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<div class="add">

<b>let </b><font color="Maroon" title="c1">AFP</font> be   <a href="diraf.html#NM2" title="DIRAF:NM.2">AffinPlane</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <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">AFP</font>  st <font color="Maroon" title="c1">AFP</font> <a href="translac.html#NR1" title="TRANSLAC:NR.1">satisfies_Fano</a>  &amp; <font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR11" title="AFF_2:NR.11">satisfies_des</a>  &amp; <font color="Olive" title="b1">f</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  holds <br/> ex <font color="Olive" title="b2">g</font> being  <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">AFP</font> st <br/>( <font color="Olive" title="b2">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b2">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">f</font> )</span><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">AFP</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">AFP</font> <a href="translac.html#NR1" title="TRANSLAC:NR.1">satisfies_Fano</a>  &amp; <font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR11" title="AFF_2:NR.11">satisfies_des</a>  &amp; <font color="Maroon" title="c2">f</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  implies  ex <font color="Olive" title="b1">g</font> being  <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">AFP</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b1">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font> ) )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:26"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c1">AFP</font> <a href="translac.html#NR1" title="TRANSLAC:NR.1">satisfies_Fano</a>  &amp; <font color="Maroon" title="c1">AFP</font> <a href="aff_2.html#NR11" title="AFF_2:NR.11">satisfies_des</a>  )
 <b>and </b><br/><a NAME="E2:26"/><i><font color="Green" title="E25">A2</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">g</font> being  <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">AFP</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b1">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font> )</span><br/>

<div><i><font color="Green" title="E26">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_1"/><i><font color="Green" title="E27">A4</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">AFP</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">g</font> being  <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">AFP</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b1">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font> )</span><br/><b>set </b><font color="Maroon" title="c3">g</font> =  <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">AFP</font>;<br/><a NAME="E2:26_1"/><i><font color="Green" title="E28">A5</font></i>: 
 <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">AFP</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>by </b><i><a class="ref" href="transgeo.html#T99" title="TRANSGEO:th.99">TRANSGEO:99</a></i>;<br/><a NAME="E3:26_1"/>
<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">AFP</font></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</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">AFP</font></span>)</span> <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">AFP</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></i>;<br/><b>hence </b><a NAME="E4:26_1"/>
 ex <font color="Olive" title="b1">g</font> being  <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">AFP</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b1">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font> )
 <b>by </b><i><a class="txt" href="translac.html#E1:26_1"><i><font color="Green" title="E27">A4</font></i></a>, <a class="txt" href="translac.html#E2:26_1"><i><font color="Green" title="E28">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_2"/><i><font color="Green" title="E27">A6</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">AFP</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">g</font> being  <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">AFP</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b1">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font> )</span><br/><b>consider </b><font color="Maroon" title="c3">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font>;<br/><b>set </b><font color="Maroon" title="c4">b</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">a</font>;<br/><a NAME="E3:26_2"/>
<font color="Maroon" title="c3">a</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="c3">a</font>
 <b>by </b><i><a class="txt" href="translac.html#E2:26"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="translac.html#E1:26_2"><i><font color="Green" title="E27">A6</font></i></a>, <a class="ref" href="transgeo.html#D11" title="TRANSGEO:def.11">TRANSGEO:def 11</a></i>;<br/><b>then consider </b><font color="Maroon" title="c5">c</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><b> such that </b><br/><a NAME="E5:26_2"/><i><font color="Green" title="E28">A7</font></i>: 
not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a</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">a</font>,<font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T22" title="AFF_1:th.22">AFF_1:22</a></i>;<br/><a NAME="E6:26_2"/><i><font color="Green" title="E29">A8</font></i>: 
( not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</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">a</font> &amp; not  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">c</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">a</font>,<font color="Maroon" title="c3">a</font> )
 <b>by </b><i><a class="txt" href="translac.html#E5:26_2"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><b>consider </b><font color="Maroon" title="c6">d</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><b> such that </b><br/><a NAME="E8:26_2"/><i><font color="Green" title="E30">A9</font></i>: 
( <font color="Maroon" title="c5">c</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">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF: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">a</font>,<font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="ref" href="diraf.html#T47" title="DIRAF:th.47">DIRAF:47</a></i>;<br/><b>consider </b><font color="Maroon" title="c7">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AFP</font><b> such that </b><br/><a NAME="E10:26_2"/><i><font color="Green" title="E31">A10</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</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">a</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c7">p</font>
 <b>and </b><br/><a NAME="E11:26_2"/><i><font color="Green" title="E32">A11</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>,<font color="Maroon" title="c7">p</font>
 <b>by </b><i><a class="txt" href="translac.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="translac.html#E6:26_2"><i><font color="Green" title="E29">A8</font></i></a>, <a class="txt" href="translac.html#E8:26_2"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="translac.html#T4" target="_self" title="TRANSLAC:th.4">Th4</a></i>;<br/><b>consider </b><font color="Maroon" title="c8">h</font> being   <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">AFP</font><b> such that </b><br/><a NAME="E13:26_2"/><i><font color="Green" title="E33">A12</font></i>: 
<font color="Maroon" title="c8">h</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>and </b><br/><a NAME="E14:26_2"/><i><font color="Green" title="E34">A13</font></i>: 
<font color="Maroon" title="c8">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="translac.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="translac.html#T9" target="_self" title="TRANSLAC:th.9">Th9</a></i>;<br/><a NAME="E15:26_2"/><i><font color="Green" title="E35">A14</font></i>: 
<font color="Maroon" title="c8">h</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="txt" href="translac.html#E6:26_2"><i><font color="Green" title="E29">A8</font></i></a>, <a class="txt" href="translac.html#E8:26_2"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="translac.html#E13:26_2"><i><font color="Green" title="E33">A12</font></i></a>, <a class="txt" href="translac.html#E14:26_2"><i><font color="Green" title="E34">A13</font></i></a>, <a class="ref" href="translac.html#T5" target="_self" title="TRANSLAC:th.5">Th5</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">f1</font> being   <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">AFP</font><b> such that </b><br/><a NAME="E17:26_2"/><i><font color="Green" title="E36">A15</font></i>: 
<font color="Maroon" title="c9">f1</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>and </b><br/><a NAME="E18:26_2"/><i><font color="Green" title="E37">A16</font></i>: 
<font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="translac.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="translac.html#T9" target="_self" title="TRANSLAC:th.9">Th9</a></i>;<br/><b>consider </b><font color="Maroon" title="c10">f2</font> being   <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">AFP</font><b> such that </b><br/><a NAME="E20:26_2"/><i><font color="Green" title="E38">A17</font></i>: 
<font color="Maroon" title="c10">f2</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>and </b><br/><a NAME="E21:26_2"/><i><font color="Green" title="E39">A18</font></i>: 
<font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</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="c3">a</font>
 <b>by </b><i><a class="txt" href="translac.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="translac.html#T9" target="_self" title="TRANSLAC:th.9">Th9</a></i>;<br/><b>consider </b><font color="Maroon" title="c11">f3</font> being   <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">AFP</font><b> such that </b><br/><a NAME="E23:26_2"/><i><font color="Green" title="E40">A19</font></i>: 
<font color="Maroon" title="c11">f3</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>and </b><br/><a NAME="E24:26_2"/><i><font color="Green" title="E41">A20</font></i>: 
<font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 <b>by </b><i><a class="txt" href="translac.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="translac.html#T9" target="_self" title="TRANSLAC:th.9">Th9</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">f4</font> being   <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">AFP</font><b> such that </b><br/><a NAME="E26:26_2"/><i><font color="Green" title="E42">A21</font></i>: 
<font color="Maroon" title="c12">f4</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>and </b><br/><a NAME="E27:26_2"/><i><font color="Green" title="E43">A22</font></i>: 
<font color="Maroon" title="c12">f4</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="txt" href="translac.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="translac.html#T9" target="_self" title="TRANSLAC:th.9">Th9</a></i>;<br/><a NAME="E28:26_2"/><i><font color="Green" title="E44">A23</font></i>: 
<font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a>  <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>by </b><i><a class="txt" href="translac.html#E20:26_2"><i><font color="Green" title="E38">A17</font></i></a>, <a class="ref" href="transgeo.html#T104" title="TRANSGEO:th.104">TRANSGEO:104</a></i>;<br/><a NAME="E29:26_2"/><i><font color="Green" title="E45">A24</font></i>: 
<font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:26_2_1"/>
<font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font>
 
<b>by </b><i><a class="txt" href="translac.html#E24:26_2"><i><font color="Green" title="E41">A20</font></i></a>, <a class="ref" href="transgeo.html#T4" title="TRANSGEO:th.4">TRANSGEO:4</a></i>;<br/>
<a NAME="E2:26_2_1"/><b>then </b><i><font color="Green" title="E46">A25</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="txt" href="translac.html#E18:26_2"><i><font color="Green" title="E37">A16</font></i></a>, <a class="ref" href="funct_2.html#T70" title="FUNCT_2:th.70">FUNCT_2:70</a></i>;<br/>
<a NAME="E3:26_2_1"/>
<font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a>  <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 
<b>by </b><i><a class="txt" href="translac.html#E23:26_2"><i><font color="Green" title="E40">A19</font></i></a>, <a class="ref" href="transgeo.html#T104" title="TRANSGEO:th.104">TRANSGEO:104</a></i>;<br/>
<a NAME="E4:26_2_1"/><b>then </b>
<font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 
<b>by </b><i><a class="txt" href="translac.html#E17:26_2"><i><font color="Green" title="E36">A15</font></i></a>, <a class="ref" href="transgeo.html#T105" title="TRANSGEO:th.105">TRANSGEO:105</a></i>;<br/>
<a NAME="E5:26_2_1"/><b>then </b><i><font color="Green" title="E47">A26</font></i>: 
<font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c8">h</font>
 
<b>by </b><i><a class="txt" href="translac.html#E13:26_2"><i><font color="Green" title="E33">A12</font></i></a>, <a class="txt" href="translac.html#E14:26_2"><i><font color="Green" title="E34">A13</font></i></a>, <a class="txt" href="translac.html#E2:26_2_1"><i><font color="Green" title="E46">A25</font></i></a>, <a class="ref" href="transgeo.html#T103" title="TRANSGEO:th.103">TRANSGEO:103</a></i>;<br/>
<a NAME="E6:26_2_1"/>
<font color="Maroon" title="c12">f4</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">f4</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font>
 
<b>by </b><i><a class="txt" href="translac.html#E21:26_2"><i><font color="Green" title="E39">A18</font></i></a>, <a class="ref" href="transgeo.html#T4" title="TRANSGEO:th.4">TRANSGEO:4</a></i>;<br/>
<a NAME="E7:26_2_1"/><b>then </b><i><font color="Green" title="E48">A27</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font>
 
<b>by </b><i><a class="txt" href="translac.html#E27:26_2"><i><font color="Green" title="E43">A22</font></i></a>, <a class="ref" href="funct_2.html#T70" title="FUNCT_2:th.70">FUNCT_2:70</a></i>;<br/>
<a NAME="E8:26_2_1"/>
<font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 
<b>by </b><i><a class="txt" href="translac.html#E26:26_2"><i><font color="Green" title="E42">A21</font></i></a>, <a class="txt" href="translac.html#E28:26_2"><i><font color="Green" title="E44">A23</font></i></a>, <a class="ref" href="transgeo.html#T105" title="TRANSGEO:th.105">TRANSGEO:105</a></i>;<br/>
<a NAME="E9:26_2_1"/><b>then </b>
<font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="translac.html#E13:26_2"><i><font color="Green" title="E33">A12</font></i></a>, <a class="txt" href="translac.html#E15:26_2"><i><font color="Green" title="E35">A14</font></i></a>, <a class="txt" href="translac.html#E5:26_2_1"><i><font color="Green" title="E47">A26</font></i></a>, <a class="txt" href="translac.html#E7:26_2_1"><i><font color="Green" title="E48">A27</font></i></a>, <a class="ref" href="transgeo.html#T103" title="TRANSGEO:th.103">TRANSGEO:103</a></i>;<br/>
<a NAME="E10:26_2_1"/><b>then </b>
<font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/>
<a NAME="E11:26_2_1"/><b>then </b>
<font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</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">AFP</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T88" title="FUNCT_2:th.88">FUNCT_2:88</a></i>;<br/>
<b>then </b><font color="Maroon" title="c9">f1</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font>
<b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></i>
<br/>.= 
<font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">f3</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="translac.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="translac.html#E23:26_2"><i><font color="Green" title="E40">A19</font></i></a>, <a class="txt" href="translac.html#E28:26_2"><i><font color="Green" title="E44">A23</font></i></a>, <a class="ref" href="translac.html#T12" target="_self" title="TRANSLAC:th.12">Th12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
;<br/>
<b>then </b><font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</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">AFP</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T88" title="FUNCT_2:th.88">FUNCT_2:88</a></i>
<br/>.= 
<font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font>
<b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></i>
;<br/>
<b>hence </b><a NAME="E14:26_2_1"/>
<font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c12">f4</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c11">f3</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E30:26_2"/><i><font color="Green" title="E46">A28</font></i>: 
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="txt" href="translac.html#E11:26_2"><i><font color="Green" title="E32">A11</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E31:26_2"/><b>then </b><i><font color="Green" title="E47">A29</font></i>: 
<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c6">d</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E32:26_2"/>
<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c11">f3</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c12">f4</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font>
 <b>by </b><i><a class="txt" href="translac.html#E24:26_2"><i><font color="Green" title="E41">A20</font></i></a>, <a class="txt" href="translac.html#E27:26_2"><i><font color="Green" title="E43">A22</font></i></a>, <a class="txt" href="translac.html#E30:26_2"><i><font color="Green" title="E46">A28</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E33:26_2"/><b>then </b>
<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c11">f3</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c12">f4</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font>
 <b>by </b><i><a class="txt" href="translac.html#E23:26_2"><i><font color="Green" title="E40">A19</font></i></a>, <a class="txt" href="translac.html#E24:26_2"><i><font color="Green" title="E41">A20</font></i></a>, <a class="txt" href="translac.html#E26:26_2"><i><font color="Green" title="E42">A21</font></i></a>, <a class="ref" href="translac.html#T13" target="_self" title="TRANSLAC:th.13">Th13</a></i>;<br/><a NAME="E34:26_2"/><b>then </b><i><font color="Green" title="E48">A30</font></i>: 
<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font>
 <b>by </b><i><a class="txt" href="translac.html#E1:26"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="translac.html#E23:26_2"><i><font color="Green" title="E40">A19</font></i></a>, <a class="txt" href="translac.html#E26:26_2"><i><font color="Green" title="E42">A21</font></i></a>, <a class="txt" href="translac.html#E29:26_2"><i><font color="Green" title="E45">A24</font></i></a>, <a class="ref" href="translac.html#T12" target="_self" title="TRANSLAC:th.12">Th12</a></i>;<br/><a NAME="E35:26_2"/>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c3">a</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">a</font>
 <b>by </b><i><a class="txt" href="translac.html#E10:26_2"><i><font color="Green" title="E31">A10</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E36:26_2"/><b>then </b>
<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font>
 <b>by </b><i><a class="txt" href="translac.html#E18:26_2"><i><font color="Green" title="E37">A16</font></i></a>, <a class="txt" href="translac.html#E21:26_2"><i><font color="Green" title="E39">A18</font></i></a>, <a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E37:26_2"/><b>then </b><i><font color="Green" title="E49">A31</font></i>: 
<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font>
 <b>by </b><i><a class="txt" href="translac.html#E17:26_2"><i><font color="Green" title="E36">A15</font></i></a>, <a class="txt" href="translac.html#E18:26_2"><i><font color="Green" title="E37">A16</font></i></a>, <a class="txt" href="translac.html#E20:26_2"><i><font color="Green" title="E38">A17</font></i></a>, <a class="ref" href="translac.html#T13" target="_self" title="TRANSLAC:th.13">Th13</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_2_2"/>
<font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c3">a</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:26_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E3:26_2_2"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c3">a</font> &amp;  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c7">p</font>,<font color="Maroon" title="c3">a</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">a</font> )
 <b>by </b><i><a class="txt" href="translac.html#E10:26_2"><i><font color="Green" title="E31">A10</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a>, <a class="ref" href="aff_1.html#T16" title="AFF_1:th.16">AFF_1:16</a></i>;<br/><a NAME="E4:26_2_2"/><b>then </b>
<font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="translac.html#E5:26_2"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="aff_1.html#T17" title="AFF_1:th.17">AFF_1:17</a></i>;<br/><a NAME="E5:26_2_2"/><b>then </b>
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</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">a</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="txt" href="translac.html#E8:26_2"><i><font color="Green" title="E30">A9</font></i></a>, <a class="txt" href="translac.html#E31:26_2"><i><font color="Green" title="E47">A29</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a></i>;<br/><a NAME="E6:26_2_2"/><b>then </b>
( <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">c</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">a</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a></i>;<br/><a NAME="E7:26_2_2"/><b>then </b>
(  <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c3">a</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">a</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">d</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><a NAME="E8:26_2_2"/><b>then </b>
<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c3">a</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">a</font>
 <b>by </b><i><a class="txt" href="translac.html#E5:26_2"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="translac.html#E8:26_2"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="aff_1.html#T13" title="AFF_1:th.13">AFF_1:13</a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>;<br/><a NAME="E9:26_2_2"/><b>then </b>
 <a href="aff_1.html#R1" title="AFF_1:pred.1">LIN</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</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">a</font>
 <b>by </b><i><a class="ref" href="aff_1.html#D1" title="AFF_1:def.1">AFF_1:def 1</a></i>;<br/><b>hence </b><a NAME="E10:26_2_2"/>
contradiction
 <b>by </b><i><a class="txt" href="translac.html#E5:26_2"><i><font color="Green" title="E28">A7</font></i></a>, <a class="ref" href="aff_1.html#T15" title="AFF_1:th.15">AFF_1:15</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><a NAME="E39:26_2"/><b>then </b>
( <font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">p</font> &amp; <font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  )
 <b>by </b><i><a class="txt" href="translac.html#E17:26_2"><i><font color="Green" title="E36">A15</font></i></a>, <a class="txt" href="translac.html#E20:26_2"><i><font color="Green" title="E38">A17</font></i></a>, <a class="txt" href="translac.html#E34:26_2"><i><font color="Green" title="E48">A30</font></i></a>, <a class="txt" href="translac.html#E37:26_2"><i><font color="Green" title="E49">A31</font></i></a>, <a class="ref" href="aff_1.html#T14" title="AFF_1:th.14">AFF_1:14</a>, <a class="ref" href="transgeo.html#T105" title="TRANSGEO:th.105">TRANSGEO:105</a></i>;<br/><a NAME="E40:26_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</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">AFP</font></span>)</span>
 <b>by </b><i><a class="ref" href="transgeo.html#D11" title="TRANSGEO:def.11">TRANSGEO:def 11</a></i>;<br/><a NAME="E41:26_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c9">f1</font></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</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">AFP</font></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T55" title="RELAT_1:th.55">RELAT_1:55</a></i>;<br/><a NAME="E42:26_2"/><b>then </b>
<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">AFP</font></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</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">AFP</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T88" title="FUNCT_2:th.88">FUNCT_2:88</a></i>;<br/><a NAME="E43:26_2"/><b>then </b>
<font color="Maroon" title="c10">f2</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</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">AFP</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="ref" href="funct_2.html#T23" title="FUNCT_2:th.23">FUNCT_2:23</a></i>
<br/>.= 
<font color="Maroon" title="c10">f2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">f1</font> <a href="funct_2.html#K2" title="FUNCT_2:func.2">"</a> </span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#T70" title="FUNCT_2:th.70">FUNCT_2:70</a></i>
<br/>.= 
<font color="Maroon" title="c2">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="translac.html#E18:26_2"><i><font color="Green" title="E37">A16</font></i></a>, <a class="txt" href="translac.html#E21:26_2"><i><font color="Green" title="E39">A18</font></i></a>, <a class="ref" href="transgeo.html#T4" title="TRANSGEO:th.4">TRANSGEO:4</a></i>
;<br/><a NAME="E45:26_2"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c10">f2</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">a</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="c3">a</font> &amp; <font color="Maroon" title="c10">f2</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c10">f2</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  )
 <b>by </b><i><a class="txt" href="translac.html#E20:26_2"><i><font color="Green" title="E38">A17</font></i></a>, <a class="ref" href="transgeo.html#T105" title="TRANSGEO:th.105">TRANSGEO:105</a></i>;<br/><b>hence </b><a NAME="E46:26_2"/>
 ex <font color="Olive" title="b1">g</font> being  <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">AFP</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b1">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font> )
 <b>by </b><i><a class="txt" href="translac.html#E2:26"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="translac.html#E20:26_2"><i><font color="Green" title="E38">A17</font></i></a>, <a class="ref" href="transgeo.html#T103" title="TRANSGEO:th.103">TRANSGEO:103</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:26"/>
 ex <font color="Olive" title="b1">g</font> being  <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">AFP</font> st <br/>( <font color="Olive" title="b1">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b1">g</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c2">f</font> )
 <b>by </b><i><a class="txt" href="translac.html#E3:26"><i><font color="Green" title="E26">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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