<?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">p</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="c3">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><b>that </b><br/><a NAME="E1:84"/><i><font color="Green" title="E54">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="transgeo.html#NR6" title="TRANSGEO:NR.6">is_Dil</a> 
 <b>and </b><br/><a NAME="E2:84"/><i><font color="Green" title="E55">A2</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font>
 <b>and </b><br/><a NAME="E3:84"/><i><font color="Green" title="E56">A3</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> holds  <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font>
 ;<br/>

<a NAME="E4:84"/><i><font color="Green" title="E57">A4</font></i>: 
for <font color="Olive" title="b1">y</font>, <font color="Olive" title="b2">z</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>  st not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font> holds <br/><font color="Olive" title="b1">y</font>,<font color="Olive" title="b2">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">z</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</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>assume </b><a NAME="E1:84_1"/><i><font color="Green" title="E58">A5</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>
 ;<br/>

<a NAME="E2:84_1"/>
( <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font> &amp; <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="transgeo.html#E3:84"><i><font color="Green" title="E56">A3</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/>
<b>hence </b><a NAME="E3:84_1"/>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:84_1"><i><font color="Green" title="E58">A5</font></i></a>, <a class="ref" href="pasch.html#T20" title="PASCH:th.20">PASCH:20</a></i>;<br/>


</div><b>end;</b></div>
<b>let </b><font color="Maroon" title="c4">y</font>, <font color="Maroon" title="c5">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font>;<br/>



<a NAME="E5:84"/>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> implies <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:84_2"/><i><font color="Green" title="E58">A6</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>
 ;<br/>

<div><i><font color="Green" title="E59">A7</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:84_2_1"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">z</font>
 ;<br/><a NAME="E2:84_2_1"/><b>then </b>
<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c4">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:84"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="transgeo.html#E3:84"><i><font color="Green" title="E56">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E3:84_2_1"/>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:84_2_2"/><i><font color="Green" title="E60">A8</font></i>: 
( <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c4">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">z</font> &amp; <font color="Maroon" title="c5">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">p</font> )
 ;<br/><b>then consider </b><font color="Maroon" title="c6">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="E3:84_2_2"/><i><font color="Green" title="E61">A9</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c6">q</font>
 <b>by </b><i><a class="ref" href="diraf.html#T43" title="DIRAF:th.43">DIRAF:43</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">r</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="E5:84_2_2"/><i><font color="Green" title="E62">A10</font></i>: 
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font>
 <b>and </b><br/><a NAME="E6:84_2_2"/><i><font color="Green" title="E63">A11</font></i>: 
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c6">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="ref" href="diraf.html#T31" title="DIRAF:th.31">DIRAF:31</a></i>;<br/><a NAME="E7:84_2_2"/><i><font color="Green" title="E64">A12</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">q</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_2_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:84_2_2_1"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">q</font>
 ;<br/>

<a NAME="E2:84_2_2_1"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c6">q</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">p</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c4">y</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:84_2"><i><font color="Green" title="E58">A6</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/>
<b>hence </b><a NAME="E3:84_2_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E1:84_2_2"><i><font color="Green" title="E60">A8</font></i></a>, <a class="txt" href="transgeo.html#E3:84_2_2"><i><font color="Green" title="E61">A9</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="E8:84_2_2"/><b>then </b><i><font color="Green" title="E65">A13</font></i>: 
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E5:84_2_2"><i><font color="Green" title="E62">A10</font></i></a>, <a class="txt" href="transgeo.html#E6:84_2_2"><i><font color="Green" title="E63">A11</font></i></a>, <a class="ref" href="pasch.html#T21" title="PASCH:th.21">PASCH:21</a></i>;<br/><a NAME="E9:84_2_2"/><i><font color="Green" title="E66">A14</font></i>: 
<font color="Maroon" title="c6">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">r</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:84_2_2_2"/>
<font color="Maroon" title="c6">q</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">r</font>
 ;<br/>

<a NAME="E2:84_2_2_2"/><b>then </b>
<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c4">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c5">z</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E6:84_2_2"><i><font color="Green" title="E63">A11</font></i></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/>
<a NAME="E3:84_2_2_2"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</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="E4:84_2_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E7:84_2_2"><i><font color="Green" title="E64">A12</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>


</div><b>end;</b></div><a NAME="E10:84_2_2"/>
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="84_2_2_3"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:84_2_2_3"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font>
 ;<br/>

<a NAME="E2:84_2_2_3"/><b>then </b><i><font color="Green" title="E67">A15</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c2">p</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E3:84_2_2_3"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c5">z</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:84_2"><i><font color="Green" title="E58">A6</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/>
<a NAME="E4:84_2_2_3"/><b>then </b>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">p</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font>
 
<b>by </b><i><a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/>
<a NAME="E5:84_2_2_3"/><b>then </b>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">y</font>
 
<b>by </b><i><a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/>
<a NAME="E6:84_2_2_3"/><b>then </b>
<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c4">y</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E1:84_2_2"><i><font color="Green" title="E60">A8</font></i></a>, <a class="txt" href="transgeo.html#E5:84_2_2"><i><font color="Green" title="E62">A10</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/>
<a NAME="E7:84_2_2_3"/><b>then </b>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c4">y</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font>,<font color="Maroon" title="c6">q</font> )
 
<b>by </b><i><a class="txt" href="transgeo.html#E9:84_2_2"><i><font color="Green" title="E66">A14</font></i></a>, <a class="txt" href="transgeo.html#E2:84_2_2_3"><i><font color="Green" title="E67">A15</font></i></a>, <a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a>, <a class="ref" href="diraf.html#T39" title="DIRAF:th.39">DIRAF:39</a></i>;<br/>
<b>hence </b><a NAME="E8:84_2_2_3"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E3:84_2_2"><i><font color="Green" title="E61">A9</font></i></a>, <a class="txt" href="transgeo.html#E9:84_2_2"><i><font color="Green" title="E66">A14</font></i></a>, <a class="txt" href="transgeo.html#E2:84_2_2_3"><i><font color="Green" title="E67">A15</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="E11:84_2_2"/><b>then </b><i><font color="Green" title="E67">A16</font></i>: 
<font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c7">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E4:84"><i><font color="Green" title="E57">A4</font></i></a></i>;<br/><a NAME="E12:84_2_2"/><i><font color="Green" title="E68">A17</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="transgeo.html#E5:84_2_2"><i><font color="Green" title="E62">A10</font></i></a>, <a class="ref" href="transgeo.html#T58" target="_self" title="TRANSGEO:th.58">Th58</a></i>;<br/><a NAME="E13:84_2_2"/><i><font color="Green" title="E69">A18</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="transgeo.html#E6:84_2_2"><i><font color="Green" title="E63">A11</font></i></a>, <a class="ref" href="transgeo.html#T58" target="_self" title="TRANSGEO:th.58">Th58</a></i>;<br/><a NAME="E14:84_2_2"/>
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E1:84"><i><font color="Green" title="E54">A1</font></i></a>, <a class="txt" href="transgeo.html#E7:84_2_2"><i><font color="Green" title="E64">A12</font></i></a>, <a class="ref" href="transgeo.html#T59" target="_self" title="TRANSGEO:th.59">Th59</a></i>;<br/><a NAME="E15:84_2_2"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E12:84_2_2"><i><font color="Green" title="E68">A17</font></i></a>, <a class="txt" href="transgeo.html#E13:84_2_2"><i><font color="Green" title="E69">A18</font></i></a>, <a class="ref" href="pasch.html#T21" title="PASCH:th.21">PASCH:21</a></i>;<br/><a NAME="E16:84_2_2"/><b>then </b><i><font color="Green" title="E70">A19</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">r</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="ref" href="diraf.html#T5" title="DIRAF:th.5">DIRAF:5</a></i>;<br/><a NAME="E17:84_2_2"/>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">q</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">r</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E8:84_2_2"><i><font color="Green" title="E65">A13</font></i></a>, <a class="txt" href="transgeo.html#E9:84_2_2"><i><font color="Green" title="E66">A14</font></i></a>, <a class="txt" href="transgeo.html#E11:84_2_2"><i><font color="Green" title="E67">A16</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a></i>;<br/><b>hence </b><a NAME="E18:84_2_2"/>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E9:84_2_2"><i><font color="Green" title="E66">A14</font></i></a>, <a class="txt" href="transgeo.html#E16:84_2_2"><i><font color="Green" title="E70">A19</font></i></a>, <a class="ref" href="diraf.html#T6" title="DIRAF:th.6">DIRAF:6</a>, <a class="ref" href="funct_2.html#T85" title="FUNCT_2:th.85">FUNCT_2:85</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:84_2"/>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E2:84"><i><font color="Green" title="E55">A2</font></i></a>, <a class="txt" href="transgeo.html#E3:84"><i><font color="Green" title="E56">A3</font></i></a>, <a class="txt" href="transgeo.html#E2:84_2"><i><font color="Green" title="E59">A7</font></i></a>, <a class="ref" href="diraf.html#T7" title="DIRAF:th.7">DIRAF:7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:84"/>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c5">z</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E4:84"><i><font color="Green" title="E57">A4</font></i></a></i>;<br/>


</div>
