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<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">g</font>, <font color="Olive" title="b2">f1</font>, <font color="Olive" title="b3">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>  st <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="c1">AFP</font> <a href="translac.html#NR1" title="TRANSLAC:NR.1">satisfies_Fano</a>  &amp; <font color="Olive" title="b1">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b2">f1</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b3">f2</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b2">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b2">f1</font> &amp; <font color="Olive" title="b1">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">f2</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b3">f2</font> holds <br/><font color="Olive" title="b2">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b3">f2</font></span><br/><b>let </b><font color="Maroon" title="c2">g</font>, <font color="Maroon" title="c3">f1</font>, <font color="Maroon" title="c4">f2</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="aff_2.html#NR11" title="AFF_2:NR.11">satisfies_des</a>  &amp; <font color="Maroon" title="c1">AFP</font> <a href="translac.html#NR1" title="TRANSLAC:NR.1">satisfies_Fano</a>  &amp; <font color="Maroon" title="c2">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Maroon" title="c3">f1</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Maroon" title="c4">f2</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a>  &amp; <font color="Maroon" title="c2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">f1</font> &amp; <font color="Maroon" title="c2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c4">f2</font> implies <font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font> )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:28"/><i><font color="Green" title="E25">A1</font></i>: 
( <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="c1">AFP</font> <a href="translac.html#NR1" title="TRANSLAC:NR.1">satisfies_Fano</a>  )
 <b>and </b><br/><a NAME="E2:28"/>
<font color="Maroon" title="c2">g</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>and </b><br/><a NAME="E3:28"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c3">f1</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>and </b><br/><a NAME="E4:28"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c4">f2</font> <a href="transgeo.html#NR9" title="TRANSGEO:NR.9">is_Tr</a> 
 <b>and </b><br/><a NAME="E5:28"/><i><font color="Green" title="E28">A4</font></i>: 
<font color="Maroon" title="c2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">f1</font>
 <b>and </b><br/><a NAME="E6:28"/><i><font color="Green" title="E29">A5</font></i>: 
<font color="Maroon" title="c2">g</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c4">f2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font></span><br/>

<b>set </b><font color="Maroon" title="c5">h</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c3">f1</font>;<br/>
<a NAME="E7:28"/><i><font color="Green" title="E30">A6</font></i>: 
<font color="Maroon" title="c4">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#E4:28"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="transgeo.html#T104" title="TRANSGEO:th.104">TRANSGEO:104</a></i>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">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="c3">f1</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="c4">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="c3">f1</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">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="c3">f1</font></span>)</span></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="c4">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">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="c3">f1</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="c4">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c4">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="c3">f1</font></span>)</span> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">f1</font></span>)</span>
<b>by </b><i><a class="txt" href="translac.html#E1:28"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="translac.html#E3:28"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="translac.html#E7:28"><i><font color="Green" title="E30">A6</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="c4">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> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">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> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">f1</font></span>)</span></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"><span class="p2">(<span class="default"><font color="Maroon" title="c4">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> <span class="p2">(<span class="default"><font color="Maroon" title="c4">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> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f1</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">f1</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="c2">g</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="c2">g</font>
<b>by </b><i><a class="txt" href="translac.html#E5:28"><i><font color="Green" title="E28">A4</font></i></a>, <a class="txt" href="translac.html#E6:28"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="funct_1.html#T66" title="FUNCT_1:th.66">FUNCT_1:66</a></i>
<br/>.= 
 <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#T88" title="FUNCT_2:th.88">FUNCT_2:88</a></i>
;<br/>
<a NAME="E9:28"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c3">f1</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>
 
<b>by </b><i><a class="txt" href="translac.html#E1:28"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="translac.html#E3:28"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="translac.html#E7:28"><i><font color="Green" title="E30">A6</font></i></a>, <a class="ref" href="translac.html#T15" target="_self" title="TRANSLAC:th.15">Th15</a>, <a class="ref" href="transgeo.html#T105" title="TRANSGEO:th.105">TRANSGEO:105</a></i>;<br/>
<a NAME="E10:28"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">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="c4">f2</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>hence </b><a NAME="E11:28"/>
<font color="Maroon" title="c3">f1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">f2</font>
 <b>by </b><i><a class="ref" href="transgeo.html#T13" title="TRANSGEO:th.13">TRANSGEO:13</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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