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<a NAME="E1:56_1_1"/>
 <a href="waybel35.html#K5" title="WAYBEL35:func.5">SupBelow</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:56_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel35.html#K5" title="WAYBEL35:func.5">SupBelow</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">C</font>
 ;<br/>

<a NAME="E2:56_1_1_1"/><b>then </b>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="waybel35.html#K4" title="WAYBEL35:func.4">SetBelow</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c4">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel35.html#D10" target="_self" title="WAYBEL35:def.10">Def10</a></i>;<br/>
<b>hence </b><a NAME="E3:56_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:56_1_1"/>
 <a href="waybel35.html#K5" title="WAYBEL35:func.5">SupBelow</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">C</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>
 ;<br/>


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