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

<b>let </b><font color="Maroon" title="c1">CS</font> be   <a href="transgeo.html#NM1" title="TRANSGEO:NM.1">CongrSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</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">CS</font>;<br/>



<b>assume </b><a NAME="E1:36"/>
( <font color="Maroon" title="c2">f</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a> <font color="Maroon" title="c1">CS</font> &amp; <font color="Maroon" title="c3">g</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a> <font color="Maroon" title="c1">CS</font> )
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green" title="E21">A1</font></i>: 
( <font color="Maroon" title="c2">f</font> <a href="transgeo.html#R1" title="TRANSGEO:pred.1">is_FormalIz_of</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">CS</font> &amp; <font color="Maroon" title="c3">g</font> <a href="transgeo.html#R1" title="TRANSGEO:pred.1">is_FormalIz_of</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">CS</font> )
 
<b>by </b><i><a class="ref" href="transgeo.html#D4" target="_self" title="TRANSGEO:def.4">Def4</a></i>;<br/>
<div><i><font color="Green" title="E22">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font>, <font color="Maroon" title="c6">x</font>, <font color="Maroon" title="c7">y</font>, <font color="Maroon" title="c8">z</font>, <font color="Maroon" title="c9">t</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">CS</font>;<br/><b>assume </b><a NAME="E1:36_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">CS</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">z</font>,<font color="Maroon" title="c9">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">CS</font> &amp; <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font> )
 ;<br/><a NAME="E2:36_1"/><b>then </b>
( <font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> &amp; <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">z</font>,<font color="Maroon" title="c9">t</font> &amp; <font color="Maroon" title="c4">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">b</font> )
 <b>by </b><i><a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></i>;<br/><a NAME="E3:36_1"/><b>then </b>
<font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c8">z</font>,<font color="Maroon" title="c9">t</font>
 <b>by </b><i><a class="ref" href="transgeo.html#D5" target="_self" title="TRANSGEO:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E4:36_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">x</font>,<font color="Maroon" title="c7">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">z</font>,<font color="Maroon" title="c9">t</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">CS</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font>, <font color="Maroon" title="c6">z</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">CS</font>;<br/><a NAME="E1:36_2"/>
<font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c4">x</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c6">z</font>
 <b>by </b><i><a class="ref" href="transgeo.html#D5" target="_self" title="TRANSGEO:def.5">Def5</a></i>;<br/><b>hence </b><a NAME="E2:36_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c6">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">CS</font>
 <b>by </b><i><a class="ref" href="analoaf.html#D2" title="ANALOAF:def.2">ANALOAF:def 2</a></i>;<br/></div><b>end;</b></div>
<a NAME="E5:36"/><b>then </b>
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">g</font> <a href="transgeo.html#R1" title="TRANSGEO:pred.1">is_FormalIz_of</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">CS</font>
 
<b>by </b><i><a class="txt" href="transgeo.html#E2:36"><i><font color="Green" title="E21">A1</font></i></a>, <a class="txt" href="transgeo.html#E3:36"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="transgeo.html#T26" target="_self" title="TRANSGEO:th.26">Th26</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">g</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a> <font color="Maroon" title="c1">CS</font>
 <b>by </b><i><a class="ref" href="transgeo.html#D4" target="_self" title="TRANSGEO:def.4">Def4</a></i>;<br/>


</div>
