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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>, <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">OAS</font>  st <font color="Olive" title="b1">f</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a> &amp; <font color="Olive" title="b2">g</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a> holds <br/><font color="Olive" title="b1">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Olive" title="b2">g</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a></span><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">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#V2" title="TRANSGEO:attr.2">positive_dilatation</a> &amp; <font color="Maroon" title="c3">g</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a> implies <font color="Maroon" title="c2">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">g</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a> )</span><br/>



<b>assume </b><a NAME="E1:43"/>
( <font color="Maroon" title="c2">f</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a> &amp; <font color="Maroon" title="c3">g</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a> )
 ; <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="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">g</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a></span><br/>

<a NAME="E2:43"/><b>then </b>
( <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">OAS</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">OAS</font> &amp; <font color="Maroon" title="c1">OAS</font> is   <a href="transgeo.html#NM1" title="TRANSGEO:NM.1">CongrSpace</a> )
 
<b>by </b><i><a class="ref" href="transgeo.html#D6" target="_self" title="TRANSGEO:def.6">Def6</a>, <a class="ref" href="transgeo.html#T40" target="_self" title="TRANSGEO:th.40">Th40</a></i>;<br/>
<a NAME="E3:43"/><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#R3" title="TRANSGEO:pred.3">is_DIL_of</a> <font color="Maroon" title="c1">OAS</font>
 
<b>by </b><i><a class="ref" href="transgeo.html#T39" target="_self" title="TRANSGEO:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E4:43"/>
<font color="Maroon" title="c2">f</font> <a href="transgeo.html#K1" title="TRANSGEO:func.1">*</a> <font color="Maroon" title="c3">g</font> is <a href="transgeo.html#V2" title="TRANSGEO:attr.2">positive_dilatation</a>
 <b>by </b><i><a class="ref" href="transgeo.html#D6" target="_self" title="TRANSGEO:def.6">Def6</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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