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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>



<span class="kw">assume </span><a NAME="E1:59"/>
( <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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:59"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A1</font></span>: 
( <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> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="transgeo.html#D6" target="_self" title="TRANSGEO:def.6">Def6</a></span>;<br/>
<a NAME="E3:59"/>
<font color="Maroon" title="c1">OAS</font> is   <a href="transgeo.html#NM1" title="TRANSGEO:NM.1">CongrSpace</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="transgeo.html#T40" target="_self" title="TRANSGEO:th.40">Th40</a></span>;<br/>
<a NAME="E4:59"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59"><span class="lab"><font color="Green" title="E26">A1</font></span></a>, <a class="ref" href="transgeo.html#T39" target="_self" title="TRANSGEO:th.39">Th39</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:59"/>
<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 class="kw">by</span> <span class="lab"><a class="ref" href="transgeo.html#D6" target="_self" title="TRANSGEO:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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