></span></a>, <a class="txt" href="#E7:6_2_4_7"><span class="lab"><font color="Green" title="E50">A169</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E16:6_2_4_7"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:6_2_4"><span class="lab"><font color="Green" title="E36">A136</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E35:6_2_4"/><span class="lab"><font color="Green" title="E48">A170</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_2_4"><span class="lab"><font color="Green" title="E29">A127</font></span></a>, <a class="txt" href="#E28:6_2_4"><span class="lab"><font color="Green" title="E44">A163</font></span></a>, <a class="txt" href="#E32:6_2_4"><span class="lab"><font color="Green" title="E45">A164</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E36:6_2_4"/><span class="lab"><font color="Green" title="E49">A171</font></span>: 
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_8"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_8"/>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_4_8"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_2_4_8"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</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="E4:6_2_4_8"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:6_2_4_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E37:6_2_4"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:6_2_4"><span class="lab"><font color="Green" title="E38">A149</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E38:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</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="E39:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c16">a9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c24">e9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E40:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c23">e</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="E41:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A172</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c23">e</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="E42:6_2_4"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:6_2_4"><span class="lab"><font color="Green" title="E42">A161</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E43:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E44:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c17">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E45:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E46:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A173</font></span>: 
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c25">e1</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="E47:6_2_4"/>
<font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">a19</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:6_2_4"><span class="lab"><font color="Green" title="E43">A162</font></span></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E48:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">a19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c26">e19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E49:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A174</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E50:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A175</font></span>: 
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:6"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="txt" href="#E2:6_2"><span class="lab"><font color="Green" title="E17">A94</font></span></a>, <a class="txt" href="#E4:6_2"><span class="lab"><font color="Green" title="E19">A96</font></span></a>, <a class="txt" href="#E3:6_2_4"><span class="lab"><font color="Green" title="E29">A127</font></span></a>, <a class="txt" href="#E6:6_2_4"><span class="lab"><font color="Green" title="E32">A130</font></span></a>, <a class="txt" href="#E8:6_2_4"><span class="lab"><font color="Green" title="E34">A134</font></span></a>, <a class="txt" href="#E9:6_2_4"><span class="lab"><font color="Green" title="E35">A135</font></span></a>, <a class="txt" href="#E17:6_2_4"><span class="lab"><font color="Green" title="E41">A152</font></span></a>, <a class="txt" href="#E33:6_2_4"><span class="lab"><font color="Green" title="E46">A165</font></span></a>, <a class="txt" href="#E34:6_2_4"><span class="lab"><font color="Green" title="E47">A166</font></span></a>, <a class="txt" href="#E35:6_2_4"><span class="lab"><font color="Green" title="E48">A170</font></span></a>, <a class="txt" href="#E36:6_2_4"><span class="lab"><font color="Green" title="E49">A171</font></span></a>, <a class="txt" href="#E41:6_2_4"><span class="lab"><font color="Green" title="E50">A172</font></span></a>, <a class="txt" href="#E46:6_2_4"><span class="lab"><font color="Green" title="E51">A173</font></span></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</a></span>;<br/><a NAME="E51:6_2_4"/>
not  <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_2"><span class="lab"><font color="Green" title="E21">A98</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E52:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A176</font></span>: 
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:6"><span class="lab"><font color="Green" title="E13">A9</font></span></a>, <a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="txt" href="#E3:6_2"><span class="lab"><font color="Green" title="E18">A95</font></span></a>, <a class="txt" href="#E5:6_2"><span class="lab"><font color="Green" title="E20">A97</font></span></a>, <a class="txt" href="#E3:6_2_4"><span class="lab"><font color="Green" title="E29">A127</font></span></a>, <a class="txt" href="#E5:6_2_4"><span class="lab"><font color="Green" title="E31">A129</font></span></a>, <a class="txt" href="#E7:6_2_4"><span class="lab"><font color="Green" title="E33">A132</font></span></a>, <a class="txt" href="#E8:6_2_4"><span class="lab"><font color="Green" title="E34">A134</font></span></a>, <a class="txt" href="#E17:6_2_4"><span class="lab"><font color="Green" title="E41">A152</font></span></a>, <a class="txt" href="#E33:6_2_4"><span class="lab"><font color="Green" title="E46">A165</font></span></a>, <a class="txt" href="#E34:6_2_4"><span class="lab"><font color="Green" title="E47">A166</font></span></a>, <a class="txt" href="#E35:6_2_4"><span class="lab"><font color="Green" title="E48">A170</font></span></a>, <a class="txt" href="#E41:6_2_4"><span class="lab"><font color="Green" title="E50">A172</font></span></a>, <a class="txt" href="#E46:6_2_4"><span class="lab"><font color="Green" title="E51">A173</font></span></a>, <a class="txt" href="#E49:6_2_4"><span class="lab"><font color="Green" title="E52">A174</font></span></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</a></span>;<br/><a NAME="E53:6_2_4"/><span class="lab"><font color="Green" title="E55">A177</font></span>: 
<font color="Maroon" title="c25">e1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_9"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_9"/>
<font color="Maroon" title="c25">e1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_4_9"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:6_2_4"><span class="lab"><font color="Green" title="E42">A161</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_2_4_9"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2"><span class="lab"><font color="Green" title="E17">A94</font></span></a>, <a class="txt" href="#E6:6_2_4"><span class="lab"><font color="Green" title="E32">A130</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:6_2_4_9"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_2"><span class="lab"><font color="Green" title="E16">A93</font></span></a>, <a class="txt" href="#E7:6_2"><span class="lab"><font color="Green" title="E22">A99</font></span></a>, <a class="txt" href="#E3:6_2_4"><span class="lab"><font color="Green" title="E29">A127</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><a NAME="E54:6_2_4"/><span class="lab"><font color="Green" title="E56">A178</font></span>: 
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E52:6_2_4"><span class="lab"><font color="Green" title="E54">A176</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E55:6_2_4"/><span class="lab"><font color="Green" title="E57">A179</font></span>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:6_2_4"><span class="lab"><font color="Green" title="E37">A148</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/><a NAME="E56:6_2_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c18">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E57:6_2_4"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c12">b</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="E58:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c23">e</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/><a NAME="E59:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A180</font></span>: 
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:6_2_4"><span class="lab"><font color="Green" title="E40">A151</font></span></a>, <a class="txt" href="#E54:6_2_4"><span class="lab"><font color="Green" title="E56">A178</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E60:6_2_4"/><span class="lab"><font color="Green" title="E59">A181</font></span>: 
<font color="Maroon" title="c14">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c12">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_2_4_10"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_2_4_10"/>
<font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_2_4_10"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o9</font>,<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:6_2_4_10"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_2_4"><span class="lab"><font color="Green" title="E28">A126</font></span></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E61:6_2_4"/>
<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c24">e9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:6_2_4"><span class="lab"><font color="Green" title="E57">A179</font></span></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E62:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c20">c9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c18">b9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E63:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c12">b</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="E64:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E59:6_2_4"><span class="lab"><font color="Green" title="E58">A180</font></span></a>, <a class="txt" href="#E60:6_2_4"><span class="lab"><font color="Green" title="E59">A181</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E65:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c25">e1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:6_2_4"><span class="lab"><font color="Green" title="E39">A150</font></span></a>, <a class="txt" href="#E50:6_2_4"><span class="lab"><font color="Green" title="E53">A175</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E66:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c19">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c19</font>,<font color="Maroon" title="c26">e19</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="E67:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c19">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E68:6_2_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E69:6_2_4"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E70:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c26">e19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E71:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c26">e19</font>,<font color="Maroon" title="c19">b19</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">b19</font>,<font color="Maroon" title="c21">c19</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E72:6_2_4"/><span class="kw">then </span><span class="lab"><font color="Green" title="E60">A182</font></span>: 
<font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c13">b1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E73:6_2_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E55:6_2_4"><span class="lab"><font color="Green" title="E57">A179</font></span></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/><a NAME="E74:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c24">e9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></span>;<br/><a NAME="E75:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c24">e9</font>,<font color="Maroon" title="c18">b9</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b9</font>,<font color="Maroon" title="c20">c9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></span>;<br/><a NAME="E76:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c23">e</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></span>;<br/><a NAME="E77:6_2_4"/><span class="kw">then </span>
<font color="Maroon" title="c25">e1</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:6_2_4"><span class="lab"><font color="Green" title="E39">A150</font></span></a>, <a class="txt" href="#E50:6_2_4"><span class="lab"><font color="Green" title="E53">A175</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><span class="kw">hence </span><a NAME="E78:6_2_4"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E53:6_2_4"><span class="lab"><font color="Green" title="E55">A177</font></span></a>, <a class="txt" href="#E72:6_2_4"><span class="lab"><font color="Green" title="E60">A182</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</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="E14:6_2"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:6_2"><span class="lab"><font color="Green" title="E24">A101</font></span></a>, <a class="txt" href="#E11:6_2"><span class="lab"><font color="Green" title="E25">A108</font></span></a>, <a class="txt" href="#E12:6_2"><span class="lab"><font color="Green" title="E26">A117</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E13:6"/><span class="kw">then </span><span class="lab"><font color="Green" title="E16">A183</font></span>: 
( not <font color="Maroon" title="c2">o</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">c</font>,<font color="Maroon" title="c5">b</font> implies <font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E4:6"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E5:6"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E6:6"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E7:6"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E8:6"><span class="lab"><font color="Green" title="E12">A8</font></span></a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c9">o</font>, <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c11">a1</font>, <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c15">c1</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"> ( <font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</a>  &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> implies <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> )</span><br/><span class="kw">assume </span><a NAME="E1:6_3"/>
<font color="Maroon" title="c1">X</font> is  <a href="conaffm.html#V5" title="CONAFFM:attr.5">satisfying_LIN</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="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> &amp; not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> implies <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E2:6_3"/><span class="lab"><font color="Green" title="E17">A184</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">and </span><br/><a NAME="E3:6_3"/><span class="lab"><font color="Green" title="E18">A185</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E4:6_3"/><span class="lab"><font color="Green" title="E19">A186</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">and </span><br/><a NAME="E5:6_3"/><span class="lab"><font color="Green" title="E20">A187</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E6:6_3"/><span class="lab"><font color="Green" title="E21">A188</font></span>: 
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">and </span><br/><a NAME="E7:6_3"/><span class="lab"><font color="Green" title="E22">A189</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">and </span><br/><a NAME="E8:6_3"/><span class="lab"><font color="Green" title="E23">A190</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</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="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> &amp; <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> implies <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> )</span><br/><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E9:6_3"/><span class="lab"><font color="Green" title="E24">A191</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font>
 <span class="kw">and </span><br/><a NAME="E10:6_3"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</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="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c16">a9</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c17">b9</font> = <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c18">c9</font> = <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c19">o9</font> = <font color="Maroon" title="c9">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="E25">A192</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:6_3_1"/><span class="lab"><font color="Green" title="E26">A193</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E2:6_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A194</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_3"><span class="lab"><font color="Green" title="E18">A185</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E3:6_3_1"/><span class="lab"><font color="Green" title="E28">A195</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_3"><span class="lab"><font color="Green" title="E20">A187</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E4:6_3_1"/>
not <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_3_1_1"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_3_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_3_1"><span class="lab"><font color="Green" title="E26">A193</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_3_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b9</font>,<font color="Maroon" title="c19">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:6_3_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E5:6_3_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</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="E6:6_3_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_3"><span class="lab"><font color="Green" title="E23">A190</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:6_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A196</font></span>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_3_1"><span class="lab"><font color="Green" title="E27">A194</font></span></a>, <a class="txt" href="#E3:6_3_1"><span class="lab"><font color="Green" title="E28">A195</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E6:6_3_1"/><span class="lab"><font color="Green" title="E30">A197</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_3"><span class="lab"><font color="Green" title="E19">A186</font></span></a>, <a class="txt" href="#E1:6_3_1"><span class="lab"><font color="Green" title="E26">A193</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E7:6_3_1"/>
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_3"><span class="lab"><font color="Green" title="E21">A188</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E8:6_3_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A198</font></span>: 
( <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font> or <font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">c1</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_3_1"><span class="lab"><font color="Green" title="E30">A197</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/><a NAME="E9:6_3_1"/>
not <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_3_1_2"/>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_3_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_3_1"><span class="lab"><font color="Green" title="E26">A193</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E3:6_3_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">c9</font>,<font color="Maroon" title="c19">o9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E4:6_3_1_2"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o9</font>,<font color="Maroon" title="c18">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E5:6_3_1_2"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</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="E6:6_3_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_3"><span class="lab"><font color="Green" title="E22">A189</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E10:6_3_1"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_3_1"><span class="lab"><font color="Green" title="E29">A196</font></span></a>, <a class="txt" href="#E8:6_3_1"><span class="lab"><font color="Green" title="E31">A198</font></span></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><span class="lab"><font color="Green" title="E26">A199</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_3_2"/><span class="lab"><font color="Green" title="E27">A200</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E2:6_3_2"/><span class="lab"><font color="Green" title="E28">A201</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E3:6_3_2"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_3_2_1"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_3_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o9</font>,<font color="Maroon" title="c18">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></span>;<br/>
<a NAME="E3:6_3_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</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="E4:6_3_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_3"><span class="lab"><font color="Green" title="E22">A189</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E4:6_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_3"><span class="lab"><font color="Green" title="E17">A184</font></span></a>, <a class="txt" href="#E9:6_3"><span class="lab"><font color="Green" title="E24">A191</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><a NAME="E5:6_3_2"/><span class="kw">then </span>
<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6_3_2"><span class="lab"><font color="Green" title="E27">A200</font></span></a>, <a class="txt" href="#E2:6_3_2"><span class="lab"><font color="Green" title="E28">A201</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/><span class="kw">hence </span><a NAME="E6:6_3_2"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</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="6_3_3"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:6_3_3"/><span class="lab"><font color="Green" title="E27">A202</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c15">c1</font>,<font color="Maroon" title="c13">b1</font>
 <span class="kw">and </span><br/><a NAME="E2:6_3_3"/><span class="lab"><font color="Green" title="E28">A203</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font></span><br/><a NAME="E3:6_3_3"/><span class="lab"><font color="Green" title="E29">A204</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_3"><span class="lab"><font color="Green" title="E17">A184</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E4:6_3_3"/><span class="lab"><font color="Green" title="E30">A205</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_3"><span class="lab"><font color="Green" title="E18">A185</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E5:6_3_3"/><span class="lab"><font color="Green" title="E31">A206</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_3"><span class="lab"><font color="Green" title="E19">A186</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E6:6_3_3"/><span class="lab"><font color="Green" title="E32">A207</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c13">b1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_3"><span class="lab"><font color="Green" title="E20">A187</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E7:6_3_3"/><span class="lab"><font color="Green" title="E33">A208</font></span>: 
<font color="Maroon" title="c11">a1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_3"><span class="lab"><font color="Green" title="E21">A188</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/><a NAME="E8:6_3_3"/><span class="lab"><font color="Green" title="E34">A209</font></span>: 
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_3_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_3_3_1"/><span class="lab"><font color="Green" title="E35">A210</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c15">c1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_3_3_1"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">c1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_3_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_3_3_1_1"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">c1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_3_3_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:6_3"><span class="lab"><font color="Green" title="E21">A188</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E3:6_3_3_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_3"><span class="lab"><font color="Green" title="E17">A184</font></span></a>, <a class="txt" href="#E2:6_3_3"><span class="lab"><font color="Green" title="E28">A203</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:6_3_3_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</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="E5:6_3_3_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E6:6_3_3_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">a9</font>,<font color="Maroon" title="c18">c9</font>,<font color="Maroon" title="c19">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E7:6_3_3_1_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o9</font>,<font color="Maroon" title="c18">c9</font>,<font color="Maroon" title="c16">a9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E8:6_3_3_1_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:6_3_3_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:6_3"><span class="lab"><font color="Green" title="E22">A189</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:6_3_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:6_3"><span class="lab"><font color="Green" title="E19">A186</font></span></a>, <a class="txt" href="#E1:6_3_3_1"><span class="lab"><font color="Green" title="E35">A210</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:6_3_3_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_3"><span class="lab"><font color="Green" title="E17">A184</font></span></a>, <a class="txt" href="#E7:6_3"><span class="lab"><font color="Green" title="E22">A189</font></span></a>, <a class="txt" href="#E2:6_3_3"><span class="lab"><font color="Green" title="E28">A203</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><a NAME="E9:6_3_3"/>
not <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_3_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_3_3_2"/><span class="lab"><font color="Green" title="E35">A211</font></span>: 
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_3_3_2"/><span class="lab"><font color="Green" title="E36">A212</font></span>: 
<font color="Maroon" title="c9">o</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">b1</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_3_3_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:6_3_3_2_1"/>
<font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:6_3_3_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c11">a1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:6_3"><span class="lab"><font color="Green" title="E20">A187</font></span></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></span>;<br/>
<a NAME="E3:6_3_3_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_3"><span class="lab"><font color="Green" title="E17">A184</font></span></a>, <a class="txt" href="#E2:6_3_3"><span class="lab"><font color="Green" title="E28">A203</font></span></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></span>;<br/>
<a NAME="E4:6_3_3_2_1"/><span class="kw">then </span>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c9">o</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="E5:6_3_3_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c9">o</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>;<br/>
<a NAME="E6:6_3_3_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">a9</font>,<font color="Maroon" title="c17">b9</font>,<font color="Maroon" title="c19">o9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<a NAME="E7:6_3_3_2_1"/><span class="kw">then </span>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o9</font>,<font color="Maroon" title="c16">a9</font>,<font color="Maroon" title="c17">b9</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></span>;<br/>
<a NAME="E8:6_3_3_2_1"/><span class="kw">then </span>
 <a href="analmetr.html#R5" title="ANALMETR:pred.5">LIN</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c12">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:6_3_3_2_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:6_3"><span class="lab"><font color="Green" title="E23">A190</font></span></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:6_3_3_2"/>
<font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c10">a</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c9">o</font>,<font color="Maroon" title="c13">b1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:6_3"><span class="lab"><font color="Green" title="E17">A184</font></span></a>, <a class="txt" href="#E2:6_3_3"><span class="lab"><font color="Green" title="E28">A203</font></span></a>, <a class="txt" href="#E1:6_3_3_2"><span class="lab"><font color="Green" title="E35">A211</font></span></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:6_3_3_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:6_3"><span class="lab"><font color="Green" title="E18">A185</font></span></a>, <a class="txt" href="#E8:6_3"><span class="lab"><font color="Green" title="E23">A190</font></span></a>, <a class="txt" href="#E2:6_3_3_2"><span class="lab"><font color="Green" title="E36">A212</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><a NAME="E10:6_3_3"/><span class="kw">then </span>
<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:6"><span class="lab"><font color="Green" title="E15">A92</font></span></a>, <a class="txt" href="#E1:6_3_3"><span class="lab"><font color="Green" title="E27">A202</font></span></a>, <a class="txt" href="#E3:6_3_3"><span class="lab"><font color="Green" title="E29">A204</font></span></a>, <a class="txt" href="#E4:6_3_3"><span class="lab"><font color="Green" title="E30">A205</font></span></a>, <a class="txt" href="#E5:6_3_3"><span class="lab"><font color="Green" title="E31">A206</font></span></a>, <a class="txt" href="#E6:6_3_3"><span class="lab"><font color="Green" title="E32">A207</font></span></a>, <a class="txt" href="#E7:6_3_3"><span class="lab"><font color="Green" title="E33">A208</font></span></a>, <a class="txt" href="#E8:6_3_3"><span class="lab"><font color="Green" title="E34">A209</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E11:6_3_3"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</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="E15:6_3"/>
<font color="Maroon" title="c12">b</font>,<font color="Maroon" title="c14">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c15">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:6_3"><span class="lab"><font color="Green" title="E25">A192</font></span></a>, <a class="txt" href="#E13:6_3"><span class="lab"><font color="Green" title="E26">A199</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E15:6"/>
<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c7">c</font> <a href="analmetr.html#R4" title="ANALMETR:pred.4">_|_</a> <font color="Maroon" title="c6">b1</font>,<font color="Maroon" title="c8">c1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:6"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="txt" href="#E2:6"><span class="lab"><font color="Green" title="E6">A2</font></span></a>, <a class="txt" href="#E3:6"><span class="lab"><font color="Green" title="E7">A3</font></span></a>, <a class="txt" href="#E4:6"><span class="lab"><font color="Green" title="E8">A4</font></span></a>, <a class="txt" href="#E5:6"><span class="lab"><font color="Green" title="E9">A5</font></span></a>, <a class="txt" href="#E6:6"><span class="lab"><font color="Green" title="E10">A6</font></span></a>, <a class="txt" href="#E7:6"><span class="lab"><font color="Green" title="E11">A7</font></span></a>, <a class="txt" href="#E8:6"><span class="lab"><font color="Green" title="E12">A8</font></span></a>, <a class="txt" href="#E11:6"><span class="lab"><font color="Green" title="E14">A91</font></span></a>, <a class="txt" href="#E13:6"><span class="lab"><font color="Green" title="E16">A183</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
