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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="conaffm.html#NR5" title="CONAFFM:NR.5">LIN_holds_in</a> <font color="Maroon" title="c1">X</font> implies  <a href="conaffm.html#NR4" title="CONAFFM:NR.4">ODES_holds_in</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<b>assume </b><a NAME="E1:7"/><i><font color="Green" title="E5">A1</font></i>: 
 <a href="conaffm.html#NR5" title="CONAFFM:NR.5">LIN_holds_in</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="conaffm.html#NR4" title="CONAFFM:NR.4">ODES_holds_in</a> <font color="Maroon" title="c1">X</font></span><br/>

<b>let </b><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>; <i><font color="Red">:: according to </font></i><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>













<b>assume </b><a NAME="E2:7"/><i><font color="Green" title="E6">A2</font></i>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="E3:7"/><i><font color="Green" title="E7">A3</font></i>: 
 <a href="conaffm.html#NR6" title="CONAFFM:NR.6">LIN1_holds_in</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="conaffm.html#T3" target="_self" title="CONAFFM:th.3">Th3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>now </b></a><div class="add"><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="conaffm.html#NR5" title="CONAFFM:NR.5">LIN_holds_in</a> <font color="Maroon" title="c1">X</font> &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/><b>assume </b><a NAME="E1:7_1"/><i><font color="Green" title="E8">A4</font></i>: 
 <a href="conaffm.html#NR5" title="CONAFFM:NR.5">LIN_holds_in</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/><b>assume </b><a NAME="E2:7_1"/><i><font color="Green" title="E9">A5</font></i>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/><b>assume </b><a NAME="E3:7_1"/><i><font color="Green" title="E10">A6</font></i>: 
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:()"><i><font color="Red">::  thesis: </font></i></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/><b>reconsider </b><font color="Maroon" title="c16">a'</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c17">a1'</font> = <font color="Maroon" title="c11">a1</font>, <font color="Maroon" title="c18">b'</font> = <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c19">b1'</font> = <font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c20">c'</font> = <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c21">c1'</font> = <font color="Maroon" title="c15">c1</font>, <font color="Maroon" title="c22">o'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><div><i><font color="Green" title="E11">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_1_1"/><i><font color="Green" title="E12">A8</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_1_1"/><b>then </b><i><font color="Green" title="E13">A9</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E3:7_1_1"/><i><font color="Green" title="E14">A10</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E4:7_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="7_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_1"><i><font color="Green" title="E12">A8</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_1_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:7_1_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:7_1_1"/><b>then </b><i><font color="Green" title="E15">A11</font></i>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_1"><i><font color="Green" title="E13">A9</font></i></a>, <a class="txt" href="conaffm.html#E3:7_1_1"><i><font color="Green" title="E14">A10</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E6:7_1_1"/><i><font color="Green" title="E16">A12</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_1"><i><font color="Green" title="E12">A8</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E7:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E8:7_1_1"/><b>then </b><i><font color="Green" title="E17">A13</font></i>: 
( <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E6:7_1_1"><i><font color="Green" title="E16">A12</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E9:7_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="7_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_1"><i><font color="Green" title="E12">A8</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_1_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:7_1_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E10:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_1"><i><font color="Green" title="E15">A11</font></i></a>, <a class="txt" href="conaffm.html#E8:7_1_1"><i><font color="Green" title="E17">A13</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><i><font color="Green" title="E12">A14</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_1_2"/><i><font color="Green" title="E13">A15</font></i>: 
(  <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> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_1_2"/><i><font color="Green" title="E14">A16</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><a NAME="E3:7_1_2"/><i><font color="Green" title="E15">A17</font></i>: 
<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="7_1_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_1_2_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_1_2_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:7_1_2"/><i><font color="Green" title="E16">A18</font></i>: 
<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="7_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_2_2"/><i><font color="Green" title="E17">A19</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_1_2_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_2"><i><font color="Green" title="E13">A15</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_2_2"><i><font color="Green" title="E17">A19</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_1_2_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_1_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:7_1_2_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:7_1_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_2"><i><font color="Green" title="E13">A15</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:7_1_2"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_2"><i><font color="Green" title="E14">A16</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E7:7_1_2"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E3:7_1_2"><i><font color="Green" title="E15">A17</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E8:7_1_2"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E9:7_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E10:7_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E11:7_1_2"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E12:7_1_2"/><b>then </b><i><font color="Green" title="E17">A20</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E13:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E14:7_1_2"/><b>then </b><i><font color="Green" title="E18">A21</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_1_2"><i><font color="Green" title="E16">A18</font></i></a>, <a class="txt" href="conaffm.html#E12:7_1_2"><i><font color="Green" title="E17">A20</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E15:7_1_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_2"><i><font color="Green" title="E13">A15</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E16:7_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E17:7_1_2"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E18:7_1_2"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E19:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_2"><i><font color="Green" title="E14">A16</font></i></a>, <a class="txt" href="conaffm.html#E14:7_1_2"><i><font color="Green" title="E18">A21</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><i><font color="Green" title="E13">A22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_1_3"/><i><font color="Green" title="E14">A23</font></i>: 
(  <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> &amp; 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> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_1_3"/><i><font color="Green" title="E15">A24</font></i>: 
<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="7_1_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_1_3_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:7_1_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_1_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:7_1_3_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E7:7_1_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:7_1_3"/><i><font color="Green" title="E16">A25</font></i>: 
<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="7_1_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_3_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_1_3_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:7_1_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_1_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:7_1_3_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E7:7_1_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:7_1_3"/><i><font color="Green" title="E17">A26</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_3"><i><font color="Green" title="E14">A23</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E5:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_3"><i><font color="Green" title="E14">A23</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:7_1_3"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E3:7_1_3"><i><font color="Green" title="E16">A25</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E7:7_1_3"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_3"><i><font color="Green" title="E15">A24</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E8:7_1_3"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E9:7_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E10:7_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E11:7_1_3"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E12:7_1_3"/><b>then </b><i><font color="Green" title="E18">A27</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E13:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E14:7_1_3"/><b>then </b><i><font color="Green" title="E19">A28</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_1_3"><i><font color="Green" title="E17">A26</font></i></a>, <a class="txt" href="conaffm.html#E12:7_1_3"><i><font color="Green" title="E18">A27</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E15:7_1_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_3"><i><font color="Green" title="E14">A23</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E16:7_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E17:7_1_3"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E18:7_1_3"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E19:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7_1_3"><i><font color="Green" title="E16">A25</font></i></a>, <a class="txt" href="conaffm.html#E14:7_1_3"><i><font color="Green" title="E19">A28</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_1_4"/><i><font color="Green" title="E14">A29</font></i>: 
( 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> &amp; 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> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_1_4"/><i><font color="Green" title="E15">A30</font></i>: 
( <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_1"/><i><font color="Green" title="E16">A31</font></i>: 
<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="7_1_4_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_1_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_1_4_1_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_1_4_1_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_1_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:7_1_4_1"/><i><font color="Green" title="E17">A32</font></i>: 
<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="7_1_4_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_1_2"/><i><font color="Green" title="E18">A33</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_1_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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_1_4_1_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green" title="E14">A29</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4_1_2"><i><font color="Green" title="E18">A33</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_1_4_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_1_4_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_1_4_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:7_1_4_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:7_1_4_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:7_1_4_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="7_1_4_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_1_3"/><i><font color="Green" title="E18">A34</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_1_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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_1_4_1_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green" title="E14">A29</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4_1_3"><i><font color="Green" title="E18">A34</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_1_4_1_3"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_1_4_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_1_4_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:7_1_4_1_3"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:7_1_4_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_1_4_1"/>
( <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4_1"><i><font color="Green" title="E16">A31</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4_1"><i><font color="Green" title="E17">A32</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:7_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="7_1_4_2"><b>proof </b></a><div class="add">

<b>consider </b><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><b> such that </b><br/><a NAME="E2:7_1_4_2"/><i><font color="Green" title="E16">A35</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c24">p'</font> = <font color="Maroon" title="c23">p</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E5:7_1_4_2"/><i><font color="Green" title="E17">A36</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">p1'</font> = <font color="Maroon" title="c25">p1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E7:7_1_4_2"/>
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="7_1_4_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_2_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4_2"><i><font color="Green" title="E16">A35</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:7_1_4_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7_1"><i><font color="Green" title="E10">A6</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_2"><i><font color="Green" title="E17">A36</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:7_1_4_2"/><b>then </b>
not <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c26">p1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c27">e'</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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><b> such that </b><br/><a NAME="E10:7_1_4_2"/><i><font color="Green" title="E18">A37</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">p'</font>,<font color="Maroon" title="c27">e'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c26">p1'</font>,<font color="Maroon" title="c27">e'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c28">e</font> = <font color="Maroon" title="c27">e'</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E12:7_1_4_2"/>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_1_4_2"><i><font color="Green" title="E18">A37</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_1_4_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:7_1_4_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4_2"><i><font color="Green" title="E16">A35</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:7_1_4_2"/><b>then </b><i><font color="Green" title="E19">A38</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:7_1_4_2"/>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_1_4_2"><i><font color="Green" title="E18">A37</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:7_1_4_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:7_1_4_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4_2"><i><font color="Green" title="E17">A36</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E19:7_1_4_2"/><b>then </b><i><font color="Green" title="E20">A39</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E20:7_1_4_2"/><i><font color="Green" title="E21">A40</font></i>: 
<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="7_1_4_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_2_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E15:7_1_4_2"><i><font color="Green" title="E19">A38</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:7_1_4_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green" title="E14">A29</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E21:7_1_4_2"/>
<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="7_1_4_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_2_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E19:7_1_4_2"><i><font color="Green" title="E20">A39</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:7_1_4_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green" title="E14">A29</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E22:7_1_4_2"/>
 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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E15:7_1_4_2"><i><font color="Green" title="E19">A38</font></i></a>, <a class="txt" href="conaffm.html#E19:7_1_4_2"><i><font color="Green" title="E20">A39</font></i></a>, <a class="txt" href="conaffm.html#E20:7_1_4_2"><i><font color="Green" title="E21">A40</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><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><b> such that </b><br/><a NAME="E5:7_1_4"/><i><font color="Green" title="E16">A41</font></i>: 
(  <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> &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="Maroon" title="c23">e</font> &amp; <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> &amp; <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/><b>reconsider </b><font color="Maroon" title="c24">e'</font> = <font color="Maroon" title="c23">e</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E7:7_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="7_1_4_3"><b>proof </b></a><div class="add">

<b>consider </b><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><b> such that </b><br/><a NAME="E2:7_1_4_3"/><i><font color="Green" title="E17">A42</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">p'</font> = <font color="Maroon" title="c25">p</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E5:7_1_4_3"/><i><font color="Green" title="E18">A43</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c28">p1'</font> = <font color="Maroon" title="c27">p1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E7:7_1_4_3"/><i><font color="Green" title="E19">A44</font></i>: 
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="7_1_4_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_3_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E3:7_1_4_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E3:7_1"><i><font color="Green" title="E10">A6</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:7_1_4_3"/>
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="7_1_4_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_3_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_3_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4_3"><i><font color="Green" title="E17">A42</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E3:7_1_4_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4_3"><i><font color="Green" title="E18">A43</font></i></a>, <a class="txt" href="conaffm.html#E7:7_1_4_3"><i><font color="Green" title="E19">A44</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E9:7_1_4_3"/><b>then </b>
not <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c28">p1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c29">e1'</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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><b> such that </b><br/><a NAME="E11:7_1_4_3"/><i><font color="Green" title="E20">A45</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">p'</font>,<font color="Maroon" title="c29">e1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c28">p1'</font>,<font color="Maroon" title="c29">e1'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c30">e1</font> = <font color="Maroon" title="c29">e1'</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E13:7_1_4_3"/>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E11:7_1_4_3"><i><font color="Green" title="E20">A45</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E14:7_1_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E15:7_1_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4_3"><i><font color="Green" title="E17">A42</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E16:7_1_4_3"/><b>then </b><i><font color="Green" title="E21">A46</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E17:7_1_4_3"/>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E11:7_1_4_3"><i><font color="Green" title="E20">A45</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E18:7_1_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E19:7_1_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4_3"><i><font color="Green" title="E18">A43</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E20:7_1_4_3"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E21:7_1_4_3"/>
 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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E16:7_1_4_3"><i><font color="Green" title="E21">A46</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><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><b> such that </b><br/><a NAME="E9:7_1_4"/><i><font color="Green" title="E17">A47</font></i>: 
(  <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> &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="Maroon" title="c25">e1</font> )
 ;<br/><b>reconsider </b><font color="Maroon" title="c26">e1'</font> = <font color="Maroon" title="c25">e1</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E11:7_1_4"/><i><font color="Green" title="E18">A48</font></i>: 
( <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> &amp; <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> &amp; <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="7_1_4_4"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_4"/><i><font color="Green" title="E19">A49</font></i>: 
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_4_1"/>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:7_1_4_4_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:7_1_4_4_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:7_1_4_4_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_1_4_4_1"/><b>then </b><i><font color="Green" title="E20">A50</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:7_1_4_4_1"/>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green" title="E17">A47</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:7_1_4_4_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c19">b1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:7_1_4_4_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c19">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E9:7_1_4_4_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E10:7_1_4_4_1"/>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_4_1"><i><font color="Green" title="E20">A50</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:7_1_4_4"/><i><font color="Green" title="E20">A51</font></i>: 
<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="7_1_4_4_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_4_2"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_4_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c22">o'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_4_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E4:7_1_4_4_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E5:7_1_4_4_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:7_1_4_4"/>
<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="7_1_4_4_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_4_3"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_4_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c21">c1'</font>,<font color="Maroon" title="c22">o'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green" title="E17">A47</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_4_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c21">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E4:7_1_4_4_3"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_1_4_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:7_1_4_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green" title="E14">A29</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E7:7_1_4_4_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_1_4_4"/>
( <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> &amp; <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1_4_4"><i><font color="Green" title="E19">A49</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4_4"><i><font color="Green" title="E20">A51</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E12:7_1_4"/><i><font color="Green" title="E19">A52</font></i>: 
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="7_1_4_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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="c10">a</font>,<font color="Maroon" title="c23">e</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_5"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_1_4_5"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_1_4_5"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:7_1_4_5"/><b>then </b><i><font color="Green" title="E20">A53</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:7_1_4_5"/>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<b>hence </b><a NAME="E7:7_1_4_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E11:7_1_4"><i><font color="Green" title="E18">A48</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_5"><i><font color="Green" title="E20">A53</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E13:7_1_4"/><i><font color="Green" title="E20">A54</font></i>: 
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_6"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_6"/>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:7_1_4_6"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:7_1_4_6"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:7_1_4_6"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_1_4_6"/><b>then </b><i><font color="Green" title="E21">A55</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:7_1_4_6"/>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green" title="E17">A47</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:7_1_4_6"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_6"><i><font color="Green" title="E21">A55</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E8:7_1_4_6"/>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E14:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E15:7_1_4"/><b>then </b><i><font color="Green" title="E21">A56</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_1"><i><font color="Green" title="E8">A4</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E1:7_1_4"><i><font color="Green" title="E14">A29</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green" title="E17">A47</font></i></a>, <a class="txt" href="conaffm.html#E11:7_1_4"><i><font color="Green" title="E18">A48</font></i></a>, <a class="txt" href="conaffm.html#E12:7_1_4"><i><font color="Green" title="E19">A52</font></i></a>, <a class="txt" href="conaffm.html#E13:7_1_4"><i><font color="Green" title="E20">A54</font></i></a>, <a class="ref" href="conaffm.html#D5" target="_self" title="CONAFFM:def.5">Def5</a></i>;<br/><a NAME="E16:7_1_4"/><i><font color="Green" title="E22">A57</font></i>: 
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="7_1_4_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1_4_7"/>
 <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c22">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E4:7_1_4_7"/><b>then </b>
<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c22">o'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E5:7_1_4_7"/><b>then </b><i><font color="Green" title="E23">A58</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:7_1_4_7"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E8:7_1_4_7"/><b>then </b>
<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E9:7_1_4_7"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E10:7_1_4_7"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4_7"><i><font color="Green" title="E23">A58</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E11:7_1_4_7"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_1_4_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E14:7_1_4_7"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E15:7_1_4_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E17:7_1_4"/>
<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>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1_4_8"><b>proof </b></a><div class="add">

<a NAME="E1:7_1_4_8"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E2:7_1_4_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E3:7_1_4_8"/><b>then </b>
<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E4:7_1_4_8"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:7_1_4_8"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:7_1_4_8"/><b>then </b><i><font color="Green" title="E23">A59</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:7_1_4_8"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c21">c1'</font>,<font color="Maroon" title="c26">e1'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green" title="E17">A47</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E8:7_1_4_8"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c21">c1'</font>,<font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c26">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E9:7_1_4_8"/><b>then </b>
<font color="Maroon" title="c21">c1'</font>,<font color="Maroon" title="c17">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1'</font>,<font color="Maroon" title="c26">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E10:7_1_4_8"/><b>then </b>
<font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c21">c1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c21">c1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E11:7_1_4_8"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E12:7_1_4_8"/>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="txt" href="conaffm.html#E6:7_1_4_8"><i><font color="Green" title="E23">A59</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E18:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1"><i><font color="Green" title="E9">A5</font></i></a>, <a class="txt" href="conaffm.html#E2:7_1_4"><i><font color="Green" title="E15">A30</font></i></a>, <a class="txt" href="conaffm.html#E5:7_1_4"><i><font color="Green" title="E16">A41</font></i></a>, <a class="txt" href="conaffm.html#E9:7_1_4"><i><font color="Green" title="E17">A47</font></i></a>, <a class="txt" href="conaffm.html#E11:7_1_4"><i><font color="Green" title="E18">A48</font></i></a>, <a class="txt" href="conaffm.html#E15:7_1_4"><i><font color="Green" title="E21">A56</font></i></a>, <a class="txt" href="conaffm.html#E16:7_1_4"><i><font color="Green" title="E22">A57</font></i></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E9:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_1"><i><font color="Green" title="E11">A7</font></i></a>, <a class="txt" href="conaffm.html#E6:7_1"><i><font color="Green" title="E12">A14</font></i></a>, <a class="txt" href="conaffm.html#E7:7_1"><i><font color="Green" title="E13">A22</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E5:7"/><b>then </b><i><font color="Green" title="E8">A60</font></i>: 
( 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> )
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="conaffm.html#E2:7"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/>
<div><i><font color="Green" title="E9">A61</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2"><b>now </b></a><div class="add"><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>assume </b><a NAME="E1:7_2"/><i><font color="Green" title="E10">A62</font></i>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/><b>assume </b><a NAME="E2:7_2"/><i><font color="Green" title="E11">A63</font></i>: 
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:()"><i><font color="Red">::  thesis: </font></i></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/><b>reconsider </b><font color="Maroon" title="c16">a'</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c17">a1'</font> = <font color="Maroon" title="c11">a1</font>, <font color="Maroon" title="c18">b'</font> = <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c19">b1'</font> = <font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c20">c'</font> = <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c21">c1'</font> = <font color="Maroon" title="c15">c1</font>, <font color="Maroon" title="c22">o'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><div><i><font color="Green" title="E12">A64</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_2_1"/><i><font color="Green" title="E13">A65</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_2_1"/><b>then </b><i><font color="Green" title="E14">A66</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E3:7_2_1"/><i><font color="Green" title="E15">A67</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E4:7_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="7_2_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_1"><i><font color="Green" title="E13">A65</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_2_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:7_2_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_2_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:7_2_1"/><b>then </b><i><font color="Green" title="E16">A68</font></i>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_1"><i><font color="Green" title="E14">A66</font></i></a>, <a class="txt" href="conaffm.html#E3:7_2_1"><i><font color="Green" title="E15">A67</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E6:7_2_1"/><i><font color="Green" title="E17">A69</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_1"><i><font color="Green" title="E13">A65</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E7:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E8:7_2_1"/><b>then </b><i><font color="Green" title="E18">A70</font></i>: 
( <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E6:7_2_1"><i><font color="Green" title="E17">A69</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E9:7_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="7_2_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_1"><i><font color="Green" title="E13">A65</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_2_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:7_2_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_2_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E10:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_1"><i><font color="Green" title="E16">A68</font></i></a>, <a class="txt" href="conaffm.html#E8:7_2_1"><i><font color="Green" title="E18">A70</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><i><font color="Green" title="E13">A71</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_2_2"/><i><font color="Green" title="E14">A72</font></i>: 
(  <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> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_2_2"/><i><font color="Green" title="E15">A73</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/><a NAME="E3:7_2_2"/><i><font color="Green" title="E16">A74</font></i>: 
<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="7_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_2_2_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_2_2_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:7_2_2"/><i><font color="Green" title="E17">A75</font></i>: 
<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="7_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_2_2"/><i><font color="Green" title="E18">A76</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_2_2_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_2"><i><font color="Green" title="E14">A72</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_2_2"><i><font color="Green" title="E18">A76</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_2_2_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_2_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:7_2_2_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:7_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_2"><i><font color="Green" title="E14">A72</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:7_2_2"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_2"><i><font color="Green" title="E15">A73</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E7:7_2_2"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E3:7_2_2"><i><font color="Green" title="E16">A74</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E8:7_2_2"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E9:7_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E10:7_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E11:7_2_2"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E12:7_2_2"/><b>then </b><i><font color="Green" title="E18">A77</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E13:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E14:7_2_2"/><b>then </b><i><font color="Green" title="E19">A78</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_2_2"><i><font color="Green" title="E17">A75</font></i></a>, <a class="txt" href="conaffm.html#E12:7_2_2"><i><font color="Green" title="E18">A77</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E15:7_2_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_2"><i><font color="Green" title="E14">A72</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E16:7_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E17:7_2_2"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E18:7_2_2"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E19:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_2"><i><font color="Green" title="E15">A73</font></i></a>, <a class="txt" href="conaffm.html#E14:7_2_2"><i><font color="Green" title="E19">A78</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><i><font color="Green" title="E14">A79</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_2_3"/><i><font color="Green" title="E15">A80</font></i>: 
(  <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> &amp; 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> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_2_3"/><i><font color="Green" title="E16">A81</font></i>: 
<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="7_2_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_2_3_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:7_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_2_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:7_2_3_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E7:7_2_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:7_2_3"/><i><font color="Green" title="E17">A82</font></i>: 
<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="7_2_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_3_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_2_3_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E4:7_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E5:7_2_3_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E6:7_2_3_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E7:7_2_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:7_2_3"/><i><font color="Green" title="E18">A83</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_3"><i><font color="Green" title="E15">A80</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E5:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_3"><i><font color="Green" title="E15">A80</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E6:7_2_3"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E3:7_2_3"><i><font color="Green" title="E17">A82</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E7:7_2_3"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_3"><i><font color="Green" title="E16">A81</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E8:7_2_3"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E9:7_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E10:7_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E11:7_2_3"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E12:7_2_3"/><b>then </b><i><font color="Green" title="E19">A84</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E13:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E14:7_2_3"/><b>then </b><i><font color="Green" title="E20">A85</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_2_3"><i><font color="Green" title="E18">A83</font></i></a>, <a class="txt" href="conaffm.html#E12:7_2_3"><i><font color="Green" title="E19">A84</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E15:7_2_3"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_3"><i><font color="Green" title="E15">A80</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E16:7_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E17:7_2_3"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E18:7_2_3"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><b>hence </b><a NAME="E19:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7_2_3"><i><font color="Green" title="E17">A82</font></i></a>, <a class="txt" href="conaffm.html#E14:7_2_3"><i><font color="Green" title="E20">A85</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_2_4"/><i><font color="Green" title="E15">A86</font></i>: 
( 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> &amp; 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> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_2_4"/><i><font color="Green" title="E16">A87</font></i>: 
( <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:7_2_4_1"/><i><font color="Green" title="E17">A88</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E2:7_2_4_1"/><i><font color="Green" title="E18">A89</font></i>: 
<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="7_2_4_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_1_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<a NAME="E3:7_2_4_1_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_2_4_1_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_2_4_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:7_2_4_1"/><i><font color="Green" title="E19">A90</font></i>: 
<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="7_2_4_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_1_2"/><i><font color="Green" title="E20">A91</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_1_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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_2_4_1_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4_1_2"><i><font color="Green" title="E20">A91</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_2_4_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_2_4_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_2_4_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:7_2_4_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:7_2_4_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E4:7_2_4_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="7_2_4_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_1_3"/><i><font color="Green" title="E20">A92</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_1_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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_2_4_1_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4_1_3"><i><font color="Green" title="E20">A92</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_2_4_1_3"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E5:7_2_4_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E6:7_2_4_1_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E7:7_2_4_1_3"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E8:7_2_4_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:7_2_4_1"/>
( <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4_1"><i><font color="Green" title="E17">A88</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4_1"><i><font color="Green" title="E18">A89</font></i></a>, <a class="txt" href="conaffm.html#E3:7_2_4_1"><i><font color="Green" title="E19">A90</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:7_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="7_2_4_2"><b>proof </b></a><div class="add">

<b>consider </b><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><b> such that </b><br/><a NAME="E2:7_2_4_2"/><i><font color="Green" title="E17">A93</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c24">p'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E5:7_2_4_2"/><i><font color="Green" title="E18">A94</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">p1'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E7:7_2_4_2"/>
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="7_2_4_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_2_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4_2"><i><font color="Green" title="E17">A93</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E3:7_2_4_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4_2"><i><font color="Green" title="E18">A94</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E4:7_2_4_2_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_2_4_2_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E6:7_2_4_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2"><i><font color="Green" title="E11">A63</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:7_2_4_2"/><b>then </b>
not <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c26">p1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c27">e'</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><b> such that </b><br/><a NAME="E10:7_2_4_2"/><i><font color="Green" title="E19">A95</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">p'</font>,<font color="Maroon" title="c27">e'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c26">p1'</font>,<font color="Maroon" title="c27">e'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c28">e</font> = <font color="Maroon" title="c27">e'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E12:7_2_4_2"/>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_2_4_2"><i><font color="Green" title="E19">A95</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_2_4_2"/><b>then </b><i><font color="Green" title="E20">A96</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:7_2_4_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4_2"><i><font color="Green" title="E17">A93</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:7_2_4_2"/><b>then </b><i><font color="Green" title="E21">A97</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:7_2_4_2"/>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_2_4_2"><i><font color="Green" title="E19">A95</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:7_2_4_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:7_2_4_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4_2"><i><font color="Green" title="E18">A94</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E19:7_2_4_2"/><b>then </b><i><font color="Green" title="E22">A98</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E20:7_2_4_2"/><i><font color="Green" title="E23">A99</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4_2"><i><font color="Green" title="E17">A93</font></i></a>, <a class="txt" href="conaffm.html#E13:7_2_4_2"><i><font color="Green" title="E20">A96</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E21:7_2_4_2"/><i><font color="Green" title="E24">A100</font></i>: 
<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="7_2_4_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_2_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E15:7_2_4_2"><i><font color="Green" title="E21">A97</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_2_4_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E4:7_2_4_2_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E5:7_2_4_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E22:7_2_4_2"/>
<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="7_2_4_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_2_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E19:7_2_4_2"><i><font color="Green" title="E22">A98</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_2_4_2_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:7_2_4_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E23:7_2_4_2"/>
 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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E15:7_2_4_2"><i><font color="Green" title="E21">A97</font></i></a>, <a class="txt" href="conaffm.html#E19:7_2_4_2"><i><font color="Green" title="E22">A98</font></i></a>, <a class="txt" href="conaffm.html#E20:7_2_4_2"><i><font color="Green" title="E23">A99</font></i></a>, <a class="txt" href="conaffm.html#E21:7_2_4_2"><i><font color="Green" title="E24">A100</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><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><b> such that </b><br/><a NAME="E5:7_2_4"/><i><font color="Green" title="E17">A101</font></i>: 
(  <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> &amp;  <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> &amp; <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> &amp; <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> &amp; <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/><b>reconsider </b><font color="Maroon" title="c24">e'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E7:7_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="7_2_4_3"><b>proof </b></a><div class="add">

<b>consider </b><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><b> such that </b><br/><a NAME="E2:7_2_4_3"/><i><font color="Green" title="E18">A102</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c26">p'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<b>consider </b><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><b> such that </b><br/><a NAME="E5:7_2_4_3"/><i><font color="Green" title="E19">A103</font></i>: 
( <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> &amp; <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> )
 <b>by </b><i><a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c28">p1'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E7:7_2_4_3"/>
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="7_2_4_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_3_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4_3"><i><font color="Green" title="E18">A102</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E3:7_2_4_3_1"/><b>then </b>
<font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c28">p1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_2_4_3_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c28">p1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E5:7_2_4_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E6:7_2_4_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E7:7_2_4_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4_3"><i><font color="Green" title="E19">A103</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:7_2_4_3_1"/><b>then </b><i><font color="Green" title="E20">A104</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E9:7_2_4_3_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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E10:7_2_4_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="txt" href="conaffm.html#E8:7_2_4_3_1"><i><font color="Green" title="E20">A104</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E11:7_2_4_3_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E12:7_2_4_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_2_4_3_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E14:7_2_4_3_1"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E15:7_2_4_3_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E16:7_2_4_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E17:7_2_4_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="txt" href="conaffm.html#E8:7_2_4_3_1"><i><font color="Green" title="E20">A104</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E18:7_2_4_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E8:7_2_4_3"/><b>then </b>
not <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">p'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c28">p1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c29">e1'</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><b> such that </b><br/><a NAME="E10:7_2_4_3"/><i><font color="Green" title="E20">A105</font></i>: 
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">p'</font>,<font color="Maroon" title="c29">e1'</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c28">p1'</font>,<font color="Maroon" title="c29">e1'</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T74" title="AFF_1:th.74">AFF_1:74</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c30">e1</font> = <font color="Maroon" title="c29">e1'</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/>
<a NAME="E12:7_2_4_3"/>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_2_4_3"><i><font color="Green" title="E20">A105</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E13:7_2_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E14:7_2_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4_3"><i><font color="Green" title="E18">A102</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E15:7_2_4_3"/><b>then </b><i><font color="Green" title="E21">A106</font></i>: 
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E16:7_2_4_3"/>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E10:7_2_4_3"><i><font color="Green" title="E20">A105</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E17:7_2_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E18:7_2_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4_3"><i><font color="Green" title="E19">A103</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<b>hence </b><a NAME="E19:7_2_4_3"/>
 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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E15:7_2_4_3"><i><font color="Green" title="E21">A106</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>then consider </b><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><b> such that </b><br/><a NAME="E9:7_2_4"/><i><font color="Green" title="E18">A107</font></i>: 
(  <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> &amp; <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/><b>reconsider </b><font color="Maroon" title="c26">e1'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><a NAME="E11:7_2_4"/><i><font color="Green" title="E19">A108</font></i>: 
( <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> &amp; <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> &amp; <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="7_2_4_4"><b>proof </b></a><div class="add">

<a NAME="E1:7_2_4_4"/><i><font color="Green" title="E20">A109</font></i>: 
<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>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_2_4_4_1"><b>proof </b></a><div class="add">

<a NAME="E1:7_2_4_4_1"/>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E2:7_2_4_4_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:7_2_4_4_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:7_2_4_4_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_2_4_4_1"/><b>then </b><i><font color="Green" title="E21">A110</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E6:7_2_4_4_1"/>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green" title="E18">A107</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E7:7_2_4_4_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E8:7_2_4_4_1"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">e1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E9:7_2_4_4_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<b>hence </b><a NAME="E10:7_2_4_4_1"/>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="txt" href="conaffm.html#E5:7_2_4_4_1"><i><font color="Green" title="E21">A110</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:7_2_4_4"/><i><font color="Green" title="E21">A111</font></i>: 
<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="7_2_4_4_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_4_2"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_4_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c22">o'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E3:7_2_4_4_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<b>hence </b><a NAME="E4:7_2_4_4_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:7_2_4_4"/>
<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="7_2_4_4_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_4_3"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_4_3"/><b>then </b>
<font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c22">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green" title="E18">A107</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E3:7_2_4_4_3"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E4:7_2_4_4_3"/><b>then </b><i><font color="Green" title="E22">A112</font></i>: 
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E5:7_2_4_4_3"/>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:7_2_4_4_3"/><b>then </b><i><font color="Green" title="E23">A113</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4_4"><i><font color="Green" title="E21">A111</font></i></a>, <a class="txt" href="conaffm.html#E4:7_2_4_4_3"><i><font color="Green" title="E22">A112</font></i></a>, <a class="ref" href="analmetr.html#T82" title="ANALMETR:th.82">ANALMETR:82</a></i>;<br/>
<a NAME="E7:7_2_4_4_3"/><b>then </b><i><font color="Green" title="E24">A114</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<a NAME="E8:7_2_4_4_3"/>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E6:7_2_4_4_3"><i><font color="Green" title="E23">A113</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E9:7_2_4_4_3"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E10:7_2_4_4_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E11:7_2_4_4_3"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E12:7_2_4_4_3"/><b>then </b>
<font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c22">o'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c17">a1'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/>
<a NAME="E13:7_2_4_4_3"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">a1'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<a NAME="E14:7_2_4_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E15:7_2_4_4_3"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="txt" href="conaffm.html#E7:7_2_4_4_3"><i><font color="Green" title="E24">A114</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E16:7_2_4_4_3"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:7_2_4_4"/>
( <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> &amp; <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4_4"><i><font color="Green" title="E20">A109</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4_4"><i><font color="Green" title="E21">A111</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E12:7_2_4"/><i><font color="Green" title="E20">A115</font></i>: 
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="7_2_4_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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="c12">b</font>,<font color="Maroon" title="c10">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_5"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_4_5"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/>
<a NAME="E4:7_2_4_5"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/>
<b>hence </b><a NAME="E5:7_2_4_5"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E13:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E14:7_2_4"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E15:7_2_4"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c16">a'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c24">e'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E16:7_2_4"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E17:7_2_4"/><b>then </b><i><font color="Green" title="E21">A116</font></i>: 
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E18:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green" title="E18">A107</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E19:7_2_4"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E20:7_2_4"/><b>then </b>
<font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c17">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c26">e1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E21:7_2_4"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E22:7_2_4"/><b>then </b><i><font color="Green" title="E22">A117</font></i>: 
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E23:7_2_4"/>
<font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">a1'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green" title="E18">A107</font></i></a>, <a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E24:7_2_4"/><b>then </b>
<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">a1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c26">e1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E25:7_2_4"/><b>then </b><i><font color="Green" title="E23">A118</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E26:7_2_4"/><b>then </b><i><font color="Green" title="E24">A119</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="txt" href="conaffm.html#E11:7_2_4"><i><font color="Green" title="E19">A108</font></i></a>, <a class="txt" href="conaffm.html#E12:7_2_4"><i><font color="Green" title="E20">A115</font></i></a>, <a class="txt" href="conaffm.html#E17:7_2_4"><i><font color="Green" title="E21">A116</font></i></a>, <a class="txt" href="conaffm.html#E22:7_2_4"><i><font color="Green" title="E22">A117</font></i></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</a></i>;<br/><a NAME="E27:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E28:7_2_4"/><b>then </b><i><font color="Green" title="E25">A120</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E3:7"><i><font color="Green" title="E7">A3</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="txt" href="conaffm.html#E11:7_2_4"><i><font color="Green" title="E19">A108</font></i></a>, <a class="txt" href="conaffm.html#E17:7_2_4"><i><font color="Green" title="E21">A116</font></i></a>, <a class="txt" href="conaffm.html#E22:7_2_4"><i><font color="Green" title="E22">A117</font></i></a>, <a class="txt" href="conaffm.html#E25:7_2_4"><i><font color="Green" title="E23">A118</font></i></a>, <a class="ref" href="conaffm.html#D6" target="_self" title="CONAFFM:def.6">Def6</a></i>;<br/><a NAME="E29:7_2_4"/><i><font color="Green" title="E26">A121</font></i>: 
( <font color="Maroon" title="c25">e1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">c1</font> &amp; <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="7_2_4_6"><b>proof </b></a><div class="add">

<a NAME="E1:7_2_4_6"/><i><font color="Green" title="E27">A122</font></i>: 
<font color="Maroon" title="c25">e1</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="7_2_4_6_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_6_1"/>
<font color="Maroon" title="c25">e1</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_6_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green" title="E18">A107</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_4_6_1"/><b>then </b>
<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="c14">c</font>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:7_2_4_6_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E2:7_2_4_6"/>
<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="7_2_4_6_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_6_2"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_6_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E9:7_2_4"><i><font color="Green" title="E18">A107</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_2_4_6_2"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E2:7_2_4"><i><font color="Green" title="E16">A87</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:7_2_4_6_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2"><i><font color="Green" title="E10">A62</font></i></a>, <a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:7_2_4_6"/>
( <font color="Maroon" title="c25">e1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c15">c1</font> &amp; <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4_6"><i><font color="Green" title="E27">A122</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E30:7_2_4"/><i><font color="Green" title="E27">A123</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E28:7_2_4"><i><font color="Green" title="E25">A120</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E31:7_2_4"/><i><font color="Green" title="E28">A124</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E32:7_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c18">b'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E33:7_2_4"/><b>then </b>
 <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>
 <b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/><a NAME="E34:7_2_4"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/><a NAME="E35:7_2_4"/><b>then </b><i><font color="Green" title="E29">A125</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="txt" href="conaffm.html#E30:7_2_4"><i><font color="Green" title="E27">A123</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E36:7_2_4"/><i><font color="Green" title="E30">A126</font></i>: 
<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="7_2_4_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_2_4_7"/>
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_2_4_7"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c22">o'</font>,<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<b>hence </b><a NAME="E3:7_2_4_7"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_2_4"><i><font color="Green" title="E15">A86</font></i></a>, <a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E37:7_2_4"/>
<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c24">e'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E31:7_2_4"><i><font color="Green" title="E28">A124</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E38:7_2_4"/><b>then </b>
<font color="Maroon" title="c20">c'</font>,<font color="Maroon" title="c18">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c18">b'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E39:7_2_4"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E40:7_2_4"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E35:7_2_4"><i><font color="Green" title="E29">A125</font></i></a>, <a class="txt" href="conaffm.html#E36:7_2_4"><i><font color="Green" title="E30">A126</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E41:7_2_4"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="txt" href="conaffm.html#E26:7_2_4"><i><font color="Green" title="E24">A119</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E42:7_2_4"/><b>then </b>
<font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c19">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c21">c1'</font>,<font color="Maroon" title="c26">e1'</font>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E43:7_2_4"/><b>then </b>
<font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c19">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E44:7_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E45:7_2_4"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E46:7_2_4"/><b>then </b>
<font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c26">e1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E47:7_2_4"/><b>then </b>
<font color="Maroon" title="c26">e1'</font>,<font color="Maroon" title="c19">b1'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c19">b1'</font>,<font color="Maroon" title="c21">c1'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E48:7_2_4"/><b>then </b><i><font color="Green" title="E31">A127</font></i>: 
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E49:7_2_4"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E31:7_2_4"><i><font color="Green" title="E28">A124</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E50:7_2_4"/><b>then </b>
<font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c24">e'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E51:7_2_4"/><b>then </b>
<font color="Maroon" title="c24">e'</font>,<font color="Maroon" title="c18">b'</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c18">b'</font>,<font color="Maroon" title="c20">c'</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E52:7_2_4"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="analmetr.html#T48" title="ANALMETR:th.48">ANALMETR:48</a></i>;<br/><a NAME="E53:7_2_4"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_2_4"><i><font color="Green" title="E17">A101</font></i></a>, <a class="txt" href="conaffm.html#E26:7_2_4"><i><font color="Green" title="E24">A119</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><b>hence </b><a NAME="E54:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E29:7_2_4"><i><font color="Green" title="E26">A121</font></i></a>, <a class="txt" href="conaffm.html#E48:7_2_4"><i><font color="Green" title="E31">A127</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E8:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E4:7_2"><i><font color="Green" title="E12">A64</font></i></a>, <a class="txt" href="conaffm.html#E5:7_2"><i><font color="Green" title="E13">A71</font></i></a>, <a class="txt" href="conaffm.html#E6:7_2"><i><font color="Green" title="E14">A79</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<a NAME="E7:7"/><b>then </b><i><font color="Green" title="E10">A128</font></i>: 
( 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> )
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7"><i><font color="Green" title="E6">A2</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3"><b>now </b></a><div class="add"><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="conaffm.html#NR5" title="CONAFFM:NR.5">LIN_holds_in</a> <font color="Maroon" title="c1">X</font> &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/><b>assume </b><a NAME="E1:7_3"/>
 <a href="conaffm.html#NR5" title="CONAFFM:NR.5">LIN_holds_in</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/><b>assume </b><a NAME="E2:7_3"/><i><font color="Green" title="E11">A129</font></i>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/><b>assume </b><a NAME="E3:7_3"/><i><font color="Green" title="E12">A130</font></i>: 
( <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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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/><b>reconsider </b><font color="Maroon" title="c16">a'</font> = <font color="Maroon" title="c10">a</font>, <font color="Maroon" title="c17">b'</font> = <font color="Maroon" title="c12">b</font>, <font color="Maroon" title="c18">c'</font> = <font color="Maroon" title="c14">c</font>, <font color="Maroon" title="c19">o'</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> <b>by </b><i><a class="ref" href="analmetr.html#T47" title="ANALMETR:th.47">ANALMETR:47</a></i>;<br/><div><i><font color="Green" title="E13">A131</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_3_1"/><i><font color="Green" title="E14">A132</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_3_1"/><b>then </b><i><font color="Green" title="E15">A133</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E3:7_3_1"/><i><font color="Green" title="E16">A134</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E4:7_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="7_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_3_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_3_1"><i><font color="Green" title="E14">A132</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c17">b'</font>,<font color="Maroon" title="c19">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:7_3_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:7_3_1"/><b>then </b><i><font color="Green" title="E17">A135</font></i>: 
<font color="Maroon" title="c11">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3_1"><i><font color="Green" title="E15">A133</font></i></a>, <a class="txt" href="conaffm.html#E3:7_3_1"><i><font color="Green" title="E16">A134</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E6:7_3_1"/><i><font color="Green" title="E18">A136</font></i>: 
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_1"><i><font color="Green" title="E14">A132</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E7:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E8:7_3_1"/><b>then </b><i><font color="Green" title="E19">A137</font></i>: 
( <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E6:7_3_1"><i><font color="Green" title="E18">A136</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/><a NAME="E9:7_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="7_3_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_3_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E1:7_3_1"><i><font color="Green" title="E14">A132</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E3:7_3_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c18">c'</font>,<font color="Maroon" title="c19">o'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E4:7_3_1_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o'</font>,<font color="Maroon" title="c18">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E5:7_3_1_2"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E6:7_3_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E10:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_3_1"><i><font color="Green" title="E17">A135</font></i></a>, <a class="txt" href="conaffm.html#E8:7_3_1"><i><font color="Green" title="E19">A137</font></i></a>, <a class="ref" href="analmetr.html#T51" title="ANALMETR:th.51">ANALMETR:51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><i><font color="Green" title="E14">A138</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_3_2"/><i><font color="Green" title="E15">A139</font></i>: 
( <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> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_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="7_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o'</font>,<font color="Maroon" title="c18">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/>
<a NAME="E3:7_3_2_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E4:7_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E3:7_3_2"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="txt" href="conaffm.html#E3:7_3"><i><font color="Green" title="E12">A130</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><a NAME="E4:7_3_2"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7_3_2"><i><font color="Green" title="E15">A139</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/><b>hence </b><a NAME="E5:7_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>
 <b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_3_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:7_3_3"/><i><font color="Green" title="E15">A140</font></i>: 
( 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> &amp; <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:()"><i><font color="Red">::  thesis: </font></i></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="E2:7_3_3"/><i><font color="Green" title="E16">A141</font></i>: 
( <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> &amp; <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> &amp; <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> &amp; <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> &amp; <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> )
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/><a NAME="E3:7_3_3"/><i><font color="Green" title="E17">A142</font></i>: 
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="7_3_3_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_3_1"/><i><font color="Green" title="E18">A143</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_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="7_3_3_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_3_3_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_3_3_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green" title="E15">A140</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_3_3_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:7_3_3_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:7_3_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c18">c'</font>,<font color="Maroon" title="c19">o'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:7_3_3_1_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o'</font>,<font color="Maroon" title="c18">c'</font>,<font color="Maroon" title="c16">a'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E8:7_3_3_1_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E9:7_3_3_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:7_3_3_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3_1"><i><font color="Green" title="E18">A143</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:7_3_3_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green" title="E15">A140</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E4:7_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="7_3_3_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_3_3_2"/><i><font color="Green" title="E18">A144</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_3_3_2"/><i><font color="Green" title="E19">A145</font></i>: 
<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="7_3_3_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<a NAME="E2:7_3_3_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>;<br/>
<a NAME="E3:7_3_3_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green" title="E15">A140</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>;<br/>
<a NAME="E4:7_3_3_2_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T81" title="ANALMETR:th.81">ANALMETR:81</a></i>;<br/>
<a NAME="E5:7_3_3_2_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>;<br/>
<a NAME="E6:7_3_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font>,<font color="Maroon" title="c19">o'</font>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<a NAME="E7:7_3_3_2_1"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c19">o'</font>,<font color="Maroon" title="c16">a'</font>,<font color="Maroon" title="c17">b'</font>
 
<b>by </b><i><a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/>
<a NAME="E8:7_3_3_2_1"/><b>then </b>
 <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>
 
<b>by </b><i><a class="ref" href="analmetr.html#T55" title="ANALMETR:th.55">ANALMETR:55</a></i>;<br/>
<b>hence </b><a NAME="E9:7_3_3_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="ref" href="analmetr.html#D11" title="ANALMETR:def.11">ANALMETR:def 11</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:7_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>
 
<b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green" title="E15">A140</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3_2"><i><font color="Green" title="E18">A144</font></i></a>, <a class="ref" href="analmetr.html#T84" title="ANALMETR:th.84">ANALMETR:84</a></i>;<br/>
<b>hence </b><a NAME="E4:7_3_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="conaffm.html#E2:7_3"><i><font color="Green" title="E11">A129</font></i></a>, <a class="txt" href="conaffm.html#E2:7_3_3_2"><i><font color="Green" title="E19">A145</font></i></a>, <a class="ref" href="analmetr.html#T85" title="ANALMETR:th.85">ANALMETR:85</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E5:7_3_3"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E6:7"><i><font color="Green" title="E9">A61</font></i></a>, <a class="txt" href="conaffm.html#E1:7_3_3"><i><font color="Green" title="E15">A140</font></i></a>, <a class="txt" href="conaffm.html#E2:7_3_3"><i><font color="Green" title="E16">A141</font></i></a>, <a class="txt" href="conaffm.html#E3:7_3_3"><i><font color="Green" title="E17">A142</font></i></a></i>;<br/><b>hence </b><a NAME="E6:7_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>
 <b>by </b><i><a class="ref" href="analmetr.html#T83" title="ANALMETR:th.83">ANALMETR:83</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><b>hence </b><a NAME="E8:7_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>
 <b>by </b><i><a class="txt" href="conaffm.html#E5:7_3"><i><font color="Green" title="E13">A131</font></i></a>, <a class="txt" href="conaffm.html#E6:7_3"><i><font color="Green" title="E14">A138</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:7"/>
<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>
 <b>by </b><i><a class="txt" href="conaffm.html#E1:7"><i><font color="Green" title="E5">A1</font></i></a>, <a class="txt" href="conaffm.html#E2:7"><i><font color="Green" title="E6">A2</font></i></a>, <a class="txt" href="conaffm.html#E5:7"><i><font color="Green" title="E8">A60</font></i></a>, <a class="txt" href="conaffm.html#E7:7"><i><font color="Green" title="E10">A128</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
