<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">OAS</font> be   <a href="analoaf.html#NM1" title="ANALOAF:NM.1">OAffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>;<br/><b>let </b><font color="Maroon" title="c4">f</font> be   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">OAS</font>;<br/>







<b>assume </b><a NAME="E1:76"/><i><font color="Green" title="E46">A1</font></i>: 
( <font color="Maroon" title="c4">f</font> <a href="transgeo.html#NR7" title="TRANSGEO:NR.7">is_Tr</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> )
 ;<br/>

<a NAME="E2:76"/><b>then </b><i><font color="Green" title="E47">A2</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">OAS</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/>
<a NAME="E3:76"/><i><font color="Green" title="E48">A3</font></i>: 
<font color="Maroon" title="c4">f</font> <a href="transgeo.html#NR6" title="TRANSGEO:NR.6">is_Dil</a> 
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="transgeo.html#D9" target="_self" title="TRANSGEO:def.9">Def9</a></i>;<br/>
<a NAME="E4:76"/><i><font color="Green" title="E49">A4</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<a NAME="E5:76"/><b>then </b><i><font color="Green" title="E50">A5</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E6:76"/><i><font color="Green" title="E51">A6</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:76_1"/><i><font color="Green" title="E52">A7</font></i>: 
<font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 ;<br/><a NAME="E2:76_1"/><i><font color="Green" title="E53">A8</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E3:76"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:76_1_1"/><i><font color="Green" title="E54">A9</font></i>: 
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 ;<br/><a NAME="E2:76_1_1"/><i><font color="Green" title="E55">A10</font></i>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:76_1_1_1"/>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="transgeo.html#E5:76"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="transgeo.html#E6:76"><i><font color="Green" title="E51">A6</font></i></a>, <a class="txt" href="transgeo.html#E87"><i><font color="Green" title="E43">Lm6</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/>
<a NAME="E2:76_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/>
<a NAME="E3:76_1_1_1"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76_1"><i><font color="Green" title="E52">A7</font></i></a>, <a class="txt" href="transgeo.html#E1:76_1_1"><i><font color="Green" title="E54">A9</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/>
<a NAME="E4:76_1_1_1"/><b>then </b>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:76_1_1_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="diraf.html#T13" title="DIRAF:th.13">DIRAF:13</a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon" title="c5">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><b> such that </b><br/><a NAME="E4:76_1_1"/><i><font color="Green" title="E56">A11</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="diraf.html#T43" title="DIRAF:th.43">DIRAF:43</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><b> such that </b><br/><a NAME="E6:76_1_1"/><i><font color="Green" title="E57">A12</font></i>: 
( <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">x</font> &amp; <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">x</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E6:76"><i><font color="Green" title="E51">A6</font></i></a>, <a class="txt" href="transgeo.html#E1:76_1"><i><font color="Green" title="E52">A7</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/><a NAME="E7:76_1_1"/><i><font color="Green" title="E58">A13</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:76_1_1_2"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 ;<br/>

<a NAME="E2:76_1_1_2"/><b>then </b>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E6:76_1_1"><i><font color="Green" title="E57">A12</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/>
<a NAME="E3:76_1_1_2"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/>
<a NAME="E4:76_1_1_2"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E4:76"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/>
<a NAME="E5:76_1_1_2"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>;<br/>
<b>hence </b><a NAME="E6:76_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E1:76_1"><i><font color="Green" title="E52">A7</font></i></a>, <a class="txt" href="transgeo.html#E4:76_1_1"><i><font color="Green" title="E56">A11</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>;<br/>


</div><b>end;</b></div><a NAME="E8:76_1_1"/><i><font color="Green" title="E59">A14</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:76_1_1_3"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 ;<br/>

<a NAME="E2:76_1_1_3"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E3:76_1_1_3"/><b>then </b>
( <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">x</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E6:76_1_1"><i><font color="Green" title="E57">A12</font></i></a>, <a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a>, <a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/>
<a NAME="E4:76_1_1_3"/><b>then </b>
( <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E4:76"><i><font color="Green" title="E49">A4</font></i></a>, <a class="txt" href="transgeo.html#E7:76_1_1"><i><font color="Green" title="E58">A13</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E5:76_1_1_3"/><b>then </b>
( <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/>
<a NAME="E6:76_1_1_3"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/>
<a NAME="E7:76_1_1_3"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">q</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/>
<b>hence </b><a NAME="E8:76_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E4:76_1_1"><i><font color="Green" title="E56">A11</font></i></a>, <a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/>


</div><b>end;</b></div><a NAME="E9:76_1_1"/><i><font color="Green" title="E60">A15</font></i>: 
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="transgeo.html#E4:76_1_1"><i><font color="Green" title="E56">A11</font></i></a>, <a class="txt" href="transgeo.html#E86"><i><font color="Green" title="E42">Lm5</font></i></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/><a NAME="E10:76_1_1"/>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c6">x</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E6:76_1_1"><i><font color="Green" title="E57">A12</font></i></a>, <a class="ref" href="diraf.html#D3" title="DIRAF:def.3">DIRAF:def 3</a></i>;<br/><a NAME="E11:76_1_1"/><b>then </b><i><font color="Green" title="E61">A16</font></i>: 
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="ref" href="diraf.html#T13" title="DIRAF:th.13">DIRAF:13</a></i>;<br/><a NAME="E12:76_1_1"/><i><font color="Green" title="E62">A17</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1_4"><b>proof </b></a><div class="add">

<a NAME="E1:76_1_1_4"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E6:76_1_1"><i><font color="Green" title="E57">A12</font></i></a>, <a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/>
<a NAME="E2:76_1_1_4"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E9:76_1_1"><i><font color="Green" title="E60">A15</font></i></a>, <a class="ref" href="analoaf.html#D5" title="ANALOAF:def.5">ANALOAF:def 5</a></i>;<br/>
<a NAME="E3:76_1_1_4"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c6">x</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></i>;<br/>
<a NAME="E4:76_1_1_4"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c6">x</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/>
<b>hence </b><a NAME="E5:76_1_1_4"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>


</div><b>end;</b></div><a NAME="E13:76_1_1"/>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1_5"><b>proof </b></a><div class="add">

<a NAME="E1:76_1_1_5"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E4:76"><i><font color="Green" title="E49">A4</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E2:76_1_1_5"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/>
<a NAME="E3:76_1_1_5"/><b>then </b>
( <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E9:76_1_1"><i><font color="Green" title="E60">A15</font></i></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a>, <a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></i>;<br/>
<a NAME="E4:76_1_1_5"/><b>then </b>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/>
<b>hence </b><a NAME="E5:76_1_1_5"/>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/>


</div><b>end;</b></div><a NAME="E14:76_1_1"/><b>then </b>
 <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E8:76_1_1"><i><font color="Green" title="E59">A14</font></i></a>, <a class="txt" href="transgeo.html#E11:76_1_1"><i><font color="Green" title="E61">A16</font></i></a>, <a class="txt" href="transgeo.html#E12:76_1_1"><i><font color="Green" title="E62">A17</font></i></a>, <a class="ref" href="pasch.html#T15" title="PASCH:th.15">PASCH:15</a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font><b> such that </b><br/><a NAME="E16:76_1_1"/><i><font color="Green" title="E63">A18</font></i>: 
(  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="diraf.html#R1" title="DIRAF:pred.1">Mid</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E2:76_1_1"><i><font color="Green" title="E55">A10</font></i></a>, <a class="txt" href="transgeo.html#E8:76_1_1"><i><font color="Green" title="E59">A14</font></i></a>, <a class="ref" href="pasch.html#T35" title="PASCH:th.35">PASCH:35</a></i>;<br/><a NAME="E17:76_1_1"/><i><font color="Green" title="E64">A19</font></i>: 
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c3">b</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E16:76_1_1"><i><font color="Green" title="E63">A18</font></i></a>, <a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a></i>;<br/><a NAME="E18:76_1_1"/><i><font color="Green" title="E65">A20</font></i>: 
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1_6"><b>proof </b></a><div class="add">

<a NAME="E1:76_1_1_6"/><i><font color="Green" title="E66">A21</font></i>: 
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E3:76"><i><font color="Green" title="E48">A3</font></i></a>, <a class="txt" href="transgeo.html#E5:76"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="transgeo.html#T60" target="_self" title="TRANSGEO:th.60">Th60</a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/>
<b>hence </b><a NAME="E2:76_1_1_6"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="transgeo.html#E5:76"><i><font color="Green" title="E50">A5</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>;<br/>

<a NAME="E3:76_1_1_6"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/>
<b>hence </b><a NAME="E4:76_1_1_6"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="transgeo.html#E5:76"><i><font color="Green" title="E50">A5</font></i></a>, <a class="txt" href="transgeo.html#E1:76_1_1_6"><i><font color="Green" title="E66">A21</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:76_1_1"/><i><font color="Green" title="E66">A22</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="transgeo.html#E2:76"><i><font color="Green" title="E47">A2</font></i></a>, <a class="ref" href="transgeo.html#D9" target="_self" title="TRANSGEO:def.9">Def9</a></i>;<br/><a NAME="E20:76_1_1"/><b>then </b><i><font color="Green" title="E67">A23</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E4:76_1_1"><i><font color="Green" title="E56">A11</font></i></a>, <a class="txt" href="transgeo.html#E18:76_1_1"><i><font color="Green" title="E65">A20</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>;<br/><a NAME="E21:76_1_1"/><i><font color="Green" title="E68">A24</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="76_1_1_7"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:76_1_1_7"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 ;<br/>

<a NAME="E2:76_1_1_7"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:76"><i><font color="Green" title="E46">A1</font></i></a>, <a class="txt" href="transgeo.html#E3:76"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="transgeo.html#T67" target="_self" title="TRANSGEO:th.67">Th67</a></i>;<br/>
<a NAME="E3:76_1_1_7"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c5">q</font> )
 
<b>by </b><i><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/>
<b>hence </b><a NAME="E4:76_1_1_7"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E19:76_1_1"><i><font color="Green" title="E66">A22</font></i></a>, <a class="txt" href="transgeo.html#E20:76_1_1"><i><font color="Green" title="E67">A23</font></i></a>, <a class="ref" href="diraf.html#T39" title="DIRAF:th.39">DIRAF:39</a></i>;<br/>


</div><b>end;</b></div><a NAME="E22:76_1_1"/><i><font color="Green" title="E69">A25</font></i>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E8:76_1_1"><i><font color="Green" title="E59">A14</font></i></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/><a NAME="E23:76_1_1"/><i><font color="Green" title="E70">A26</font></i>: 
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">y</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E11:76_1_1"><i><font color="Green" title="E61">A16</font></i></a>, <a class="txt" href="transgeo.html#E17:76_1_1"><i><font color="Green" title="E64">A19</font></i></a>, <a class="ref" href="diraf.html#T34" title="DIRAF:th.34">DIRAF:34</a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/><a NAME="E24:76_1_1"/><b>then </b><i><font color="Green" title="E71">A27</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E22:76_1_1"><i><font color="Green" title="E69">A25</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>;<br/><a NAME="E25:76_1_1"/><i><font color="Green" title="E72">A28</font></i>: 
( <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> &amp; <font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">q</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E21:76_1_1"><i><font color="Green" title="E68">A24</font></i></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/><a NAME="E26:76_1_1"/><i><font color="Green" title="E73">A29</font></i>: 
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E3:76"><i><font color="Green" title="E48">A3</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/><a NAME="E27:76_1_1"/>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">y</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font>,<font color="Maroon" title="c7">y</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E17:76_1_1"><i><font color="Green" title="E64">A19</font></i></a>, <a class="txt" href="transgeo.html#E22:76_1_1"><i><font color="Green" title="E69">A25</font></i></a>, <a class="txt" href="transgeo.html#E23:76_1_1"><i><font color="Green" title="E70">A26</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>;<br/><a NAME="E28:76_1_1"/><b>then </b>
( <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">y</font> )
 <b>by </b><i><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/><a NAME="E29:76_1_1"/><b>then </b>
( <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">y</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c5">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">y</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E25:76_1_1"><i><font color="Green" title="E72">A28</font></i></a>, <a class="txt" href="transgeo.html#E26:76_1_1"><i><font color="Green" title="E73">A29</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/><a NAME="E30:76_1_1"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c7">y</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E25:76_1_1"><i><font color="Green" title="E72">A28</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/><a NAME="E31:76_1_1"/><b>then </b>
<font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c3">b</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/><a NAME="E32:76_1_1"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c7">y</font>,<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c3">b</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a>, <a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/><b>hence </b><a NAME="E33:76_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E17:76_1_1"><i><font color="Green" title="E64">A19</font></i></a>, <a class="txt" href="transgeo.html#E20:76_1_1"><i><font color="Green" title="E67">A23</font></i></a>, <a class="txt" href="transgeo.html#E21:76_1_1"><i><font color="Green" title="E68">A24</font></i></a>, <a class="txt" href="transgeo.html#E24:76_1_1"><i><font color="Green" title="E71">A27</font></i></a>, <a class="ref" href="diraf.html#T38" title="DIRAF:th.38">DIRAF:38</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E4:76_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:76_1"><i><font color="Green" title="E53">A8</font></i></a>, <a class="ref" href="diraf.html#D4" title="DIRAF:def.4">DIRAF:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:76"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="ref" href="diraf.html#T7" title="DIRAF:th.7">DIRAF:7</a></i>;<br/>


</div>
