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<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">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="E1:62"/><i><font color="Green" title="E35">A1</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#NR6" title="TRANSGEO:NR.6">is_Dil</a> 
 ;<br/>

<div><i><font color="Green" title="E36">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_1"/><i><font color="Green" title="E37">A3</font></i>: 
( <font color="Maroon" title="c2">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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> or for <font color="Olive" title="b1">z</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">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">z</font> )
 ;<br/><b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</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="E2:62_1"/><i><font color="Green" title="E38">A4</font></i>: 
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">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#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/><div><i><font color="Green" title="E39">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_1_1"/>
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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>
 ;<br/><a NAME="E2:62_1_1"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/><b>hence </b><a NAME="E3:62_1_1"/>
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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="ref" href="diraf.html#T25" title="DIRAF:th.25">DIRAF:25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_1_2"/><i><font color="Green" title="E40">A6</font></i>: 
for <font color="Olive" title="b1">z</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">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">z</font>
 ;<br/><b>assume </b><a NAME="E2:62_1_2"/><i><font color="Green" title="E41">A7</font></i>: 
not <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c5">z</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="E4:62_1_2"/><i><font color="Green" title="E42">A8</font></i>: 
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">z</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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="c5">z</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E2:62_1"><i><font color="Green" title="E38">A4</font></i></a>, <a class="ref" href="transgeo.html#T61" target="_self" title="TRANSGEO:th.61">Th61</a></i>;<br/><b>set </b><font color="Maroon" title="c6">t</font> = <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>;<br/><a NAME="E5:62_1_2"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">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#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="transgeo.html#E4:62_1_2"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="transgeo.html#T60" target="_self" title="TRANSGEO:th.60">Th60</a></i>;<br/><a NAME="E6:62_1_2"/><b>then </b><i><font color="Green" title="E43">A9</font></i>: 
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">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#E4:62_1_2"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></i>;<br/><a NAME="E7:62_1_2"/>
(  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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="c5">z</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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="c2">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> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">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#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="transgeo.html#E1:62_1_2"><i><font color="Green" title="E40">A6</font></i></a>, <a class="txt" href="transgeo.html#E4:62_1_2"><i><font color="Green" title="E42">A8</font></i></a>, <a class="ref" href="transgeo.html#T60" target="_self" title="TRANSGEO:th.60">Th60</a></i>;<br/><a NAME="E8:62_1_2"/><b>then </b>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">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#T40" title="DIRAF:th.40">DIRAF:40</a></i>;<br/><a NAME="E9:62_1_2"/><b>then </b>
( <font color="Maroon" title="c5">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">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="c5">z</font>,<font color="Maroon" title="c2">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="c4">y</font>,<font color="Maroon" title="c2">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#E1:62_1_2"><i><font color="Green" title="E40">A6</font></i></a>, <a class="ref" href="diraf.html#T27" title="DIRAF:th.27">DIRAF:27</a></i>;<br/><b>hence </b><a NAME="E10:62_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E2:62_1_2"><i><font color="Green" title="E41">A7</font></i></a>, <a class="txt" href="transgeo.html#E6:62_1_2"><i><font color="Green" title="E43">A9</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E5:62_1"/>
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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#E1:62_1"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="transgeo.html#E3:62_1"><i><font color="Green" title="E39">A5</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_2"/><i><font color="Green" title="E37">A10</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</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="Olive" title="b1">x</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b2">y</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font>
 ;<br/><b>assume </b><a NAME="E2:62_2"/><i><font color="Green" title="E38">A11</font></i>: 
<font color="Maroon" title="c2">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>
 ;<br/><b>given </b><font color="Maroon" title="c3">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><a NAME="E4:62_2"/><i><font color="Green" title="E39">A12</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font>
 ;<br/><b>consider </b><font color="Maroon" title="c4">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="E6:62_2"/><i><font color="Green" title="E40">A13</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1">(<span class="default"><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></span>)</span> <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#E2:62_2"><i><font color="Green" title="E38">A11</font></i></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/><a NAME="E7:62_2"/><i><font color="Green" title="E41">A14</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E6:62_2"><i><font color="Green" title="E40">A13</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/><a NAME="E8:62_2"/>
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">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#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/><a NAME="E9:62_2"/><b>then </b><i><font color="Green" title="E42">A15</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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#E4:62_2"><i><font color="Green" title="E39">A12</font></i></a>, <a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/><a NAME="E10:62_2"/><b>then </b><i><font color="Green" title="E43">A16</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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">x</font>
 <b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/><a NAME="E11:62_2"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">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#E9:62_2"><i><font color="Green" title="E42">A15</font></i></a>, <a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/><a NAME="E12:62_2"/><b>then </b><i><font color="Green" title="E44">A17</font></i>: 
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/><a NAME="E13:62_2"/>
<font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">y</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E4:62_2"><i><font color="Green" title="E39">A12</font></i></a>, <a class="txt" href="transgeo.html#E6:62_2"><i><font color="Green" title="E40">A13</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">z</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="E15:62_2"/><i><font color="Green" title="E45">A18</font></i>: 
not  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">x</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#T43" title="DIRAF:th.43">DIRAF:43</a></i>;<br/><a NAME="E16:62_2"/>
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">z</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">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#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/><a NAME="E17:62_2"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">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#E4:62_2"><i><font color="Green" title="E39">A12</font></i></a>, <a class="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/><a NAME="E18:62_2"/><b>then </b><i><font color="Green" title="E46">A19</font></i>: 
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">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">x</font>
 <b>by </b><i><a class="ref" href="diraf.html#T36" title="DIRAF:th.36">DIRAF:36</a></i>;<br/><div><i><font color="Green" title="E47">A20</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:62_2_1"/>
<font color="Maroon" title="c5">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">z</font>
 ;<br/><a NAME="E2:62_2_1"/><b>then </b>
<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c4">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">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#E1:62"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="transgeo.html#T51" target="_self" title="TRANSGEO:th.51">Th51</a></i>;<br/><a NAME="E3:62_2_1"/><b>then </b>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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="ref" href="diraf.html#D5" title="DIRAF:def.5">DIRAF:def 5</a></i>;<br/><a NAME="E4:62_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="c2">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="c4">y</font> &amp;  <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">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="c5">z</font> )
 <b>by </b><i><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="E5:62_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E7:62_2"><i><font color="Green" title="E41">A14</font></i></a>, <a class="txt" href="transgeo.html#E10:62_2"><i><font color="Green" title="E43">A16</font></i></a>, <a class="txt" href="transgeo.html#E15:62_2"><i><font color="Green" title="E45">A18</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="E20:62_2"/>
 <a href="diraf.html#R3" title="DIRAF:pred.3">LIN</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">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="c5">z</font>
 <b>by </b><i><a class="ref" href="diraf.html#T37" title="DIRAF:th.37">DIRAF:37</a></i>;<br/><a NAME="E21:62_2"/><b>then </b><i><font color="Green" title="E48">A21</font></i>: 
<font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">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">x</font>,<font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E18:62_2"><i><font color="Green" title="E46">A19</font></i></a>, <a class="ref" href="diraf.html#T40" title="DIRAF:th.40">DIRAF:40</a></i>;<br/><a NAME="E22:62_2"/>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c5">z</font>,<font color="Maroon" title="c2">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#E1:62_2"><i><font color="Green" title="E37">A10</font></i></a></i>;<br/><a NAME="E23:62_2"/><b>then </b>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E19:62_2"><i><font color="Green" title="E47">A20</font></i></a>, <a class="txt" href="transgeo.html#E21:62_2"><i><font color="Green" title="E48">A21</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/><a NAME="E24:62_2"/><b>then </b>
<font color="Maroon" title="c4">y</font>,<font color="Maroon" title="c3">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">z</font>
 <b>by </b><i><a class="txt" href="transgeo.html#E7:62_2"><i><font color="Green" title="E41">A14</font></i></a>, <a class="txt" href="transgeo.html#E12:62_2"><i><font color="Green" title="E44">A17</font></i></a>, <a class="ref" href="diraf.html#T28" title="DIRAF:th.28">DIRAF:28</a></i>;<br/><a NAME="E25:62_2"/><b>then </b>
<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c5">z</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="E26:62_2"/>
contradiction
 <b>by </b><i><a class="txt" href="transgeo.html#E15:62_2"><i><font color="Green" title="E45">A18</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>
<b>hence </b><a NAME="E4:62"/>
( ( <font color="Maroon" title="c2">f</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</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> or 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">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">x</font> ) iff for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</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="Olive" title="b1">x</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="diraf.html#R2" title="DIRAF:pred.2">'||'</a> <font color="Olive" title="b2">y</font>,<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">y</font> )
 <b>by </b><i><a class="txt" href="transgeo.html#E2:62"><i><font color="Green" title="E36">A2</font></i></a></i>;<br/>


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