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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>; <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">OAS</font>  st <font color="Olive" title="b1">f</font> is <a href="transgeo.html#V4" title="TRANSGEO:attr.4">dilatation</a> holds <br/> ex <font color="Olive" title="b2">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 <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font></span>)</span> st <br/>( <font color="Olive" title="b1">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">f'</font> &amp; <font color="Olive" title="b2">f'</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</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">OAS</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> is <a href="transgeo.html#V4" title="TRANSGEO:attr.4">dilatation</a> implies  ex <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 <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font></span>)</span> st <br/>( <font color="Maroon" title="c2">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">f'</font> &amp; <font color="Olive" title="b1">f'</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font> ) )</span><br/>



<b>assume </b><a NAME="E1:50"/>
<font color="Maroon" title="c2">f</font> is <a href="transgeo.html#V4" title="TRANSGEO:attr.4">dilatation</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">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 <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font></span>)</span> st <br/>( <font color="Maroon" title="c2">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">f'</font> &amp; <font color="Olive" title="b1">f'</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font> )</span><br/>

<a NAME="E2:50"/><b>then </b><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#R1" title="TRANSGEO:pred.1">is_FormalIz_of</a>  <a href="diraf.html#K1" title="DIRAF:func.1">lambda</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">OAS</font>
 
<b>by </b><i><a class="ref" href="transgeo.html#D8" target="_self" title="TRANSGEO:def.8">Def8</a></i>;<br/>
<a NAME="E3:50"/><i><font color="Green" title="E29">A2</font></i>: 
 <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="analoaf.html#G1" title="ANALOAF:aggr.1">AffinStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">OAS</font>,<span class="p1">(<span class="default"><a href="diraf.html#K1" title="DIRAF:func.1">lambda</a> the <a href="analoaf.html#U1" title="ANALOAF:sel.1">CONGR</a> of <font color="Maroon" title="c1">OAS</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="diraf.html#D2" title="DIRAF:def.2">DIRAF:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">f'</font> = <font color="Maroon" title="c2">f</font> as   <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 <span class="p1">(<span class="default"><a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font></span>)</span> ;<br/>
<b>take </b>
<font color="Maroon" title="c3">f'</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f'</font> &amp; <font color="Maroon" title="c3">f'</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font> )</span><br/>

<b>thus </b><a NAME="E5:50"/>
( <font color="Maroon" title="c2">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f'</font> &amp; <font color="Maroon" title="c3">f'</font> <a href="transgeo.html#R3" title="TRANSGEO:pred.3">is_DIL_of</a>  <a href="diraf.html#K2" title="DIRAF:func.2">Lambda</a> <font color="Maroon" title="c1">OAS</font> )
 <b>by </b><i><a class="txt" href="#E2:50"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="#E3:50"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="transgeo.html#D4" target="_self" title="TRANSGEO:def.4">Def4</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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