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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">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> implies <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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> ) &amp; ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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> implies <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> ) &amp; ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">OAS</font> implies <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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> ) &amp; ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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> implies <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">OAS</font> ) )</span><br/>

<a NAME="E1:3"/>
 <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>hence </b><a NAME="E2:3"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> implies <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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> ) &amp; ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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> implies <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">OAS</font> ) &amp; ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">OAS</font> implies <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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> ) &amp; ( <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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> implies <font color="Olive" title="b1">x</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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"> verum</span><br/>


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